’ o-
.r;"

.
‘

if ' gamma" ‘

I

.Ixf . m2

1

U ‘bo' .Ol‘n .'.

5

5;,

,.
“1“.JJ

:3 ‘K‘

0';‘.
.3“‘

‘. 0": VN“?

. §k€é§§§

I. a
. a»???

.
.9

.'{
‘
1..
«‘3‘;

- ..-‘.- ,. ' '3

I
1%;

“!. '
‘V.
r

#7

“-
.2:-
s;

s
O

JQE

h

..

,.a.
{

¢

   

‘-‘

       
 
  
 

\ ‘.';
9. #f’. kg‘f‘ I't ' . ‘ [fl - ‘V‘ , ;"."A" . r {‘.fi?‘

1 .. ..."‘ llu‘ l: J
9'; ?.':‘!J’1.‘v:"n 37.3 ‘ -‘:‘-‘ 'O.‘:f‘l:l;. ‘ ‘I

":7" ‘:‘%'_E;L:I:..;I...‘ “ I‘kf: :iglgy"?

”5.4: ifi'w \
.f'if.;-I.1£I'; $“*.I. ,‘I ‘
1 .40 fifflw

I ”IA...

  
    
    

.
fl“ . .

   

 
 
 
      
     
 
   
  
  
    
 
   
 
  
       
 
   
  

..,1 ‘ 4...,
.I " v ?g) Q' . .
"I I Q ~ " - '.
31!. no .I ‘ " ""I’I‘ .1 u" "'
w. e. I . - : A w WM
Ifé ‘ ’3‘."- I’ (1‘: ‘.’?“ . "l‘ . 'A‘ 'l ”as; 0.. &
‘gfifl new 'o I r ”‘.‘: >25!“ ‘1 I- . on
m. 11% ‘. (gm -.- ":I ‘v -.-.
‘39: - ' .5; .~ Nani-l no? «2v. In; m w a: ' 1-",52'!
{'.' .‘ . ’."r". ' '.‘» 3w fivr.:.~fi',$‘., are? x I}; c-‘I'
"if . ' 1, . " 1": 3$;:1‘.I.8"‘L:"'; 9‘...“ IE. pic‘s“ “I“ «fig‘:
.3 . , ~90 .‘Qq .. g r I‘ . I9 .'-_
nIo , '.' ~ ‘I . ;.. 9‘94” 2 fl} ’.'. Jinx-4. \ - q
3.- :. c . . 1“ I“ I_ .‘ r g ." _ ul {‘9‘ . . fl 0 I - .
u I 9 '.‘ ‘3 ‘ ' :4 'r‘r. r'. 326- ’\ ' ' ‘.‘5'5‘03~a'.'§,‘¢ "'0' .".""7"‘:~ '4
q ' ”5 "J m I . Mu, ‘.'.E‘I. ‘- ”’.'-‘3‘“ '. '.‘ fimrf‘ ‘( . -C' ‘I ".0 . '
1 I'l."p',.;.;b— [1- :a.""’},". '4 - ‘.‘ ‘.' '.‘“; I.” 4:1. I; _ . g . '.‘ ‘.‘3: ‘.'fiq’i.",'f..w 9‘1 .\ A"..‘1’..
.1913}4.'€‘..'a;p':‘.‘.’.‘ .' ."'-.‘I‘1-.$‘,~.f, ‘ '.‘-n). U" I" ’v")'> 714‘” .‘k “f 4"?“ ' '
‘ 9,- _ . . 7 ._ .‘ ' . . _-u u 9 - . _ ”é . v ‘7... ‘ “ 9. -. .
' "2““? “.31. ‘4 '4’. J ' ‘ I‘ ' 19’!“ f' I #30. " ‘ - '.'520" e I i "0 1..
I . ‘.‘. I " ‘.‘ ‘.' .J‘ . .‘0 '.’...l I I -_ '
w?" ' . '- ”I" ’-' 'I‘Vy‘dl :‘9’8 ‘I"€I :‘3- "" ‘ ‘ ' '3' .< 6}?¢“”“ " ‘4) “"‘4‘3
'I 9 'N V '.' '5 ' - ~ .04" "II .- H I'L . 'u‘a "' ’l .“ . ' l
. . ‘ ‘ U .I . ' -‘ ' ‘ v‘ ‘
a. wk 15‘” 1" ‘5 ‘w- -.~:-::.~.-_e. u, , «m:- '63-":
I I' I.I s- I?" .~-*“rv"“I fif‘mo’uo ' '—' - '.‘” Mo" -I~ ‘4’—
19 I‘ ‘ ' ‘."“H"' 59:“: f. t"- . I“ I I‘IJ‘I , - ' ' ”0.:“5-3 (yaw; ‘t‘~‘.§‘.?"?-";i3’."‘°-’rr°‘
.2 '; II-z'i"'I.-Jr:' "31"“: n': i.“ i" . , I _ ' 1 ,~ .. I“'.-" I (nu-E". .‘r ‘- ,2 ' “‘.‘“ '9"
.‘. . . ‘l . .‘ .‘ " ' :_‘9 : 59;! ,. ‘ “g. .'. _ r x‘ . I ‘ I '_ ‘.‘ ’ ’.‘ d, .’ ‘ _' Irv. 1'9".“ ‘ ‘.’ f. .9“ ’.‘-I“...
o -QJI ..‘_-, _-.,, .59).. -1‘90 1" _ , , ‘9 (3-. .1 I ‘ { Jc.9 .ru‘ '-“'l’¢'h"
‘ 2.: ‘y' ‘. I‘d: ‘ ‘.';‘mwa': ";I‘--‘I I’l’3‘04"‘.‘I'-.'A .‘ . . ' ' A . . ‘ '- ‘ 051‘. "W' ‘JIK‘ .‘ ’I'. '.'I I 's I“ "V ‘.'" 31.3; .1‘
{3.31. ' I'q.‘I'..'£ I; I‘é’fll'ngt sud [rid-"VJ“ I !.9$'I_ . ‘ I ‘ . .‘ - ‘ '.' 'l (III '50” 7.}‘fi.’~‘.~“§' & ,I 4" ”11"." if“ I a"
“ ""' ‘ "--- '~ ' ‘ ' " ": .
‘.'-‘55:“; 94:56.... -’ .2; _.‘I I l".-:‘_.._O.'":'~IJ atr}? :31 . , ' '(t’fu-o 1‘.‘ -_I 3:9", 2" ’03:! 1.365,? .> ”'7‘: ‘2 3.."
A.’ ‘.l .. ' ‘ "9‘ c" ' ‘ ‘ , I "I -e.- V" 3‘1 3 . ,-
.:g '1 ‘63? 3c." 9 4.0 “I I: ‘13:}- ”5’61; :0.?;";0'I;v37.-I‘ ' ' ' ' t “‘ é ‘kaijfi' h" .t ".’i:..'." “.' 5:9" 1': I,‘.‘.'
. '.‘ V'- ”o ,J I'v [- .7 ‘ ' ' ' " ’ ' c .9 RI) “a ' ' ‘ .
.. 9 . II I . A .III ..",.. . - .b O. t I ‘ ‘1‘ . ., ..
C I ‘ - ‘.‘ I . , fl 3 1... I IV . -
I ‘ ‘ 0' "'9 ' \ y 9 n I.
3'»..r--:-7-:“"-‘*':' .2 '.'...
. . .L‘ I,__ ..'--- ‘. Ah“- . 3, 30d. .J - '.'
‘4 l «13.?»‘4. " ' "1:9“ I‘ 'I 3%" 9". ‘4 . .3; ""
J I .3 .3. I ‘1‘, 'fi'...- ‘ A," RICH: A ~ 6.. ‘I 0'9 '5 '
. . - ~ , 9.. l ‘ '. . ‘.‘ ”'.‘“.
$0 ' I I o ‘5 . I I9" ' '. I
’4‘ :‘.:.L'-9:'«:0':"I.-.9‘6..-.'...'.‘ . ’1‘. t :' ‘.'. '.'. " ‘t‘l‘j‘fl" TV.“ I
.5. I? '~".“.§. “’1' :‘b:. .. I‘. 1;! I. ’I,‘ J l‘ {,':::‘E: 3‘ 2.
. - I Q - .. 9- ‘
2....” 1,3 , . .§.\.l.1.'“l;‘b“o ' ‘.‘;WFQV’?“ I. l ‘.r

‘ ~‘IIO’I . :Jafl”

. | .

" '.‘ “I" “3.0"” "’ ‘1‘...IV' «'.’.o u I o_.:t}'r..'-.l‘-:.. ‘.‘ I 1
‘.I“‘ . 9“". ' g""f‘k \\'|..3F It. ‘

I

I» ‘ ‘ " ‘3' "I'I‘I'A (' “'a'.‘ ' x

'I 9 It“; .1; _ “I . .
' , ' . ‘ O, o
I. . G. ‘6‘ :3. '.x - ‘>\(:‘$:U£L::Ié'fi

   

 

 

' ‘ ' 9 ' .M - .
0.0] Q... ¢.' 99 J. . , f. ‘8. ’fl. “.‘.
" ‘ ' t‘ ' ' ‘ 9' ~ C. , I I I .
‘ ' 4- ' - 3 -- ' - - - x "a . 1'1"93%;}':‘-.‘-;";”5:"3‘4;~1’.qu':1 '~ IWI'ER.
‘ - " a v 2. f a a .. .‘.g-;:.:g{:.a'¢‘...
' I I. — I‘ ‘ . - . ' ' I .‘ -. v
0:. .' . O I . O .. '— .
f 9 ’ n g I.. ‘. I. .fiplijy
. .F ' .
'0‘ . a
\

fim.';;';’s :.';|'13o‘
2;: 13“”. 2f

iIUHHHIHUWWWIHWIIHHHIHIWWW

3 1293 014096

This is to certify that the

dissertation entitled
" Finite Size Effects and Coupling
in
Metallic Spin—Glasses"

presented by

Lilian M. Hoines

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in PhYSiCS

V Major professor

 

 

Date December 51 1994

MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

 

LIERARY
Mlchigan State
University

 

 

 

PLACE In RETURN BOX to roman w- ‘choekoin from your mood.
TO AVOID FINES Mum on or baton data duo.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU loAn Affirmative Maud Opportunity lnltltulon
Wanna-n1

 

FINITE SIZE EFFECTS AND COUPLING
IN METALLIC SPIN-GLASSES

By

Lilian M. Hoines

A DISSERTATION

Submitted to
Michigan State University
in partial fillfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy
1994

ABSTRACT

F INITE SIZE EFFECTS AND COUPLING
IN METALLIC SPIN-GLASSES

By

Lilian M. Hoines

The quasi-static spin freezing temperature (Tf) has been measured as a function of
thickness for magnetically isolated layers of the spin-glasses (SGs) Cu1_anx where
X=O.10, 0.11, 0.12, CuMnomAuom, Ag0.91Mn0.09, Au0.97Fe0.03, and Ni1_anx where
X=O.29 and 0.31, in SG/non-SG multilayered systems. For CuMn/IL where IL = Cu, Ag,
or Au, Tf remains non-zero at spin-glass layer thickness (W50) of l monolayer. For W86
2 2 nm, the observed decreases in Tf with decreasing WSG can be fit to the generalized
scaling law [Tfmfsci' bel/be “‘ “(VG-UV with v = 1.6. This expression is, however,
incapable of describing data below WSG = 2 nm. The data in the range 2 > WSG > 0.21
nm show power law behavior that can be fit to the Fisher-Huse Droplet Excitation model

I} /7}b ~ W“ , with a = 0810.1. AgMn is found to give similar finite size effects to those

in CuMn, to within experimental uncertainties.

CuMnAu and AuFe, SGs with higher anisotropies, and NiMn, a SG with difl‘erent
magnetic interactions than CuMn, were studied to address theoretical predictions that the
lower critical dimension is afl‘ected by anisotropy and interaction type. Within
experimental uncertainty, the finite size effect behavior of Tf for all three was similar to
that observed for CuMn, suggesting that neither anisotropy nor this change in interactions
play major roles in depressing Tf. The NiMn system, however, did contain additional
uncertainties as discussed in the text.

Systems of CuMn/IL where IL is not a noble metal, ILs = Al, Mo, V, and Si, and
AgMn and AuF e with Si, all showed faster decreases in Tf with decreasing WSG than
those found for the noble metal ILs. This behavior could be attributed largely to mixing at
the interfaces.

The unusually long range coupling of CuMn through Cu and Ag ILs (out to WIL ~
20-30 nm) seen in previous studies was also approximately found for Au and CuGe ILs.
Since Au is a strong spin-orbit scatterer, and CuGe has high resistivity, it is concluded that
these two effects do not strongly affect the coupling length. All other materials tested- Al,
Mo, V, Nb, and Si gave much shorter coupling lengths of ~ 2-5 nm, indicating that the

long coupling length is dictated by the electronic structure of the IL.

ACKNOWLEDGMENTS

I would like to thank Dr. Jack Bass for his support and guidance during my time at
Michigan State University.

I would also like to thank Dr. Jerry Cowen for helpful discussions and lending me
some of his intuitive understanding.

There were many others at MSU who provided me with experimental assistance,
helpfirl discussions, or moral support. Special thanks go to Reza Loloee, Mike Wilson,
Vivion Shull, Dave Howell, Dr. Carl Foiles, Dr. Tom Kaplan, and all my friends and
family.

Finally I would like to thank the Center for Fundamental Materials Research and

the National Science Foundation for their financial support of this project.

iv

TABLE OF CONTENTS

LIST OF TABLES ......................................................................................................... ix
LIST OF ILLUSTRATIONS ........................................................................................... x
CHAPTER 1 INTRODUCTION ..................................................................................... 1
1.1 Historical Perspective .......................................................................................... 1

1.2 Experimental Signatures ...................................................................................... 5

1.3 Tf is not To - Relaxation .................................................................................... 8

1.4 Spin-Glass Concepts ......................................................................................... 10
1.4.1 Disorder and Frustration ....................................................................... 10

1.4.2 Magnetic Interactions .......................................................................... 13

1.4.3 Anisotropy ............................................................................................ 16

1.4.4 Short Range Order and Spin Density Waves (CuMn and AgMn) ......... 17

1.5 The Lower Critical Dimension (dl) ................................................................... 19

1.6 F inite Size Effects in Spin-Glasses ..................................................................... 20
1.6.1 Static Measurements of Linear Magnetization ....................................... 21

1.6.2 Static Scaling of Linear Magnetization ................................................. 23

1.6.2.1 General Finite Size Scaling ...................................................... 23

1.6.2.2 Scaling for $65 - Droplet Excitation Model .............................. 25

1.6.3 Critical Behavior of CuMn .................................................................... 27

1.5.3.1 Critical Slowing Down .............................................................. 28

1.6.3.2 Nonlinear Susceptibility Scaling ............................................... 29

1.6.4 Aging ................................................................................................... 30

1.7 Insulating SG Systems ...................................................................................... 32

1.8 Coupling ........................................................................................................... 32
1.8.1 Static measurements ............................................................................. 32

1.8.2 Dynamic Studies of Coupling ................................................................ 33

1.9 Project Goals .................................................................................................... 34
CHAPTER 2 THEORY ................................................................................................ 36
2.1 Mean Field Theory Models ............................................................................... 36

2.2 Finite Size Scaling ............................................................................................. 39

2.2 Droplet Excitation Model (D.A. Fisher, D. Huse, 1986) .................................... 42
CHAPTER 3 SAMPLE FABRICATION ...................................................................... 47
3.1 Target Production ............................................................................................. 47

3.2 Sputtering ........................................................................................................ 51
3.2.1 Sputtering Machine .............................................................................. 51

3.2.2 Cleanliness ........................................................................................... 53

3.2.3 Cooling system .................................................................................... 54

3.2.4 Sputtering parameters ........................................................................... 55
CHAPTER 4 SAMPLE CHARACTERIZATION ......................................................... 57
4.1 Compositional Analysis ..................................................................................... 57

4.2 Mechanical Determination of Film Thickness (Dektak) ..................................... 60

4.3 X-ray Diffraction ............................................................................................. 62
4.3.1 Diffractometer and Sample Alignment .................................................. 62

4.3.2 Texture Analysis .................................................................................. 65

4.3.4 Determination of the Bilayer, A ........................................................... 68

V1

4.3.5 Series Analysis ..................................................................................... 72

4.3.6 Step Model for A Reflections ............................................................... 74

4.3.7 Estimating Quality of Layers from X-ray Difl‘raction ............................ 78

4.4 Analysis of SG/Si multilayers ............................................................ , ............... 84
4.4.1 X-ray Analysis ...................................................................................... 84

4.4.2 Cross Sectional Analysis ...................................................................... 88
CHAPTER 5 EXPERIMENTAL PROCEDURES ........................................................ 92
5.1 Magnetic Measurements ................................................................................... 92
5.2 Determination of Tf .......................................................................................... 95
5.3 be - CuMn, AgMn, and AuFe .......................................................................... 99
5.4 be - NiMn ..................................................................................................... 100
5.5 Errors in Relevant Values ................................................................................ 105
CHAPTER 6 DATA ................................................................................................... 107
6.1 Finite Size Effects - CuMn .............................................................................. 107
6.1.1 Host Interlayers .................................................................................. 107

6.1.2 Non-host Interlayers ........................................................................... 111

6.2 Coupling -CuMn ............................................................................................. 114
6.2.1 Host Interlayers .................................................................................. 114

6.2.2 Non-host Interlayers ........................................................................... 116

6.3 Other SGs ....................................................................................................... 118
6.3.1 AgMn ................................................................................................. 118

6.3.2 High Anisotropy SGs, CuMnAu and AuFe ......................................... 121

6.4 Finite Size Effects of CuMn, AgMn, and AuF e with Si ILs .............................. 124
6.5 NiMn- Short Range Interaction and Reentrant SG ........................................... 127
6.5.1 Pure SG Regime ................................................................................. 130

vii

6.5.1.1 Tfi) Values ............................................................................. 130

6.5.1.2 NiMn/Cu Multilayers ............................................................. 131

6.5.2 Reentrant SG Regime ......................................................................... 133
CHAPTER 7 CONCLUSIONS .................................................................................. 140
7.1 Structure of Multilayers ................................................................................. 140

7.2 Finite Size Effects .......................................................................................... 141

7.3 Coupling ......................................................................................................... 143
Appendix Al Tf VALUES .......................................................................................... 144
REFERENCES ............................................................................................................ 153

viii

LIST OF TABLES

Table 1.1 Definitions of critical exponents ...................................................................... 27
Table 3.1 Purity of elemental targets ............................................................................ 47
Table 3.2 Purity of raw materials used in melted targets ................................................ 48
Table 3 .3 Melting temperature ranges and final size of targets ...................................... 50
Table 3.4 Plasma to target parameters and associated deposition rates .......................... 56
Table 4.1 Typical sputtered 29 and E values for each material ....................................... 67
Table 5.1 be values for CuMn, AgMn, and AuFe ....................................................... 100
Table 5.2 be values for NiMn .................................................................................... 104
Table 6.1 Estimated values of CuMn mixing with non-host metal ILs. ......................... 112
Table 6.2 Estimated interface mixing for SG/Si multilayers. ........................................ 125
Table A1.1 Finite size effect data for CuMn/X and AgMn/X X = Cu, Ag, Au ........... 144
Table A1.2 Finite size data for CuMn/X, X= Al, Mo, and V ........................................ 146
Table A1.3 Finite size effect data for CuMnAu/X and AuFe/X X = Cu,Ag, and Au... 147
Table A1 .4 Finite size effect data for NiMn/Cu ........................................................... 148
Table A1.5 Coupling data for CuMn/X X = Au, CuGe ............................................. 148
Table A1.6 Coupling data for CuMn/X X=Al, Mo, V, and Si ...................................... 149
Table A1.7 Coupling data for AuFe/Ag ....................................................................... 151
Table A1.8 Finite size effect data for X/Si X= CuMn, AgMn, AuFe .......................... 151
Table A1.9 Tfs of NiMn films grown under stringent temperature control. .................. 152

ix

LIST OF ILLUSTRATIONS

Figure 1.1 Frequency dependent a.c. susceptibility for CuMn, fi'om Mulder et. al. .7 ....... 3
Figure 1.2 Hysteresis of CuMn cooled in zero field in an applied field from Beck. .......... 7
Figure 1.3 Hysteresis of AuF e cooled in field from Prejean. ........................................... 7
Figure 1.4 Static magnetization curve for a bulk film of AuF e. ...................................... 9
Figure 1.5 Zero Field Cooled (ZF C) susceptibility at difi‘erent measuring times for

a bulk film of CuMn from Sandlund et. al .................................................................... 9
Figure 1.6 Phase diagram showing reentrant transition . .............................................. 12
Figure 1.7 Universal curves for CuMn/Cu and CuMn/Si. From Kenning et. a1. ............. 22
Figure 1.8 Finite size effect curves for CuMn with Si ILs fi'om Kenning, A1203

ILs fi'om Gavrin et. a1. and AuFe SG from Vloeberghs et. a1. ........... - .......................... 2 2
Figure 3.1 Graphite crucible and graphite cap ............................................................. 51
Figure 3.2 Schematic of inside of sputtering apparatus ................................................. 52
Figure 3.3 Close-up of target and gun assembly ......................................................... 53
Figure 3.4 Sample holder ............................................................................................. 55
Figure 4.1 Schematic of Dektak profiles. .................................................................... 61
Figure 4.2 Powder Diffractometer Orientation ............................................................. 64
Figure 4.3 Periodicities in a multilayer sample ............................................................. 64
Figure. 4.4 The effect of sample misalignment by small angle 5. .................................. 64
Figure 4.5 Exaggerated x-ray deflection due to index of refraction ............................. 69
Figure 4.6 Small angle diffraction scan and bilayer analysis. ....................................... 71
Figure 4.7 A typical plot for individual thickness calculations ....................................... 73

Figure 4.8 Large angle x-ray scans where a) a1 is significantly different from a2
b) a] ~ 3.2. .................................................................................................................. 77

X

Figure 4.9 Length scales sampled by small and large angle x-ray difl’raction beam. ....... 79

Figure 4.10 Small angle x-ray behavior on unmixed and flat mixed interfaces. ............. 79
Figure 4.11 CuMn/Al x-ray scans for decreasing Al thickness. .................................... 81
Figure. 4.12 Large angle scan of AuFe/Si 4 Mil? nm. Scan lacks A satellites, but
shows thickness modulation. ..................................................................................... 83
Figure 4.14 Small angle x-ray scans showing the degradation of CuMn/Si layering. 86
Figure 4.15 Large angle x-ray scans of CuMn/Si showing transition from a) one
amorphous layer, to b) two crystalline layers. ........................................................... 87
Figure 4.16 TEM images of cross sections of 3 nm/7 nm of a) AgMn/Si, b)
CuMn/Si and c) AuFe/Si. ........................................................................................ 90
Figure 4.17 Electron difi‘raction patterns from the samples shown in Figure 4.16. ....... 91
Figure 5.1 a) SQUID pickup coil and sample and b) resulting signal .......................... 93
Figure 5.2 Sample rod seal to the magnetometer ......................................................... 95
Figure 5.3 Comparison between Hm = 1006 and 10 G for a) CuMn/Cu 0.21
nm/30 nm and b) CuMn/Ag 0.21 nm/30 nm .......................................................... 97
Figure 5.4 a) Static magnetization and b) ac susceptibility for CuMn/Cu
2nm/30nm. ................................................................................................................ 98
Figure 6.13 An early NiMn bulk film with unusual magnetic behavior ...................... 102

Figure 6.14 X-ray diffraction scans of NiMn SG samples with a) single peak
from sample grown under good temperature control b) additional peak

suspected to be caused by warmer growth conditions. ............................................. 103
Figure. 6.15 b) Static magnetization and b) a.c. susceptibility of a 300 nm NiMn

SG film. .................................................................................................................. 106
Figure 6.1 CuMn/host multilayers showing scaling law behavior for thick SG

layers ...................................................................................................................... 110
Figure 6.2 Droplet model power law behavior of thin CuMn layers with "host"

interlayers. .............................................................................................................. 1 10
Figure 6.3 Comparison of mixing cases for a) host and b) non-host l].s ...................... 111
Figure 6.4 Tf reduction due to "non-host" interlayers. .............................................. 113
Figure 6.5 Replotted data for metallic ILs using effective SG layer thickness. ............ 113
Figure 6.6 CuMn coupling through host interlayers and CuGe ILs. ............................ 115
Figure 6.7 CuMn coupling through non-host interlayers ............................................ 117
Figure 6.8 Size efi‘ect data for AgMn. ........................................................................ 120

xi

Figure 6.9 Size effect data for AuFe. ......................................................................... 123

Figure 6.10 Finite size effects of CuMn, AgMn, and AuFe with Si IL. ...................... 126
Figure 6.11 Replotted data for Si ILs using effective SG layer thickness. .................. 126
Figure 6.12 NiMn magnetic phase diagram, based on Abdul-Razzaq and Kouvel. ..... 129
Figure 6.16 Finite size efl'ect behavior of NiMn/Cu SG multilayers ............................ 132
Figure 6.17 Susceptibility of a 500 nm NiMn film the reentrant region with several

biasing fields (Hb). .................................................................................................. 134
Figure 6.18 Static magnetization for a 300 nm RSG NiMn sputtered film .................. 136
Figure 6.19 Two different 1 vs. T (Hb =0) for two RSG NiMn films from the

same sputtering run grown under similar well controlled conditions. ........................ 137
Figure 6.20 x vs. T for RSG NiMn/Cu with 10/30 nm and 5/30 nm. ......................... 139

xii

CHAPTER 1

INTRODUCTION

1.1 Historical Perspective

The study of spin-glasses formally begins in 1971, when Carmella and Mydoshl
discovered a cusp in the low field, a.c. susceptibility versus temperature of the random
metal alloy AuFe. Although this alloy had been studied for decades before the cusp
discovery, the previous measurements were done in large magnetic field, and a field on the
order of few hundred G transforms the cusp into a broad rounded maximum. The
discovery of such a sharp feature, normally the result of collective phenomena in ordinary
phase transitions, raised the question of a potentially new type of phase transition in these
materials. Above the cusp, the material behaves as a paramagnet. Below the cusp, a new
state lacking the kind of long range order found in ferromagnets and antiferromagnets, the
spin-glass (SG) state, occurs. The spin-glass (SG) state has its own distinct properties of
remanencez, relaxation3, and hysteresisiv5 The SG spins are randomly spaced, appear to
be "frozen" in disordered directions, and exhibit slow relaxations characteristic of "glassy"
systems.3 The term spin-glass (SG) results fi'om the similarities between SG and glass

properties, based upon disorder in both.

2

The nature of the transition to the SG state has since been the subject of much
study and debate. If there is a phase transition, a transition temperature (If, for spin
fi'eezing temperature) would naturally be located at the susceptibility cusp. The peak is
less dramatic than its ferromagnetic transition signature counterpart (the rise to
demagnetization cut-off in ferromagnets is several orders of magnitude larger than the SG
cusp), but the SG cusp height is comparable to those found for antiferromagnetic material.

Other experimental evidence suggested that the transition was not a true
cooperative phase transition. SGs lack anomalies at Tf in the specific heat and resistivity‘
that are normally expected for a phase transition. The specific heat displays only a broad
peak located ~20% higher than Tf. In time, a detailed investigation of the cusp itself was
possible. Through very fine susceptibility measurement, the cusp proved to be
progressively more rounded as the measuring fiequency increased. 1’7 More importantly,
the location of this rounded peak increased slightly in temperature as the fiequency
increased, about 1% for 2.5 decades (see Figure 1.1 ). The rounding and shifting of the
peak is a result of the relaxations in the SG state, and supported an increasingly popular
idea that susceptibility peak could be simply a nonequilibrium dynamic phenomenon

rather than a phase transition.

I

X tuna/mote Mn)

8

 

 

'r

 

T n I r
0.33-
f
8
gnaw .
s; .
m:— .I
.I
O
I

 

 

 

 

A O O .1
O ! |gl r I r L 1 r n r
000 m 9.50 1000
O 0 0° 0 Temperature“)
0 O O O O O O O o o O O a}
J a A 1 l g L L 1
50 m 150

Figure 1.1 Frequency dependent a.c. susceptibility for CuMn, from Mulder et. al..7

4

Theoretical approaches likewise could not give concrete answers to the phase
transition controversy. Much of the theoretical work has been aimed at finding a mean
field theory for SGs similar to that which was so successful in explaining ferromagnetism.
Mean field theory in ferromagnetism, when the interactions are infinite ranged, leads to
good agreement with experiments, so Sherringtion and Kirkpatrick considered a similar
case for 86s.8 The SG mean field calculations gave a paradoxical result of negative
entropy due to unstable solutions for T < Tf. After years of theoretical efl'ort, what is now
believed to be the correct solution to the Sherrington-Kirkpatrick model was found by
Parisi.9 The complexity of this result however left its physical meaning obscure. Direct
approaches such as Monte Carlo methods sufl‘ered fi'om problems due to the long
relaxation times, yielding theoretical results that were ambiguous on the phase transition
question.

General consensus at the present time is in favor of a phase transition, motivated
by, among other things, the experimental discovery 'of an apparent divergence in the
nonlinear part of the susceptibility vs. temperature. 10.11

Up until the mid 1970's, most of the effort in condensed matter research focused
on ordered systems, many properties of which are now reasonably well understood. The
fact that real systems in nature, and common materials such as glass and polymers, contain
disorder, eventually led to an increase in the study of fi'ustrated and disordered systems,
including $65. In spite of their theoretical complexity,3 SGs may still be considered
simple for random systems, and so the study of them can contribute greatly to the
understanding of the physics of disorder. Attempts to solve the SG riddle theoretically,
have thus far produced valuable statistical mechanical insights, as well as statistical
mechanical methods that are usefully applied to other complex problems. For example,
similarities between the SG and combinatorial optimization problems12 led to simulated

annealing”, an analysis method proven usefirl in several applications in large scale

5

electronic circuit design. In addition, neural network modeling has been helped by a
model proposed by Hopfield that recognizes learned patterns in the brain as random
cooperative phenomena”, which require similar mathematical treatment to that developed

in SG theory.

1.2 Experimental Signatures

According to Binder and Young3, a spin-glass should possess the following
qualities: (i) a frequency dependent peak in the susceptibility, caused by "frozen" magnetic
moments at T<Tf; (ii) lack of periodic long range magnetic order; (iii) remanence and
magnetic relaxation on macroscopic time scales at T<Tf when the magnetic field is
changed. The definition of "frozen" is of course dependent on the observation time,
because the system is relaxing, leading to fiequency dependence as shown in Figure 1.1 .
Some systems contain both ferromagnetic and SG order in a mixed phase, and so may
contain some degree of long range order. These are the reentrant SGs (RSGs), and will
be discussed later.

Characteristic (i) is easily observed in a magnetic susceptibility scan with the
application of a small oscillating measuring field. Condition (ii) is verified through the lack
of the sharp neutron scattering peaks that identify long range ferromagnetism and
antiferromagnetism. 15,16

Criteria (iii) manifests itself in several ways. Thermoremanent magnetization
(TRM) may be observed by field cooling (PC) the SG from T > Tf to a point T < Tf, and
then removing the field.17 Isothermoremanent magnetization (IRM) is seen by cooling the
system in zero field (ZFC), and then applying a field for a short time and removing it. In

both cases the system will relax”, showing behavior dependent on the sample magnetic

6

history. The strong time dependence in the ZF C state indicates that it is not an equilibrium
state, while the weak time dependence of the FC state suggests equilibrium. ‘3 Other
experimental methods may probe the relaxation of the spins using difi‘erent characteristic
time scales, such as neutron echo (10'12 s < t < 108 s),19 electron spin resonance (109 s <
t < 10‘8 s),20 and muon spin resonance (t < 10" s).21 These experiments reveal rapidly
increasing relaxation times near the critical temperature. Such data have been fit to both
to In(t)21 (gradual, glass like freezing) and an algebraic form22 1'; (phase transition).
Changing the field at fixed temperatures below Tf gives rise to a hysteresis efl'ect, a
pronounced irreversibility such as that found in ferromagnets. The shapes of SG
hysteresis loops are highly dependent on magnetic history and sample anisotropy (see
Section 1.4.3). Figure 1.2 shows the hysteresis of the SG CuojsMnon when cooled
from above Tf to below Tf in zero and in an applied field.23 The horizontal shift of the FC
loop is a usually attributed to the Dyzaloshinski-Moriya uniaxial anisotropies discussed in
Section 1.4.3. Figure 1.3 shows the hysteresis of the SG A%.92F%.08 when cooled in
field.24 The AuFe loop is broad and symmetric, unlike the field cooled CuMn loop. This
feature is usually interpreted as resulting from a stabilization of anisotropy in magnetic

microdomains,24 although some controversy exists.”

 

 

 

 

 

 

 

Figure 1.2 Hysteresis behavior of CqusMnoJ, cooled from T > Tf to T < Tf in zero field
(He = 0) and in an applied field (He = 12.7kG) from Beck.24

 

    
     
  

 

u origin

Cooled tron 17K to
All unoor 25.2%

 

 

 

 

 

 

 

 

Figure 1.3 HYSICI‘CSlS behavior Of AllanFerg cooled fi’om DTf t0 T<Tf in field fi'om
Prejean.”

8

Probably the most readily recognized SG signature also stems from relaxation and
remanence. A static magnetization vs. T scan will reveal a peak in the ZF C curve and
exhibit the difference between FC and ZF C behavior. Two scans are taken, one where the
sample is cooled to below Tf in the small measuring field, and another where the sample is
ZFC and then the measuring field is applied. The two curves join each other in the vicinity
of the ZF C peak, but below the peak irreversibility occurs. In the present study, the

location of the ZFC curve maximum (see Figure 1.4) is defined as Tf.

1.3 T, is not Tc - Relaxation

Tc is the temperature where a true phase transition occurs for a system at
equilibrium. The time taken to reach equilibrium, the maximum relaxation time (t),
increases as the temperature decreases towards Tc. In a $6, at some temperature 1
becomes longer than the finite measuring time, rm. This is the temperature recorded as Tf.
Below Tf the system is no longer in equilibrium, and appears to "freeze" into the SG state.
Tf therefore should be observed at a temperature higher than Tc, and T c may be
determined only by extrapolation of the measuring time rm —> 00. The Tfs reported in this
and other studies using ZFC magnetization measurements to determine Tf are referred to
as "quasi-static" freezing temperatures. The measuring time for each data point is
relatively long, on the order of several minutes per point.

In order to extrapolate to the true Tc, dynamical experiments must be performed.
Figure 1.5 shows data from Sandlund et. al.,26 of FC curves for a bulk sputtered film
(1000 nm thick) of Cu0.36Mn0. 14. The ZFC curves show the shift of the ZF C peak as a

 

 

 

 

 

 

0.53 *- 0 ZFC
A t . .00.” 0 FC
° 0
E 0.48 » 0
3° . 0
‘.'-3
35 0.43 - o
l:
O
:3 8
5 0.38 -
‘2’ O
3 0.33 - Q
0.28 . A x I . I A I .
o 10 20 30 40

Temperature (K)

Figure 1.4 Static magnetization curve for a 500 nm thick (bulk) film of Auo.97Fe0.o3.

 

X
Mpcm
m C K
«eon-w .
x(t) ” °
3
O. 3
J L
T L I l I

 

65 a 3%

Figure 1.5 ZFC susceptibility at different measuring times for a 1000 nm (bulk) film of
cuooan0J4. From Sandlund et. al..

10

function of measuring time. Conventional critical ' slowing down predicts that 1 should

diverge when approaching Tc , according to the power law3

%.~(T’%)’"-

Here to is a microscopic relaxation time, and z and v are critical exponents, defined later
in Section 1.6.3. Since Tf is defined as the temperature where the measuring time and

relaxation time are equal, this expression may be written as26

1%) ~[(T/'Tc%] . Equation1.l

Equation 1.1 was successfully applied to Figure 1.5, where Tf is measured as the peak in
each curve, giving Tc = 66 :1: 0.2 K, and zv = 9 :t 1, using loglo‘to = -13 i 1 (where to is
in seconds).26 The zv and to values are reasonable for a 3D system of this type.27 The
CuMn sample had a quasi-static Tf = 67 i 1 K, indicating that the value of Tc is not

significantly smaller than the quasi-static Tf value.

1.4 Spin-Glass Concepts

1.4.1 Disorder and Frustration

The two conditions necessary to obtain SG behavior are believed to be disorder
and fiustration.3 Frustration, following the definition of Sherrington,28 is the inability to
simultaneously satisfy all local ordering requirements as dictated by energy considerations.
Both real 86 systems and theoretical SG models must contain these two elements to

exhibit the necessary properties to be classified a 86. Many examples exist that contain

11

either randomness or fi'ustration. A one dimensional (1D) Ising spin system with random

nearest neighbor interactions, i],
T + T - i- T - i + i

results in a disordered array of spins but no fi'ustration. A triangular antiferromagnet (for

simplicity consider Ising spins),

although contains no disorder will always be frustrated (the third spin cannot
simultaneously point up and down). Neither of these systems are considered suitable
SGs.29

Frustration plus disorder state in SG is created in two primary ways:

a) Randomly spaced elements coupled through an interaction that oscillates
between ferromagnetic and antiferromagnetic with distance. The competing ferromagnetic
and antiferromagnetic interactions create the fi'ustration. This is the situation in transition
metal/noble metal alloys (e. g. CuMn), where the dilute, randomly mixed transition metals
interact primarily via the long range oscillatory RKKY interaction. The SG state of
amorphous No.63Gd0.37 arises from the same circumstance, but the random spatial
placement of atoms is provided by an amorphous structure. Other interactions may spawn
the same result, as in EuxSr1-xS, where the randomly placed magnetic Eu atoms interact
ferromagnetically for nearest neighbors and antiferromagnetically for next nearest

neighbors.30

12

b) Addition of bond disorder. This situation often occurs in the reentrant SGs
(RSGs), systems that undergo a paramagnetic to ferromagnetic (FM) transition, then FM
to a SG-like state transition as the temperature is reduced. One way to form a reentrant
SG is to dilute one magnetic species, such as ferromagnetic (FM) nickel, with another,
such as antiferromagnetic (AF) Mn. The Ni-Mn interaction is FM, so initially as Mn is
added randomly the system remains FM. At some critical Mn concentration, enough AF
bonds from Mn—Mn neighbors have been added to create suficient disorder to form a SG-
like state at low temperatures.32 Further addition of Mn leads to a more typical SG
regime, with a single paramagnetic to SG transifion.3334 Such a reentrant phase is
predicted theoretically?” giving a magnetic phase diagram like Figure 1.6.

T/J

 

36

 

 

 

l
J. N

Figure 1.6 Phase diagram showing reentrant transition (diagram copied fi'om reference 3).

13
1.4.2 Magnetic Interactions

As stated above, SGs result from primarily one of two types of interactions - long
range oscillatory interactions, or a combination of FM and AF short range interactions.
The prototypical SGs, CuMn, AgMn, AuF e, etc. are of the first variety, containing
transition metal ions randomly distributed in a non-magnetic host. The magnetic
impurities interact via the coupling of the moment with the conduction electrons in the
host. The dominant interaction is commonly accepted to be the RKKY interaction.
Ruderrnan and Kittel originally derived this interaction to describe the coupling of nuclear
moments through the hyperfine interaction.” Kasuya36 and Yosida” later contributed an
explanation of how localized d electrons in transition metals scatter conduction electrons.

The result is an interaction with an unwieldy name, the Ruderrnan Kittel Kasuya Yosida

(RKKY) interaction: _ ..
if = iszijs, .Sj

 

#132 m ZkFRij cos(2kFR,-j ) - sin(2kFR,.j )

J(R'J) = (275)3’12 le4

Here R3 is the distance between spins Si and Si, kF is the Fermi number of the host, and

m is the mass of a conduction electron.

At very short distances, 2kFR << 1, the numerator may be expanded for x -=- kaR

3 Ni 3 ~§ 3
x +... x 3kFR

sinx—xcosx ~ x- 3

L
6

J(R,.j)~%,7_j.

so the interaction has the form:

14

This expression diverges at the origin, which does not afi‘ect the energy of the interaction
of the two moments, and causes only an apparent divergence in the self energy of a
moment, which itselfis small.38

For long distances, 2kpR >> 1, the term 2kpcos(2kpR) dominates, leaving an
oscillatory interaction that decays as UN. The classical SGs (noble metal plus transition
metal impurities) may be considered in this interaction range, since k1.- is on the order of 2
Al, and R is on the order of 2 - 20 A, depending on the impurity concentration. The 1/R3
envelope leads to a prediction of an approximately linear dependence of T f on the moment
concentration, c,39 which is not observed in the classical SGs.“°’41 Instead, the
relationship is sublinear (for CuMn, Tf ~ 00-7), a behavior not yet completely understood .

The sublinearity of Tf has been attributed to mean free path (mfp) effects.42 Vier
and Schultz40 mixed nonmagnetic impurities In, Sn, and Sb, into the $68 CuMn and
AgMn to decrease the mean free path and observe the efi‘ect on Tf. They reported that as
mfp efi‘ects are removed fi'om CuMn, Tf tends towards, but does not reach, a linear
dependence on Mn concentration. Also, for CuMn and AgMn with constant Mn
concentration, the Tf depression resulting from reducing the mfp levels ofi' as the mfp
continues to decrease, giving a value for Tt(mfp—>0) of half T,(mfp—>oo) through
extrapolation. This suggested to Vier and Schultz that a significant part of the interaction
contributing to Tf must be mfp independent. Larsen“ was able to explain both the Tf vs.
Mn concentration nonlinearity and the Tf depression saturation, through a calculation
using the original RKKY damping function of deGennes.“ Here the RKKY interaction is

R/l, representing the finite lifetime of the conduction

damped by an exponential decay, e
electrons with mfp 1.. Later, Jagannathan et. al.45 reported that Larsen's method contained
an improper phase average, and through an alternate calculation were able to show that

the mfp had little efi‘ect on the strength of the RKKY interaction. This result agreed with

15

earlier conclusions from unsuccessful attempts to fit experimental results to the
exponential form.“6

Soon after, Zhang and Levy” recalculated the interaction between transition metal
impurities in a non magnetic host, claiming that the point contact interaction for the spin
scattering used in the RKKY derivation was inappropriate. Zhang and Levy assert that
the s-d orbital mixing is the primary source of spin coupling of Mn in Cu, and so the
associated energy and angular dependence must be taken into account from the onset.
The result was the identification of two regimes regarding the interaction strength
envelope: the preasymptotic region, where R < ~ 3 nm, and the asymptotic region, where
R > ~3 nm. The interaction in asymptotic region differed fi'om the RKKY interaction only
by a constant, retaining the oscillatory nature and the 1/R3 envelope. The interaction in the
preasymptotic region, however, was found to decay more slowly, as 1/R2. Zhang and
Levy were then able to make mfp effect corrections to the preasymptotic region for CuMn
and AgMn, and argued that the preasymptotic effects were the major source of the
sublinear dependence of Tf on Mn concentration.

Short range interactions are normally thought to cause 86 behavior in insulators or
semiconductors. Here the interaction occurs via superexchange, where a ligand or anion
between two magnetic atoms transfers an electron between them. The resulting orbital
mixing may create a ferromagnetic or antiferromagnetic bond between the two moments.
SG alloys composed entirely of magnetic atoms, such as NiMn (one of the materials
studied in this thesis), can also be dominated by short range interactions. Many of the
early behaviors seen in NiMn, such as the concentration dependent magnetization, were
explained through a nearest-neighbor molecular-field model with FM Ni-Ni and Ni-Mn
interactions and AF Mn-Mn interactions.48 The strong dependence of the Mn moment
direction upon the nearest neighbor environment, and the competing AF and FM bonds,

were later confirmed through neutron diffraction work.49

16

1.4.3 Anisotropy
Other interactions present in a SG, which can be important to its primary features
(such as existence and location of Tf, degree of remanence, etc), are the anisotropic
interactions. Whereas the interactions discussed above are purely isotropic, independent
of the direction of a given spin, anisotropic interactions are crucially linked to some
particular direction, such as an easy axis in the crystal lattice or along an external field.
Anisotropy adds additional energy requirements for the spin to firlfill, thus increasing the
frustration. The Hamiltonian for a SG thus consists of two parts:
it = X,” 'l' yarns

where

Two types of anisotropy are always present in a SG, dipolar and Dyzaloshinski-

Moriya. The dipolar interaction is the classical interaction of two dipoles, giving3

H..~ mas-HS -H.)(§.-R.)/H.2]/H.3.

r: j
This term is normally very small for point dipoles. If the moment contains an orbital
character, however, as does Fe in Au, then this dipolar anisotropy can become much
larger.

The other expected anisotropy, introduced by Dzyaloshinski50 and Moriya",
results from the spin-orbit scattering of metal conduction electrons off a third atom. The
third atom may be another impurity of the same type, or an additional impurity, magnetic
or nonmagnetic. The Hamiltonian for a SG with spin-orbit anisotropic interactions of

strength D is52

l7

HDM=éZDU.§i XS}
‘J

Taking the root mean squares of the configuration averages of Jij in the isotropic part and

Dij in the anisotropic part, the mean field approximation gives53

7} ~JJ2 +202,

meaning Tf is expected to increase as anisotropic interactions increase.
Experimenta124’40354'” and theoretical’z’“ evidence strongly suggest that this mechanism is
particularly important if the third impurity is a strong spin-orbit coupler, such as Au, Pd,
Co, Fe, or Pt.

Neither of the above anisotropies are global; they do not select a single preferred
direction for all spins. They do, however, add additional interactions, increase fi'ustration,
and stabilize spin configurations.

Anisotropy strength is represented in this thesis by the anisotropy field, H A, the
field that holds the remanent magnetization in place. H A is defined by57

H A = 2K/0'.
where o is the remanent magnetization and K is the anisotropy constant. H A may be
measured directly by transverse susceptibility”
Xi = OLHA + [10)-]:
where H0 is an external field, or from a shift in the electron spin resonance frequency, to”
0) ~ ( H A + H0 ).
Hysteresis measurements, which determine the field of magnetization reversal, Hr, allow

H A determination indirectly from the relation24

K=-;’,-0'H,.

1.4.4 Short Range Order and Spin Density Waves (CuMn and AgMn)

18

Randomizing a metal alloy experimentally can be a considerable challenge. Even
two mutually soluble materials may cluster, or develop short range order, when alloying.
One commonly used method for producing random 86 samples involves annealing at high
temperature and then quenching to freeze in the thermally induced disorder. Other
methods include evaporation and sputtering, where the atoms are randomized during their
flight towards a substrate. Substrate cooling is often used to aid the fieezing of the atoms
in their random positions.

Ordering in the SG sample will often manifest itself in detectable magnetic
signatures of ferromagnetism or antiferromagnetism. Neutron studies on CuMn with Mn
concentrations of 5 - 25 at.% Mn have revealed ferromagnetic domains containing 20 to
50 atoms even for well annealed samples“, indicating a preference for Mn at the next
nearest neighbor position. X-ray studies on AgMn with 1.4 - 24 at.% Mn also show Mn
n.n.n. preferential ordering.’8 AuF e is known to almost unavoidably form Fe clusters
(nearest neighbor) when the Fe concentration exceeds ~ 12 at.%}9 and NiMn has a strong
tendency to form the ferromagnetic compound Ni3Mn for Ni rich compositions.‘so It is
suspected that no SGs experimentally studied are completely random, that all contain at
least some small amount of local ordering. In some cases, increasing ordering can lead to
a change in properties.

Another type of ordering shared by CuMn and AgMn in the SG state is apparent
spin density wave (SDW) formation“,62 A SDW is a incommensurate wave of helical
conduction electron spin directions. It was introduced by Overhauser in 1960 as a
proposed ground state of the free electron gas.63 The theory neglects correlations which
are present in real metals, and as a result SDW are seldom the ground state in pure metals.
There are a few exceptions, such as Y and Cr, where the shape of the Fermi surface
encourages long range SDW formation. Alloys with spin impurities can potentially exhibit

a SDW ground state, if the energy from the interactions of the extra stationary spins as

19

they line up with a SDW is enough to compensate for the higher energy needed for SDW
formation. It appears that CuMn and AgMn are able to support finite correlation length
SDWs through this process. Careful studies of broad, weak neutron scattering peaks
suggest the presence of a helical SDW in CuMn ~ 4 nm in length, containing about 4000
atoms.“1 A SDW modulation may be perturbed by the underlying regions of
ferromagnetic order discussed above without losing its coherence. The role of these short

SDWs in the SG state, if any, is unclear.

1.5 The Lower Critical Dimension ((11)

The lower critical dimension, d], is the dimension below which a system can no
longer support a phase transition. If the value of d] is above 3, Tc = 0 in the real 3D
system; if it is below 2, Tc will be finite in a film of "zero" thickness. One of the main foci
of finite size efi‘ect studies is how To changes as a film is thinned towards the 2D limit,
which should be affected by the value of d].

Efforts to calculate d] for 86s have proved somewhat unsatisfactory.3 High
temperature series expansions, which usually work well for systems without quenched
disorder, gave for 3D Ising SGs d1> 4.54 This value was widely believed until the early
1980's when some serious problems were noticed with the calculation.“»3 Exact partition
function calculations allow direct estimates of static quantities, but are restricted to small
samples. As a result they are mainly appropriate for the 2D lattice, giving d1> 2.“

One fruitful method for determining d1 comes from Monte Carlo simulations.
Ising SGs with short range interactions are found to have d1< 3.‘57 Heisenberg short range
SGs with no anisotropy are found to have d, > 3, but adding anisotropy drops d] below

3.‘58 Heisenberg $65 with long range, RKKY type interactions are found to have d1~ 3,

20

and to be in a different universality class than their short range Heisenberg
counterparts.59’7° These simulations suggest that two things are affecting d], the type of

interactions and the degree of anisotropy.

1.6 Finite Size Effects in Spin-Glasses

A true thermodynamic phase transition occurs only in the thermodynamic limit of
infinite volume and number of particles. Real systems are not infinite, but macroscopic
systems are large enough to produce close agreement with theory. If a system is
significantly reduced in size, the behavior near the singularity begins to deviate fi'om the
thermodynamic prediction. A thin film may be considered as infinite in two dimensions
and finite in the third. Films of ordered systems, such as ordered ferromagnets and
antiferromagnets, do not show finite size effects until the film thickness reaches a few
monolayers,71 limiting the range of study and making experiments in general rather
difficult.

Interest during the early 1980's in din and finite size scaling for SGs73 set the stage
for a finite size effect study in SGs. Theoretical and experimental evidence on 3D and 2D
RKKY-like SGs suggested that the lower critical dimension ((1,) lies between 2 and 3 (see
Section 1.5 ). Thin SG films would simultaneously provide an opportunity to explore
finite size effects on a disordered magnetic system, and allow study of behavior across a
lower critical dimension boundary. Unfortunately the magnetic signal of a single film SG
thin enough to show a significant finite size effect is comparable to the sensitivity of
modern commercial susceptometers. The solution is to make many layers of the same
thickness and decouple them magnetically; i.e. to make a multilayer. The technology to
fabricate multilayers of high enough quality has emerged only in the last decade or so, with

the advent of ultra high vacuum sputtering and evaporation techniques.

21

1.6.1 Static Measurements of Linear Magnetization

Motivated by the possibilities just described, in the mid 1980s the Michigan State
group with Kenning et. al. undertook such studies using sputtered multilayers containing
Cuo.93Mn0.o—7 and found the first evidence of finite size efi‘ects in a long-range, RKKY
type SG. Observable decreases were found in the quasi-static Tf as the SG layers were
thinned, with the decreases starting at SG thickness (W 86) ~ 50 nm. “’86 ranged fi'om
500 nm to 4 nm, and magnetic decoupling for the spin-glass layers was achieved via thick
interlayers (ILs) of amorphous Si." Later, the Mn concentration in the SG was varied
and the experiment repeated for 2 nm s “'86 S 1000 nm.” Three concentrations of 4, 7,
and 14 at.% produced Tf values for bulk samples (T fb) of 23 K, 34 K, and 62 K
respectively. When the Tfs for the thin SG layers were normalized by the appropriate
value of be for each concentration, a nearly universal behavior was found; curves for all
three concentrations collapsed almost onto one another (see Figure 1.7 ).

To check efl‘ects of conducting vs. insulating 11.5, similar studies were also done
using Cu as the IL.76 The results were qualitatively similar to the study with Si, but the
"universal" curve for the CuMn/Cu decreased more slowly with decreasing “'86 than that
for CuMn/Si. The authors postulated that this difference was primarily due to
contamination of the CuMn from diffusion of Si into the CuMn grain boundaries.
Presuming that most of this diffusion occurs during sample growth, the grth
temperature was lowed from ~ 90°C to below room temperature in an attempt to slow the
diffusion. The result was a satisfying shift of the CuMn/Si curve towards the CuMn/Cu

curve,76 with the CuMn/Cu curve unaffected by the growth temperature change.

1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

Tr/ Tr b

v I ‘T T T 1

‘ I

I'lefiIl

f‘fTv

 

111 111 1111111 . 1.1 1
100 2 34 101 2 34

22

   

Cur-anx/Cu
X X=0.l4
X X=0.07
+ X=0.04

Cur-anx/Si
0 X=0.l4

D X=0.0‘7

0 X=0.04

A 1 1 4111111

102 2 34 103

41141

Wsc (nm)

Figure 1.7 Universal curves for CuMn/Cu and CuMn/Si. From Kenning et. al.
The solid line represents the generalized scaling law with v = 1.6 and Wc=1 nm.

Tr/Tr b

100

10'1

trade»
'r'r

 

: ““CuMn/Cu

. — CuMn/Si U

_ from Kenning .- - '

j o

L ' ' CuMn/Si C (averages)

0 CuMn/A1203 from Gavrin

 

 

' + AuFe from Vloeberghs
1111 11111111111 1-111 1411M 1111 1111111
100 2 3 4 101 2 3 4 102 2 3 4 103
Wsc(nm)

Figure 1.8 Finite size effect curves for CuMn with cooled (C) and uncooled (U) Si ILs
from Kenning, A1203 ILs from Gavrin et. al. and AuFe $6 from Vloeberghs et. al.

23

1.6.2 Static Scaling of Linear Magnetization

1.6.2.1 General Finite Size Scaling

The first attempts of Kenning et. al. to fit the data in Figure 1.7 to theory utilized
the only scaling law available at the time, a general scaling law adapted for thin films. The
thin film may be considered infinite in two dimensions and finite in the third, the width of
the film, W. As W is reduced, the bulk critical temperature, ch, shifts to a new value,

Tc(W), according to

 

b
7x”? 7; ~AW')’ Equation1.2

b

C

where A is defined as the shift exponent,” with the relation A = 1/v, where v is the
correlation length exponent. This scaling law, discussed in more detail in Chapter 2, is
derived via a perturbative method and so is only expected to be valid where Tc(W) ~ ch.
The value of v found from nonlinear susceptibility measurements is v ~ 13:02 or 0.77 2
7t 2 0.91 for AgMn ‘1 and 71. = 0.62 for CuMn.78

Replacing Tc(W) by Tf, using be for T6”, and allowing both 7. and A to be fi'ee
fitting parameters, the data for Si and Cu ILs could be fit to Equation 1.2 over the entire
range of thicknesses, 2 nm 5 WSG s 1000 nm, with different values of 7. and A for each
IL. Fitting this way gave A = 0.70 for Cu IL and A. = 0.80 for Si ILs. Both values are
within the estimated uncertainties for it from the AgMn nonlinear x experiments, but
somewhat larger than the CuMn it (although the uncertainty is not given). The range of
the fit is interesting, since much of the data (Tf(2 rim) ~ 0.4be) is not in the expected
region of validity, Tf ~ be. Fitting the CuMn/Cu data only to thick “'86 2 20 nm, a

different value of A. = 0.91, or v = 1.1 i 0.3,79 was obtained. This is still in agreement

24

with the independently acquired value of v above for AgMn, but is farther from the CuMn
value.
If Equation 1.2 is considered in the region where Tf << W, the critical thickness

where Tf(W) = 0 K corresponds to W =WC, determined by

Using the exponent from the fit to the entire thickness range, the CuMn/Cu system gave
values of Wc ~ 1.0 nm, and the CuMn/Si system had a larger critical thickness, Wc ~ 3.6
nrn.80 The larger Wc value for the CuMn/Si resulted from the faster dropping of the
CuMn/ Si curve, and so was attributed largely to the interface efl‘ect of Si diflirsing into
the CuMn layer.

To test whether these results were reproducible in other SGs, this same Michigan
State group repeated the CuMn experiment using AgMn (Stubi et. al.“), a similar long
range RKKY-type low anisotropy SG.3 Two concentrations were tested, 4 and 9 at.%
Mn, and two ILs were tested, Cu and Ag. The same SG thickness range as above was
covered, 2 nm s “'56 s 1000 nm, with the addition of one AgomMnoflg/Cu data point at
WSG = 1 nm. The AgMn data for both concentrations reproduced the CuMn/Cu curve of
Kenning et. al. within mutual uncertainties, independent of which metal IL was used.

Not long after the above CuMn studies of Kenning et. al., Gavrin et. al.82 published
results on sputtered multilayers of thin Cu0.92Mn0‘03 (be = 34K) with A1203 ILs, with 4
nm 3 W56 3 125 nm. These data were fit to the scaling Equation 1.2, giving an exponent
of k = 0.64 with a critical thickness Wc = 1.95 nm. Figure 1.8 shows that these Tf data
normalized to their appropriate be fall close to the cold sputtered CuMn/ Si data discussed

above.

25

The three different values obtained for A and Wc for three difi‘erent IL materials
exposed the need to better understand the role of the IL and boundary conditions on the
finite size behavior. In the present thesis, samples containing several difl‘erent IL materials

are used to attack this problem.

1.6.2.2 Scaling for SGs - Droplet Excitation Model

The scaling theory used in all of the above cases was developed to fit data with Tc
~ ch, not for providing information in the range of WC, where Tc —) OK. In response to
the data of Kenning et. al., D.S. Fisher and DA Huse formulated a scaling model which
included dimensionality and was extendible to the region where Tf is far below be.” This
model, discussed in detail in Chapter 2, assumes that the low lying excitations in the SG
state are droplets of coherently flipping spins. The lower critical dimension is assumed to
be between 2 and 3, meaning T6 = OK for d = 2 (WSG = 0).

For Tf ~ W, the theory predicts:

 

Tb-T t
f f( )OCWSG-(I/V3)[In(_ Equation 1.3

[(W3+V2W292)V3 r1
T fb "8‘02 )]
The subscripts in the exponents denote the dimensionality, WSG and t are normalized by a
microscopic length and time, and the exponents are defined in table 1.1. Equation 1.3 is
the same as Equation 1.2, with the addition of a weak logarithmic factor in the measuring
time, 1:: At present, the difference between the Fisher-Huse logarithmically corrected

equation and Equation 1.3 is beyond experimental resolution.

For Tf << W, the model predicts

, Equation 1.4

26

where a is a compilation of critical exponents (see Section 2.2). This model was applied
to the CuMn data of Kenning et. al.79 and Stubi et. al.81 also applied this model to AgMn
data. The CuMn/Cu data were fit to Equation 1.4 for 2 nm s WSG < 20 nm, obtaining an
exponent of a = 0.5.79 Since data in this region also fit the general scaling law of
Equation 1.2, studies on thinner SG layers were needed to determine the validity of this
model, as well as help determine whether Tf is finite at “’56 = 0 nm. The AgMn/Ag and
AgMn/Cu were fit together to Equation 1.3 for 1 nm s WSG < 10 nm, obtaining an
exponent of a = 0.65.81 Since the AgMn and CuMn data lay along closely parallel curves,
the values for a might have been the same were it not for the inclusion of slightly thinner
“'86 data in the AgMn fits. This difference in a thus also suggests the need for more data
in the thickness range WSG < 2.

When the project reported in this thesis was beginning, Vranken et. al.,84 published
results on single thin films of Auo.95Fe0_05 of 4 nm s WSG s 40 nm, flash evaporated onto
a glass substrate and protected with an overlayer of SiO. AuF e is similar to CuMn, but
generally believed to have much higher anisotropy,85 (although some opinions differ”).
As in CuMn, size effect depression in Tf of AuFe was observed. The AuFe data
produced a shift exponent 1. = 1.5, much larger than that found for the CuMn case. The
Tf values also decreased faster with thinning than any of the above mentioned CuMn
studies, leading to a larger Wc (see Figure 1.8). Although these data suggest that the
AuF e SG might be different than CuMn, one must be carefiil in the comparison since the '
flash evaporation process used to produce the AuFe single films is quite different from
sputtering. We concluded that sputtered AuFe multilayers were necessary to determine
any difference between the AuFe and CuMn behaviors, and such a study also became part

of this thesis.

27
1.6.3 Critical Behavior of CuMn

A phase transition involves a divergence in the free energy (or its derivatives) of a
system, which in turn create divergences in its physical properties such as the specific heat
or magnetic susceptibility. Analysis of critical behavior attempts to describe the form of
these divergences, characterized by algebraic expressions typically containing the critical
temperature, Tc, and critical exponents. Critical exponents of interest to this discussion

are described in the following table.

Table 1.1 Definitions of critical exponents

 

 

 

 

 

 

 

 

 

 

 

Exponent Defined

7 Magnetic Susceptibility Exponent HT-Tcfi
v Correlation Length Exponent Era-Tat
[3 Order Parameter Exponent g~(T-TC)'l3
2 Dynamic Exponent I ~ £2

(For relaxation time 1)

Free Energy Exponent 9
9 (for excitation at length scale L) FNL

Barrier Exponent (for relaxation W
‘l’ of an excitation at length scale L) B” L

 

One attempts to fit experimental data to an appropriate form and thereby determine the
values of Tc and the relevant exponents. Systems that can be described with the same
critical exponents are believed to be a result of the same underlying physics, and said to be
in the same universality class. Thus the exponents for 3D should differ from those for
2D. Finding critical exponents in thin samples can help determine where the 3D —> 2D

crossover occurs, or if in fact a non-zero Tc exists in the 2D limit.

28

1.6.3.1 Critical Slowing Down

As mentioned in Section 1.3, the relaxation time for a system with a phase
transition (dzdl) should diverge as Equation 1.1. Fitting Equation 1.1 to data for a bulk
sputtered film of CuaanQM revealed reasonable exponents and a Tc very close to the
quasi-static Tf (see above). Below d1, there is no phase transition, so the dynamics of the
system should be governed by a thermally activated process. Such activated dynamics,
derived from a theoretical approach based on the droplet model, are represented by‘“5

ln(/ )~T‘”+W).
To

This equation involves both the correlation exponent and the relaxation barrier exponent
as defined in Table 1.1. Defining Tf as the temperature where the measuring time and

relaxation time are equal, the equation may be rewritten as

In( TV ) ~ T f-(HW) Equation 1.5
T0

Analysis using Equation 1.1 performed on a Cu0'36Mn0. 14/Cu multilayer with
WSG = 3 nm gave values of Tf ~Tc = 26K, loglo'to = -10, and zv =19. The latter two
values are far outside of their expected range, causing the authors to try the activated
dynamics. Using Equation 1.5, a good fit was found with Tc = OK and wv = 1.6.25,92
More complete examination of uncertainties yielded 0 < Tc < 10K and 1.6 > wv > 1.1.

Both static and dynamic analysis of CuMn/Cu multilayers show a change in the
critical exponents that strongly suggest that by WSG = 2 - 3 nm a 3D to 2D crossover has

occurred.

29

1.6.3.2 Nonlinear Susceptibility Scaling

When experimentally determining critical exponents, it is necessary to measure
properties that are sensitive to the ordering. In SGs, the higher order terms in the
expansion of the magnetization

Mfli=10+x2H2+x4H4+~

are more sensitive to the SG order than is the zero-field susceptibility.3 Here 10 is the
linear susceptibility, and the remaining terms constitute the nonlinear susceptibility, 1",.
Two difi‘erent equilibrium 1,“ studies have been done on thin SG samples; high field
magnetization, and low field a.c. susceptibility. Since the system must have time to relax
into equilibrium, these measurements must be taken far enough above Tf so that the
relaxation time is smaller than the measuring time.

For high fields, scaling theory predicts”

XnI(H,T) "’ 16F“ / 112/(1%)), Equation 1.6

or, alternatively,
x...(H, T) ~ HZB’W’GH / HZWU, Equation 1.7

where F and G are scaling firnctions, t = filly/Tc and B and y are critical exponents as
defined in Table 1.1.

In the low field limit, the 12 term dominates. A low field X", measurement involves
superimposing a small oscillating field on a static field, so that H=Ho+hsinmt Here, X2 is
expected to scale as”88

Xz~ r7. Equation 1.8

30

Gavrin et a1.82 were the first to use high field nonlinear susceptibility scaling on thin
SG layers. Data fiom a “’86 = 6 nm €00.92Ml'1008/A1203, previously shown to exhibit a
size efi‘ect Tf decrease (see Section 1.6.2.1) and data for a bulk CuMn sample were fit to
Equation 1.6. Exponents for “’56 = 6 nm of B = 0.85 and 7 = 5.1 were found using Tc =
Tf(WSG=6 nm) = 17.5 K. No information was given on the efi‘ect of Tc choice on the fit.
The exponent values difi‘ered from those found in the bulk sample, (fl=0.9, y=3.0) leading
the authors to conclude that a 3D to 2D crossover had occurred.

A similar high field study was later done on a Cuo.14Mno.14/Cu sample made by
Kenning (described in Section 1.5.1.1), with WSG = 2 nm. Fitting the data to Equation
1.6, the data best scaled to a single curve with values of T0 = 0 and exponents B = 0 and y
= 9.2."9

Since high field fits are not very sensitive to the choice of TC,90 other techniques
such as low field fits should be used in combination with the high field results. The same
CuMn/Cu “'56 = 2 nm sample discussed above was measured and fit with Equation 1.8,
and best fits were obtained with T6 = 0 :1: 5K (by setting t = T) and y = 9.3,89 in good
agreement with the values from the high field X", scaling. Although these values differ
from those found for the CuMn/A1203 WSG = 6 nm sample, the results for both samples

suggest a 3D to 2D crossover has occurred.

1.6.4 Aging

Aging studies involve measurement of the ZF C relaxation rate,

5(1):: iii/L259
m H dint", ’

after various wait times, tw. Two regimes should be considered: a) tm << 1“,. When the
measuring time is much smaller than the waiting period, the length scales probed (by 1",)

are much shorter than those over which the SG has relaxed (during 1w), allowing study of

31

equilibrium behavior. b) tm 2 1“,. The behavior is non-equilibrium, for the length scales
probed are longer than the relaxation lengths.

For the equilibrium case, tm << Tw, a 3D SG exhibited two behaviors as ‘tm was
increased, as illustrated by data for bulk CuMn films made by Kenning. The imaginary
part of the complex susceptibility, x((o)", increased with increasing frequency (or
decreasing measuring time since (0~1/‘tm),91 and S(rm) first decreased, passed through a
minimum, and then increased, peaking at tm~ 1“,. Moving to the non-equilibrium regime,
rm > 1“,, S(tm) decreased as tm increased.9‘»91

The aging behaviors for Cu036Mn0J4/Cu multilayers with WSG = 2 and 4 nm
were also measured. The “’86 = 4 nm sample showed qualitatively similar behavior in
S(tm) to that found for the 3D sample in the non-equilibrium regime, with S(rm)
decreasing as tm increased.93 The “'86 = 2 nm sample showed just the opposite trends in
the equilibrium regime as those found in 3D. S(tm) increased with increasing 111136.94 and
x(oo)" decreased with increasing to.” Both these behaviors are seen in the 2D Ising SG
Rb4(3llo.7sC°o.221‘31-95

In the non-equilibrium regime, ‘tm > tw, these measurements show qualitatively
similar behavior between the 3D film and WSG = 4 nm. In the equilibrium regime, ‘tm <<
tw, qualitatively different behavior was seen between 3D and WSG = 2 nm. The WSG = 2
nm sample is perhaps 2D in character, supported by the similarity between its behavior and

the 2D Ising 86 above.

32
1.7 Insulating SG Systems

Only one study of finite size effects with decreasing WSG in an insulating SG has
been published, on superlattices of Cd 1.anXTe/CdTefi’6 Instead of a shift in the
susceptibility peak, the authors reported the peak broadened and disappeared as WSG
decreased. The reasons for this behavior are not known.

A more conclusive study on a 2D Ising SG szCu0.78Coo.22F4 was performed by
Dekker et. al..9°’95~97 Like a 3D sample, this system showed a weakly time dependent
peak in X, with irreversibility below Tf. The high and low field X", measurements fit well
to Equations 1.7 and 1.8 giving Tc ~ 0K, B ~ 0, and 7 ~ 4.5. The Tc and B values are the
same as those found for the 2D CuMn/Cu samples above, but the exponent y is lower.

Also like the 2D CuMn/Cu SG, the Rb2Cu0.73Coo.22F4 was described by the
activated dynamics of Equation 1.5. Good agreement was found between the static and
dynamic values of Tc, B, and y. The aging behavior below Tf was similar to that found in
the 2D CuMn/Cu SG.

1.8 Coupling

1.8.1 Static measurements

The SG layers in the finite size effect studies described above were deliberately
magnetically decoupled by thick ILs of 30 nm Cu or Ag or 7 nm of Si. Preliminary
findings of Kenning et. al. using only 9 nm of Cu and 1.2 nm of Si, showed no significant
finite size effects with SG thickness,98 due to insufficient decoupling of the SG layers. To
determine the appropriate decoupling value for the Si 1L, Kenning et. al. fixed “'86 at 7
nm and varied W11. from 3 to 14 nm. They found Tf to be independent of WIL down to at

least 3 nm of Si," indicating that the coupling between the SG layers did not extend

33

beyond this limit. A similar experiment showed that coupling between 4 nm thick CuMn
layers extended out to 2 20 nm in Cu."9 Stubi et. al. found similar long range coupling of
CuMn through Ag,100 and of 4 nm thick layers of AgMn through both Cu and Ag.‘”-101
This coupling length through the metal ILs is unusually long, especially compared to those
found for layers of magnetically ordered materials. Fe layers couple up to 2 to 6 nm
through normal metal layers. 102 Materials with spiral order display a longer range
coupling more comparable to the SG case. These elements, such as Dy, contain spiral spin
density waves (SDWs) and are able to induce SDWs in a certain normal separator layers
(such as Y). The SDW induction is possible when the IL is energetically close to
supporting SDW formation (see Section 1.4.4). These systems may couple through as
much as 13 nm of their separator material,103 provided the c axis of the HCP crystals is
grown perpendicular to the layers (coupling is much shorter along other axes).1°4

As noted in Section 1.4.4, CuMn and AgMn contain finite correlation length
SDWs. Perhaps the 11.3 Cu and Ag allow the same SDW induction process to occur.
Tests of difl‘erent IL materials were needed to determine if this is a plausible explanation
and what other factors may affect this coupling length. Part of this thesis uses different

ILs to address these issues.

1.8.2 Dynamic Studies of Coupling

In 1992, after this thesis work had begun, coupling effects were studied for the
CuMn/Cu systems discussed above using the dynamic relations in Sections 1.6.4 and
1.6.3. 1. Granberg et. al. found, through scaling time dependent susceptibility data with
the relaxation time scaling Equations 1.5 and 1.6, that some interaction occurred through

WIL even greater than 30 nm. For “'86 = 4 nm, typical 2D behavior was occurred for

34

WIL 2 60 run. When 60 < wlL< 3 nm, a gradual decoupling of the CuMn layers was
observed, and for WIL < 3 nm the 56 displayed 3D dynamic behavior.105

Mattsson et. al.94 also studied these CuMn/Cu samples, and found that the form of
the relaxation rate S(t) indicated that the multilayers returned to 3D character as WIL was
thinned. wIL = 30 nm showed 2D type aging behavior, while WIL = 10 nm, S(t) started
to resemble a 3D system (see Section 1.6.4), with a minimum occurring at approximately
Tf. This was explained in terms of a domain model, where domain growth exceeds the

interlayer thickness at the time the system behaves as 3D.

1.9 Project Goals

The preceding work led this project to have 4 major goals related to finite size
effect in SGs.

First, to extend measurements of the CuMn/Cu and AgMn/Ag systems to “’86 as
thin as possible, to answer the following questions:
1) Will the general scaling law of Equation 1.3 continue to fit data as “’56 —) 1
monolayer (ML), or can a region be reached where the scaling law cannot apply?
2) Will the droplet model power law prediction hold down to “'86 = 1 ML, and if so will
the value of the exponent a be the same as that previously found for W86 2 20 nm?
3) The short range 2D insulating SG described in Section 1.7 gave Tf > 0 K. Will Tf -—)
0 as WSG —-> 1 ML in a long range metallic 86?

Second, to replace the Cu and Si ILs previously used with different materials, to
determine the following: Do metal ILs other than Ag and Cu reproduce the same
CuMn/Cu curve of Figure 1.7 ? To answer this question, [1.5 will be used that may

introduce a range of stress and roughness to the interface.

35

Third, attempt a similar finite size effect study with SGs that difi‘er fi'om CuMn in
anisotropy and interaction type to investigate the following:

1) Higher anisotropy is expected to lower d,, will this efi‘ect the finite size curve, causing
it to fall slower (or faster) with WSG reduction for a SG with higher anisotropy than
CuMn and AgMn?

2) Different interactions are expected to afi‘ect d1, will a difi‘erence be seen in the finite size
curve of a SG interactions other than RKKY-type?

The choices for the new SG materials are AuFe, similar to CuMn but with higher
anisotropy, and the SG NiMn, with short range rather than the long range RKKY type
interactions.

The fourth goal also involves an interesting trait of NiMn. For Mn concentrations
between ~16 and 24 at.% the material has a reentrant (RSG) regime (see Section 1.4.1).
Here there are two transitions as the temperature is reduced; paramagnetic to
ferromagnetic (or ferro-SG mixed phase (FSG)), and then rso to so phase (see Chapter
5). This behavior raises the additional questions of whether the reentrant regime behaves
like the SG regime, and how the characteristic temperatures for the P-FSG transition and
the F SG-SG transition behave in response to layer width reduction.

The multilayer geometry and materials used in these systems naturally suggests one
firrther experiment: to test the coupling through the difl'ering interlayers to answer the
following:

1) Do metal ILs other than Cu and Ag allow long range (~ 20 nm) coupling?

2) Do properties such as electrical resistivity, free electron density, or interface effects
affect the coupling length?

Materials for 11.3 will be chosen for their distinguishing properties, such as differing crystal

structure, lattice size, resistivity, spin-orbit coupling ability, and electronic structure.

CHAPTER2

THEORY

2.1 Mean Field Theory Models

As mentioned in Chapter 1, SGs have presented a dimcult problem to mean field
theory, causing progress to be heavily reliant upon numerical methods. Mean field models
are, however, the starting point for the Monte Carlo (1] results reviewed in Section 1.5 ,
and understanding these models and the degree to which they represent experimental SGs
lends validity and insight to the numerical results. The following briefly reviews the
development of mean field theory for $63. For more a more detailed review, see

reference 3.

The bulk of theoretical efl‘ort in this area has been based on variants of the model
by Edwards and Anderson (EA).106 In the canonical SG, the random spin placement plus
the oscillatory RKKY interaction lead to random interactions between ions. The EA
model simplifies this situation by replacing the site disorder with bond disorder, allowing
the spins to be placed on a regular lattice. The Hamiltonian for Heisenberg spins in this

system is

where J ,1- results from a random distribution. EA considered nearest neighbor

interactions only.

36

37

To determine whether the model exhibits the thermodynamic properties of a SG,
the free energy (F) must be calculated for the system by averaging over all possible states.
In non-random systems, or random systems where the observation time, rm, is longer than
the typical fluctuation time, t]; of the random variables it, all possible states may be

sampled. F may then be calculated as

F = -kBT1n[z],,

where the partition firnction, Z, is given by

Z{x} = (75:, exp[-}t{x,s,-} / kBT].
Here the random variables are the bond strengths denoted by J ,j. In the case of the SG,

tm << If, and one cannot average over the partition firnction. The average must instead
by taken over the free energy, to include all possible configurations with the same free
energy,

F = -kBT[InZ]av.
The need to average over InZ rather than Z is a source of dimculty in performing
statistical mechanics in random systems. EA used a method to do this average known as

the replica trick, where the identity

[In sz = lim W

n->0
is used and n identical replicas of the system, Z may be written as

Z" {x} = [1"Za{x} = ex -2n.%{x,Sia}/ kBT] .

a=l

For positive n this expression is more readily averaged. .

38

To characterize the phase transition, an order parameter is needed (analogous to
the magnetization in ferromagnets). An order parameter signals the transition to a
correlated phase by becoming non-zero at the transition temperature. Since there did not
appear to be any spatial correlations between spins, EA proposed an order parameter to
correlate the spins in time. As t -> no this order parameter would average over all
possible time scales and converge to a constant value

q = 15;; ((8. (0)8.- a)» .
Here the thermal average is taken before the configurational average. The EA model has
been extensively studied for Ising spins, and predicts a cusp in the zero field susceptibility.
The order parameter q is found to decay become zero for T > Tf and to a constant value
for T < Tf, indicating a change from paramagnetism to a state with temporal correlations.

Sherrington and Kirkpatrick (SK), in an efl‘ort to imitate the recent success in the
theoretical descriptions of ferromagnetism, applied mean field theory to the EA model.107
While normally an approximation, mean field theory for ferromagnetism becomes exact in
the limit of infinite-range interactions.3 SK therefore replaced the short ranged
interactions in the EA model with infinite ranged interactions. The resultant mean field
theory in the SK model predicted a second order phase transition and a cusp in the zero
field susceptibility, but also a cusp in the specific heat where none is observed
experimentally. SK also determined that their solution gave negative entropy due to
unstable solutions for T < Tf.

The SK solution relied on invariance to permutations of the spin indices in the
Hamiltonian when calculating the average of InZ. While this is true for positive integer
values of n, Parisi suggested that it is not true if n —> 0.9 This idea led to what is believed
to be the exact solution of the SK model, found through replica symmetry breaking. The
symmetry is broken by requiring all quantities involving a replica to be replica

independent, resulting in an infinite number of order parameters. While this solution is

39

inherently very complex, it does provide a stable solution for T < Tf and predict more
subtle features of the SG state, such as the additional boundaries in the magnetic phase
diagram of Figure 1.6.

Mean field theory gives a finite transition temperature for SGs, but it gives
incorrect results for critical exponents. ‘03 The model does, however, share enough
features with real SGs to have become the most widely used base for Monte Carlo
calculations to address dimensionality questions about SG systems. A few exceptions
exist; Bray, Moore and Young,70 cited in Section 1.5 , used a site disorder model to
determine that vector SGs with RKKY-like interactions are at their lower critical
dimension in 3D. Others, not described in Chapter 1, have used 3D RKKY-type
Heisenberg site disorder SG models to determine that anisotropy is needed to induce a

transition,109 or that Tc = 0.110

2.2 Finite Size Scaling

A true thermodynamic phase transition contains a singularity in the fi'ee energy, F,
only when calculated in the thermodynamic limit of infinite volume and number of
particles. This singularity in F in turn often creates singularities in its derivative physical
properties, such as the specific heat and magnetic susceptibility. Although real systems do
not extend quite to the thermodynamic limit, many still show apparent singularities which
agree with theoretical statistical mechanical calculations. The approach to a critical

temperature, T c, may be characterized by algebraic expressions, the leading term in which

 

. T - "' . . . .
rs ( T c ) , where m rs a critical exponent. The first step to finding a critical exponent
C

comes fiom Landau theory‘“,“2. The ordering of a system due to a phase transition is

described by an order parameter, such as the magnetization, M, in a ferromagnet. The

40

fi'ee energy, F, is then expanded in terms the order parameter. For the example of a
ferromagnet, it is helpful to define the alternate fi’ee energy function, A = F + MH. Since
dF = -SdT - MdH, where T is the temperature, a Legendre transformation gives

dA = -SdT + Ham/I.

Now

Expanding A in powers of M so that
A = A0(T) + rig/DMZ + A4(7)M4 +

where odd powers of M are excluded due to symmetry M <—) -M, and then expanding the

coemcients in powers of t = (T-Td/Tc, one gets for the zero field susceptibility:
[1 = A2,O + 2A2.“ + 0(t2).

, . , T—T "' . . .
The leading term contains ( T c J , where m = -1. Tins cntrcal exponent value proves to
C

 

be incorrect experimentally, not surprising since the expansion assumes that the free
energy firnction is analytic about To From the original work of Widomm, the
phenomenological practice of scaling arises allowing the exponents and Tc to be fitting
parameters to compare the theoretical form to experiment. Systems that have phase
transitions described by the same critical exponents are believed to operate under the same

physical mechanisms, and so are said to belong to the same universality class.

41

One critical exponent of particular interest to the subject of finite size effects is the

correlation exponent, v, defined by

§~ t’V Equation 2.1

where i is the correlation length. This correlation length may be limited by the size of the
sample, and since phase transitions occur via growth of correlations towards infinity, the
nature of the phase transition is also afi‘ected by the size of the sample. As a result, as a
system is reduced in size, the real behavior near the singularity begins to deviate fi'om that
seen in the bulk. For a system described by a large but finite dimension L, the critical

temperature shifts according to"

24an
T

L-i‘, Equation 2.2
c ,
where A. is defined as the shift exponent.

Fisher and Ferdinandl 14 assert that the shift exponent may be related to the
correlation exponent v of Equation 2.1 by realizing that finite size effects occur when the
correlation length at T C(L) equals the finite length L. Setting g = L in Equations 2.1 and
2.2, we get

1
xi = so that

_ W ~ L’l/V, Equation 2.3
v T

C

This is a generic result for a finite length scale L. In the layered samples reported in this
thesis, L = WSG, the width of the SG layer, be replaces Tc, and Tf replaces Tc(L).

Equation 2.3 then becomes

 

~ WSG-I/v. Equation 2.4

This is the relationship used to derive the exponent v fiom data. Formally, it should only
be valid for Tf ~ W.

2.2 Droplet Excitation Model (D.A. Fisher, D. Huse, 1986)

In 1987, Fisher and Huse83 formulated a scaling theory specific for SGs that may
be applied when Tf(W) is far away from n”. This droplet excitation model is an attractive
choice for size effect studies, as it includes spatial dimensionality fi'om its onset. (Other
commonly used models tend to be in the category of infinite range interactions
(Sherrington-Kirkpatrick) or short range models which have not been successfirlly
analyzed for any spatial dimensionality.) The low lying excitations that may dismpt SG
ordering are pictured as clusters (droplets) of coherently flipped spins. The free energy
associated with the flipping of a droplet of length scale L , in units of some microscOpic
length, is

F ~ YL 9
where Y is an interfacial tension, and 0 < [9| 3 (d-l)/2 where d is the dimension. The
lower critical dimension, d], is assumed to lie between 2 and 3, meaning a phase transition
occurs in 3 dimensions but not in 2. When (1 = 2 < d], 62 (where the subscript denotes
the dimensionality) must be negative, allowing large scale excitations to exist at low
energies, destroying the SG order at finite temperatures. The relaxation barrier for the

droplets also scales as L,

B~LK

43

For a film, of finite thickness W, that is infinite in two dimensions, two regimes

shall be considered (i) low temperature where T << Tc, and (ii) critical, where T~ Tc.

(i) Low temperature T << Tc

When L < W, the system behaves 3D, and the fi'ee energy scales with a 3D exponent
F~W%.

The temperature is then renormalized to keep the renormalized energy scale of order
unity,

TR(L) ~T -W‘93.
At lengths L > W , the system behaves 2D, and the temperature is renormalized again
using the 2D exponent
TR(L) ~ T -W“93(%)WZI ,
where 02<0< 93,since2<d1<3.
When TR(L) ~ 1 entropy dominates and disorder occurs. This happens when L = 5,
yielding

4" ~ T—V2W1+V263 where V: 1213-1 Equation 2.5

The barrier heights also scale in a similar manner:

L~W BW~WV3

L B 5 W2 W3

~§ ~ — W
i (w)

So that the relaxation time,
_ -( I + + V 9
TL~exp[B/l ]— T V3V2)W"’3 2W2 3,

44

increases as T decreases. At some point, TL 2 tm (measuring time) causing the system to

fall out of equilibrium, appearing to fi'eeze, at temperature T = T f (rm)

Tf(t,,,) ~ [WV3+V2V292 ].+v,p,

T In(t,,,)

C

For fixed tm,

+ V 6
— ~ W" where a = W3 W2 2 3 Equation 2.6
Te 1 + V2 W2

A rigorous upper bound on a can be obtained fiom a general dimensionality argument
which states 9d 3 Wd 5 d-l. This gives for d =3 93 5 ‘1’3 5 2 resulting in a S V3 S 2.
To try to better restrict the value of a, we've gathered values for W, V, and 6 from theory
and/or experiment in the literature. Monte Carlo calculations on Ising short range SGs put
a lower bound of 1 on the parameter W2 V2115. Fitting studies of temperature dependent
relaxation times in thin CuMn films to a generalized Arrhenius law, lnt ~ T (“‘1"), sets an
upper bound on this parameter of 1.6115. Similar studies done on szCuo_33Coo.22F4, a
2D short-range Ising SG with random nearest neighbor bonds, yield a value of W211; =
2.2.117 Also, non-linear susceptibility divergence and relaxation time studies on CuMn
provided boundaries on 02 and W3. Composing all these values together,

0.2 s 02 s 0.3

1 .<. W2 v2 3 2.2

0.5 3 W3 s 1
allows an estimate of 0.3 s a s 0.65.
This result should be good for Tf << be where W is small, but greater than the

average impurity spacing.83 All the S65 we've studied have an FCC lattice, giving 12

45

nearest neighbors for each atom. For impurity concentrations ~ 10 at.%, the average
separation is on the order of one atomic spacing.

Note that the limits fiom the literature averages include values fiom a short-range
Ising SG, whereas CuMn is long-range Heisenberg type. This combination may pose a
problem, since there is some evidence that short range Ising SGs and long range RKKY-
like SG are in different universality classes”, and systems in different universality classes

in general have difi‘erent critical exponents.
(ii) Critical region Tf ~ Tc

Near the bulk transition temperature, we define t a (T - I‘D/7;. Here the relaxation time
scales with the dynamical critical exponent 11W, T J ~ W23 , and ITW, T c) < tm, so that
the system will not fall out of equilibrium before the correlation length grows to the film

thickness (or no finite size effects would be seen). The correlation length below T c, as

indicated in the previous section, is thus less than W: 5 ~ |t|- V’.

For excitations L<< W, the fiee energy again scales as

FL z Y3(t) L63 where Y3 ~|t|v303.
and for L> > W,
FL ~Y2(t, W) L92.

Here, where L~ W, Y2 may be found by matching to Y3. Using Equation 2.5, the 2D

correlation length becomes:

§~ pyfl+v263 )ltlt’sgfl’z.

46

The barriers scale in a similar fashion as in the previous section,

ALM. Bw~ 14‘3”er
V2
At scale 5 3,, ~ 3,6) ~

(wrest

Making use of the relaxation time as before, and for long measuring times rm >> I, an

expression analogous to Equation 2.6 is found

 

-1
T b _ T 1 (W3+V2W292)V3]
f £( m) at WSG—(I/v)[ln(—T—’"-Z—):r Equation 2.7
Tf WSG

This expression differs from Equation 2.4 only by a weak logarithmic factor involving tm.

CHAPTER 3

SAMPLE FABRICATION

All samples referred to in this thesis were grown at MSU in the dc magnetron
sputtering system shared by the condensed matter group. Technical details of this
apparatus are given elsewherem The following gives the necessary explanations of

sputtering preparation, parameters, and materials used.

3.1 Target Production

The elemental targets Ag and Cu were purchased as 0.25" plates fi'om Angstrom
Sciences119 and cut to a cylinder of 1.25" diameter by the Physics Shop stafi‘ at MSU.
The Al, Mo, and Si targets were purchased precut to the above size from Tosoh SMD
Incl”, and the V target was bought precut from Demetron Incl“. The companies have

stated the purity of these elemental targets to be

Table 3.1 Purity of elemental targets

 

 

 

 

 

 

 

 

 

Cu 99.999%
Ag 99.999%
Al 99.999%
v 99.9%
Mo 99.99%
Si 99.999%

 

47

48

Alloy targets CuMn, AgMn, AuFe, and NiMn, and the pure target Au target, were
all made by us in an rf-induction firmace. The raw materials were of the following form

and purity

Table 3.2 Purity of raw materials used in melted targets

 

 

 

 

 

 

 

 

 

 

 

 

material purity form source
Cu 99.9999% small pellets Johnson-Mathey Electronics122
Ag 99.9999°/o small pellets Johnson-Mathey Electronics
Au 99.99% wire Sigmun Cohn Corp.123
Mn 99.9% chips Lnggtrom Sciences
Fe 99.9% chips from 01“ Tosoh SMD Inc.
precut target ‘
Ni 99.99% large pellets Angstrom Sciences

 

The pellets or chips from each material were cleaned in a dilute nitric acid solution
(H202N03 10:1) before loading into a graphite crucible. For all metals excluding Ni, the
inside of the crucible was coated with boron nitride, a generally inert substance which
prevents contamination of carbon from the crucible. The reactivity of Ni at high
temperatures with such a nitrogen compound precluded this approach for NiMn alloying.
If BNO3 is used to line the crucible, the molten NiMn dissolves a significant amount of
nitrogen, which is then expelled as a gas (along with some molten metal) as the solubility
of the nitrogen decreases in the. cooling alloy. For this material it was necessary to
purchase smaller alumina crucibles to use as a liner, and cut a graphite crucible to fit
around them. Fortunately enough heat was radiated from the graphite and conducted

through the alumina to melt the material. This arrangement limited the size of the NiMn

49

targets. Targets were made in three standard sizes. In order to reduce potential Cu
contamination during sputtering (as explained in the next section) the NiMn were cut with

a small extra "brim" along the bottom causing the target to resemble a hat.

50

Table 3.3 Melting temperature ranges and final size of targets

 

 

 

 

 

 

 

 

 

 

 

Target Melting Final Size
Temperature (C) (diameter x thickness)

CuMn , 1030 - 1100 2.25" x 025*
all concentrations

CuGe ~1010 2.25" x 0.25"

2 and 10 at.% Ge

Ag“ 91Mn0 09" 1000 - 1025 2.25” x 0.25"

Au 1060 - 1090 1.5" x ~0.15
Au0 9713:2003 1040-1130 1.5" x ~0.15

NiMn 1340 _ 1400 1 3/8" x 0.25"
all concentrations ("hat" cut)
Melted by Michael Wilson

For all targets the base pressure inside the induction fumace quartz tube was ~ 5x
10"6 torr. The tube was then backfilled to ~250 torr with 90% Ar and 10% H2 gas
mixture, the H2 removing residual oxygen fi'om the chamber. Pure Ar was used in the
case of NiMn, due to the high solubility of H2 in Ni. Typically each melt was removed,
turned over, and remelted one or two times to improve homogeneity. A cap made from a
graphite crucible with a break in the side was fiequently used on the NiMn to increase
heating fiom the top. Temperatures were read on the outside of the glowing crucible with
an optical pyrometer. The latest targets (the NiMn) were melted with the aid of a
graphite cap made fi'om another crucible. The cap, sensitive to the r.f. induction, adds

heat to the top of the melting target, encouraging homogeneous melting. Melting was

observed through a break in the cap (see Figure 3.1).

 

51

 

 

 

Figure 3.1 Graphite crucible and graphite cap

3.2 Sputtering

3.2.1 Sputtering Machine

The UHV compatible sputtering chamber holds four dc magnetron sputtering
guns, a rotatable SPAMA (Sample Positioning and Mask Assembly) plate which can hold
up to 16 samples, two available film thickness monitors (FTMs), two available
thermocouples, and a liquid nitrogen cooling system for the SPAMA plate. A computer
controlled stepping motor positions the SPAMA plate so as to hold the exposed substrate
over the chosen sputtering gun for the appropriate time to produce the desired thickness

of each layer.

52

.Nliquid N

 

 

 

 

 

 

 

 

llquld N2 teaevolr

 

COLUMATING

 

 

 

 

 

 

 

 

 

 

Figure 3.2 Schematic of inside of sputtering apparatus

A filament is located under one end of the gun parts, an anode at the other end.
Electrons emitted from the filament speed towards the anode through a space between
upper and lower gun parts, ionizing argon gas into a plasma. A negative voltage is

applied to the target to attract the ions, causing sputtering.

53

Figure 3.3 Close-up of target and gun assembly

MA are n Macrame snaru)

/ Al GUN PARTS

 

 

 

 

GAP

 

 

 

TOP GUN PART
BOTTOM GUN PART

WATER COOLED
COPPER FITTING

 

 

 

 

 

 

 

 

 

 

 

3.2.2 Cleanliness

It is the nature of the sputtering process to coat the machine parts surrounding the
target with material from the target. It is necessary to remove this material in order to
avoid contamination from the previous run and also assure the proper gap size between
target and gun needed for operation.

The collimating chimneys between the sputtering guns and the SPAMA plate are
not directly cleaned, rather the aluminum foil covering is changed between sputtering runs
using difl‘erent materials. The chimneys are kept clean between wrappings and are never
handled without gloves. The aluminum SPAMA plate, substrate holders, substrate
shutters, and sputtering gun parts 'are all etched in acid solutions to remove the deposits.
Cu, CuMn, CuGe, Mo, and V are easily removed with a solution of 3:1 HNO32H20. Al,
Si, and NiMn may be removed by the addition of ~10% HF acid. Caution must be

54

exercised when using this acid as it attacks the Al parts, which over time reduces their
size. Because the fit of the gun parts to the sputtering machine is critical they are removed
from the HF solution as soon as possible to reduce exposure. This may result in small
amounts of sputtered material remaining on the gun parts. For this reason each material
has its own associated gun parts. Ag and AgMn may be removed with a mixture of 1:1:1
H20: H202:NH40H. Au and AuFe required an exotic acid echant, and since their use
was low were not etched. Any larger deposits were mechanically removed with a razor
blade.

Other items in the sputtering chamber are not cleaned regularly because they are
not exposed to the sputtering beam and therefore cannot contaminate the sample, or, as in
the case of the magnetic confinement shield, are made of a material too reactive for acid
etching. These items are however kept clean from other contaminants while not in the
chamber.

The substrates used were <100> single crystal, polished, boron doped Si, cleaved
into 0.5" squares fi'om a Silicon Quest Internationalm 3" round wafer. All substrates
were cleaned with acetone and alcohol each for ~1 min. in an ultrasonic cleaner
immediately prior to loading in the chamber.

Upon closure the chamber was baked for ~8 hours, after which pumping
commenced until the base pressure was ~2><10‘8 torr. Ultra High Purity Ar, run through a
liquid nitrogen cold trap and a Hydrox purifier, was used to backfill the chamber to 2.5x
10'3 torr for sputtering. The estimated impurity concentration at the sputtering pressure

using this process is < 10ppm.

3.2.3 Cooling system
The sputtered atoms carry heat to the sample, so a cooling system is operated in

order to control the grth temperature. Heat in the sample is transferred through the Si

55

substrate to an oxygen free high conductivity (OFHC) Cu block, which is thermally
coupled to the SPAMA plate through an OFHC Cu shim. The SPAMA plate is cooled
through contact with a liquid nitrogen reservoir filled by the capillary tube (see Figure
3.2). The capillary tube carries high pressure nitrogen gas to the heat exchanger, where it
comes in contact with the liquid nitrogen used for the cold trap. The gas inside the
capillary tube becomes liquefied, and then proceeds to the SPAMA plate reservoir.

The temperature reading is taken fiom a thermocouple atop the OFHC Cu block

Pressure screw

    
 

Cu shim Thermocouple

............
. \
xxxxx .......

K \"n
. .q‘xxxi .
. .1 x . it

\t \x

‘I‘
* t 1
u I N
{‘5'
h; ‘
5:-
_{
‘\
1. I
a “t i:
V. . 't \ .._ '.xss
' '0 '- ‘0
. t . ecu. \flf/

Shutter Sample Substrate

Substrate
holder (Al)

  

Figure 3.4 Sample holder

3.2.4 Sputtering parameters

All samples were sputtered under 2.5 mT pressure of the backfilled UHP Ar gas.
The gas flow rates through the pinholes near the filament varied from 35-42 cm3/min. The
anode to filament voltage was typically 50-60V, and anode to filament current was 5-7
Amps. The Ar plasma to target voltage and current were adjusted to attain plasma

stability and the desired sputtering rate (usually the highest rate possible). These

56

parameters were highly material dependent, afl‘ected by the target density, conductivity,
and possibly other factors such as melting temperature. Although the computer was able
to use deposition rates to calculate the timing needed to produce the desired thicknesses
and move the sample to those locations, the plasma voltage and current must be

monitored and adjusted against drift by hand.

Table 3.4 Plasma to target parameters and associated deposition rates

 

 

 

 

 

 

 

 

 

 

 

 

 

. Plasma to target Deposition Rate
Matenal V/I (kV/mA) (A/ second)
Cu - 400/.700 14.0
CuMn -400/. 700 12.7
CuGe -370/.600 10.8

Ag -350/.480 6.0
AgMn -400/.750 6.8
Au -215/.400 8.5
AuFe -320/.400 ~6
Al -300/.890 3.3
Mo -325/1.10 8.8
V -680/1.01 6.6
Si -350/1.00 3.1

 

 

 

 

CHAPTER4

SAMPLE CHARACTERIZATION

4.1 Compositional Analysis

All SG Tf values reported in this study were normalized by the Tf of a bulk sample
of the same concentration in hopes of making the results for each series of samples
concentration independent.76 It is necessary, however, to check the actual sample
concentration: a) to predict the sputtered concentration fi'om a known target
concentration; b) to detemiine any concentration drift throughout a sample series; and c)
to compare Tf values with literature values.

Energy Dispersive X-ray (EDX) analysis was used to determine concentrations for
both targets and sputtered samples. This non-destructive process uses a beam of electrons
to excite the atoms into emitting characteristic x—rays. These x-rays are tallied, and three
major corrections are made to the ratio between the number of x-rays fi'om each element.
The element with the larger atomic number has a larger cross section and will produce
more x-rays (Z correction). The energy of a characteristic x-ray determines how likely it
is to be absorbed before it escapes the sample (A correction) and how likely it is to create
a secondary x-ray in the sample material (fluorescence or F correction). Together these
are the ZAF correction factor, and when properly taken into account atomic
concentrations can be calculated. When the ZAF factor is close to 1, few corrections are

needed to the raw ratio. All EDX data was taken on a JOEL ISM-35C Scanning Electron
5 7

58

Microscope with a Tracor Northern X-ray detector, both belonging to the Center for
Electron Optics at MSU. A hard x-ray aperture was used around the electron beam,
where W, a strong M0 x-ray absorber, is deposited on the underside of the Mo ring
opening to absorb any stray Mo x-rays that may be created by the beam. A physical
barrier was placed around the detector to prevent backscattering background x-rays
(mostly fiom the Cu chamber walls) from entering the detector. The x-ray counting,
composition calculation, and any necessary peak deconvolution were done on a dedicated
PC running Noran Inc. commercial software.

Although the presence of small amounts of material (<1 at.%) may be detected,
low counting statistics makes analysis of elements comprising < 2 at.% difficult. The
lowest concentrations checked with EDX were those of AuF e with 3 at.% Fe and CuGe
with 2 at.% Ge. Most alloys were in the 10 - 25 at.% impurity range.

The accuracy of the concentration c for this method is (c i 0.030) if the ZAF
corrections are calibrated to scans of pure samples taken at the same electron energy.
Without this calibration the error is closer to (c : 0.07c). Unfortunately nearly all the pure
standards available were bulk pieces, thicker than the depth of the electron beam
penetration. Only the thickest of the films made (1000 nm) are seen as bulk by the 20 kV
electron beam. Ifthe sample doesn't encompass the entirety of the tear shaped penetration
area, two problems may occur: a) The substrate will produce x-rays which may then cause
fluorescence in the sample. Fortunately x-rays from Si substrates are not energetic enough
to excite the metallic atoms; also they do not overlap any x-rays of interest. b) The ZAF
correction calculation assumes the entirety of the penetration area is encompassed by the
sample when calculating the secondary effects, and some error is expected when this is
not the case. A

NiMn, with its abrupt change in magnetic behavior with concentration, was given

the most attention. Because the ZAF factor is so close to unity for a NiMn alloy (typically

59

1.02), the error on the concentration was estimated by the Noran software to be less than
(c $0.070) for a thin film‘”. This result, however, does not give any indication of
potential systematic error between thick and thin films. Better concentration definition
was needed, since some of the NiMn films with thicknesses 100 - 1000 nm showed
different magnetic behaviors when the measured concentrations were the same. Three
films of varying thicknesses were made of the same concentration by sputtering one third
of each film at a time, switching between films until all were complete. The 1000 nm film,
seen as bulk to the electron beam, was taken to read the true concentration, c, while the
300 and 100 nm films gave readings of 0.89c. Using this behavior as a calibration,
corrections were made to the thin film values, after which consistency was achieved
between concentration and magnetic behavior.

The CuMn and NiMn sputtered films were approximately the same composition as
the target. AgMn and AuFe sputtered lower impurity concentrations than were originally
in the target. Stubi et. al.,“ in the AgMn study discusSed in Chapter 1, measured a T19 in
a bulk sputtered films of AgMn which was 40% lower than be measured from target
chips. This corresponded to a drop from 15.5 at.% Mn to ~ 7 at.% Mn, a loss of more
than 50% of the impurity. Since the effect was sensitive to the pressure of the Ar
sputtering gas, it was postulated that the loss was due to larger scattering angles of the
lighter Mn as it collided with the gas, preventing more Mn atoms than Ag atoms from
reaching the sample. Since the AuFe system has even greater difl‘erences in atomic mass
than the AgMn, a more pronounced effect was expected. Surprisingly, a similar loss of
50% was observed, suggesting that the scattering angle effect is not the only mechanism at
work.

Concentration 'fluctuations'in the CuMn and AgMn runs varied the W of thick
sputtered films by a few percent between samples. AuFe concentration fluctuations gave

rise to be variations of closer to 5%. Every NiMn target made produced film

60

concentrations that drifted or changed between runs, so be values from difl‘erent runs
with the same target could be quite difi‘erent. This behavior necessitated the sputtering of

many thick films; frequently every third or fourth NiMn sample grown was a thick film.

4.2 Mechanical Determination of Film Thickness (Dektak)

The film thickness monitors (FTMs) used to determine the rate of sputtering (and
hence the eventual layer thickness) have a 1 1-2 % precision in their reading, but other
factors, such as sputtering gun power fluctuations and change of F TM response with
temperature, cause larger variations in the resulting layer thicknesses. Single films 500 nm
thick are measured with the Dektak IIA surface profilometer as the first check of layer
thicknesses. The Dektak uses a sensitive needle that physically traverses the sample,
preferably over an abrupt sample edge. Typically a small piece of the film is torn away
from the substrate to expose such an edge, after which the challenge becomes finding an
area along the edge that has not lifted fi‘om the substrate. Edge lifting leads to spurious
inflated values of the thickness. The scan is always done from the substrate surface, up
over the edge, then onto the sample. This way a lifted edge may be identified by its
profile, shown'in Figure 4.1.

61

 

 

a) b)
Height

A Edge Sample A
J/ 1

Substrate

i

    

GOOd edge Lified edge

 

 

 

\/
NV

Distance (fewum)

Figure 4.1 Schematic of Dektak profiles of a) sample edge secured to substrate b) sample
edge lifted fiom substrate.

 

The standard used for calibration of this instrument is only given to an accuracy of
5% (unfortunate, since the precision of the Dektak when measuring the standard is better
than 5%). Averages from films of each material gave their nominal thickness values to
within 5%, with a standard deviation of s 5 %. An exception was found for Agoganoflg
in the AgMn/ Si series, where the AgMn thickness was ~ 10% low for both films. This
discrepancy was also noticed in the analysis of Section 4.3.4, and “'80 was adjusted
before analyzing the magnetic data. Layer thicknesses used in Chapter 6 are to be
considered as having an uncertainty : 5% to reflect the spread of thickness values found
for sputtered films.

NiMn, which was not suitable for edge production due to the hardness of the

material, was not measured with this method.

 

62

4.3 X-ray Diffraction

4.3.1 Diffractometer and Sample Alignment

0 -20 x-ray difl‘raction was used on all samples to determine layer thicknesses, size
and crystallographic orientation of crystallites, and to give some estimate of layer quality
in the multilayers. The diffractometer used was a Rigaku powder x-ray difl‘ractometer
with rotating Cu anode. Between the sample and the x-ray detector a graphite
monochrometer screens out all but the Cu-Ka radiation, wavelength 0.1542 nm. A
divergence angle of 1/60 for the x-ray beam was selected by inserting appropriate
collimating slits, one between source and sample and one between sample and
monochrometer. The fixed 0-20 orientation of the difi‘ractometer (see Figure 4.1) ensures
that only periodicities perpendicular to the sample holding surface can fulfill the Bragg

condition for an interference maximum

17» = 2d SinG. Equation. 4.1

Here I is the order number, 11. the x-ray radiation wavelength, and d the spacing producing
the maximum at 0. Since the bilayer periodicity A (Figure 4.2) is of interest in the
multilayered samples, it is necessary to carefirlly line up the surface of the sample so the
layers make angle 0 with the incident and reflected beam. Since the reflection peak could
be as narrow as 20 ~ 0.20 for a well layered sample, if the sample is tilted more than 0.20
from the desired plane the peak may be missed. If the sample is tilted less than the peak

width, the detector will still pick up part of the peak (see Figure. 4.3).

this page blank

63

 

 

fixed
X-ra source “x
, I . /\~

Rotating Cu .
anode ‘ Slit

 

 

Figure 4.2 Powder Difi'actometer Orientation

 

 

 

 

 

 

a1<

 

 

‘>A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.3 Periodicities in a multilayer sample

 

 

 

 

desired sample position actual sample position

Figure. 4.4 The effect of sample misalignment by small angle 6.

 

 

 

 

65

The difi'actometer is meant to hold a powdered sample, where the nature of the
random mixture allows every crystallographic orientation to be viewed. There is no
sophisticated sample orientation device like those found in single crystal diffractometers.
To achieve the necessary alignment, the samples were mounted on an aluminum holder
specially made by the machine shop in the MSU Physics Dept. to fit the Rigaku
difl‘ractometer and hold the sample face in position. The highest precision milling available
to make the holders is i 0.025 mm at each sample comer, introducing error in the
alignment of the sample surface of up to :1: 0. 1°. This small misalignment can result in
reduced peak height, and also a shift of peak location of 20 ~ 0.10 .

4.3.2 Texture Analysis
The first striking observation in the large angle region of 20 = 35 - 45° is the
usual presence of only one Bragg peak per material, whether multilayer or thick film. If
the sample were a distribution of randomly oriented crystallites, a powder type pattern
would be observed, showing peaks for all allowed Bragg reflections. The sputtered metal,
however, while resembling a powder with its polycrystalline nature, is highly textured with
only one orientation lying parallel to the sample surface; the <111> for fcc metals and the
<110> for bcc. (The only exception was a single film of A], where a weak <200> peak
was observed.) These orientations allow the densest packing of the sample from top to
bottom as the atoms to settle into their lowest energy state during sputtering.
The location of the reflection indicates strains are present in the sample. Even for
a thick film (500 - 1000 nm) the peak is shifted (generally to a lower value) a fraction of a
degree in 26 from it's predicted position for an annealed sample of the same material or
alloy composition. This shift corresponds to an expanded lattice parameter of up to 0.5%.
This is not unexpected for a polycrystalline film, where crystallite boundaries and defects

in crystallite growth put strains on the structure.

66

The size of the crystallites may be estimated fi'om the width of the reflection line,

via Sherrer's formula126

_ tot
Boos 6

 

S

where sis the coherence length perpendicular to the plane, it is a constant approximately
equal to 1, 3c is the x-ray wavelength, and B is the FWHM of the line in radians. When
determining the actual FWHM, the limits in the instrumental resolution of the beam must

be considered. Two effects contribute to the resolution, the first is related to the
collimating slits used in the system, the second arises fi'om the separation of the Cu Karl

and K02 lines, which are too close in wavelength to be separated by the monochrometer.

At the region of interest (20 = 3S-45°) the apparatus adds an instrumental line width of
20 ~ 0.1°. None of the samples studied had a linewidth this narrow. In order to

compensate for this effect, the instrumental linewidth was subtracted from the measured
FWHM in a gaussian fashion ,5 =\/FWHll/12 —0.12 . The results are shown in table

 

4.1.

67

Table 4.1 Typical sputtered 20 and E, values for each material

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. d Annealed d Sputtered l; - Coherence

Matenal Value127 (rim) Value (nm) Length (rim)
Cu <111> 0.2088 0.2092 62.0
Ag5111> 0.2359 0.2365 114.0

Au <111> 0.2355 0.2359 37.0

Al <111> 0.2338 0.2343 59.6

<200> 0.2024 0.2028 62.9
V <110> 0.2141 0.2137 29.2
Mo <110> 0.2225 0.2235
Si “““““““ amorphous '''' “'

CuMn <1 1 l>

10 11 12 % Mn 02113-02112 02116-02112 26.7 - 37.5
Ago 91MnQ09 <111> 0.3609 0.2369 50.9
A110 97Fe0 m <111> 0.2355 02363-02359 21.3 - 27.6
NIQ‘IIMHO 29 <111> 0.2091 02075-02072 36.3 - 38.0
NiO 69Mn031 <1 1 1> 0.2096 02084-02082 40.7 - 41.5

 

Extracting information from the Bragg peaks becomes considerably more
complicated when looking at multilayers. Neighboring materials add additional strain to
each other and so induce shifts in both peak locations, and cause broadening as the layer
thickness limits the size of the crystallites. Satellites due to the periodicity A appear
around and between the peaks, making line width analysis impossible in all but one case,
the SG/amorphous Si samples. In these samples the Bragg peak of the metallic SG
showed a width corresponding to a coherence length equal to that of the SG layer

thickness to within a few nanometers.

68

4.3.4 Determination of the Bilayer, A
The multilayered samples contain typically 50 - 200 bilayers, depending on the
value of W56. The bilayer number is chosen so that the total SG thickness is 100 - 500
run, in order to provide suitable magnetic signal strength. The bilayer thickness, A, is the
only true periodicity of a multilayer, and is capable of producing Bragg reflections
(substitute A for d in Equation 4.1). Since A is large (4 - 30 nm), the 20 reflections for
this periodicity occur at small angles. Although the reflection from higher orders of I
decrease in intensity with increasing 0, a reflections from A are also observed in the
vicinity of the material lattice parameter reflections at large angles (see Section 4.3.6 for a
model of this behavior). These will be referred to as large angle satellites.
The Bragg equation stated above is actually a simplified version neglecting the
index of refraction. This neglect is normally valid, as the index of refraction for x-rays in
metals is n = 1 - 6 where 8 is small and positive, and may be calculated from the

expression
5:22 39—"[ f +Af'+4f"].
It

Here A is the x-ray wavelength, re is the classical electron radius, and n is the atomic
number density. f is the atomic form factor, with Af and AV" its real and imaginary
corrections due to absorption edges. For most metals this value is ~10'°. The following
shows that neglecting this small change is acceptable for large angles, but not for 0 3 ~

few degrees.

69

 

 

 

 

E

Figure 4.5 Exaggerated x-ray deflection due to index of refraction

 

From the above Figure, the angle considered in Bragg's Law is actually 0",, but
the measured angle is 93. To find the relation between the two, use Snell's Law
nasin¢a = nmsin¢m
since na =1, nm = 1 - 6, and sin¢ = cos6, we get
cos0a = (1 -o)cos'0m
Considering that 6 is small (~10'4), and sin2 + c052 = 1,
sinZOa = sin20m + 26

Thus replacing this expression for sin0a in Bragg's Law yields

(2A)2 sinz 9=(12.)2 +25 Equation. 4.2

where A is the bilayer thickness. For large 0, 6 is so small as to be negligible and
Equation. 4.2 reduces to its simpler form of Equation 4.1. But for a periodicity the size
of a typical bilayer, the reflections occur at small enough 0 (~1°) that it is necessary to

include the 26 term. To determine A to the greatest possible accuracy it is desirable to

 

7O

compile the measurements for multiple orders of l. Plotting sin20 vs. 12 for several
reflections allows A to be extracted fiom a least squares fit of the slope of the line. An
average 6 may be extracted from the intercept, but the value lacks both accuracy and
precision, because our instrument and the sample holder are unable to meet the stringent
alignment conditions required to successfirlly carry out such an analysism. It is necessary
in this analysis to use the correct values for I, where 1= 1 is the first reflection after 20 =
0. Typically this reflection is at so low an angle that the first observed peak is 1= 2 or 3.
Choosing improper 1 values is signaled by a curve rather than a line in the sin20 vs. 12
plot.

A similar analysis is done with Large angle satellite reflections, but 6 may be
neglected. Using Bragg's Law in Equation 4.1, only sing vs. I need be plotted, so the

choice of starting [value is irrelevant, as long as the Is are consecutive with the peaks.

Log(lntensity)

 

0.011
(1010
(1009
(1008
(1007
(1006
(1005
(1004
(1003
(1002
(1001
(1000

sin-2

‘ l

 

71

H _ 348—3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 1‘1 1

160

120 200 240
[2

Figure 4.6 Small angle diffi'action scan and bilayer analysis (A=14nm) for an AuFe/Si

7nm / 7nm sample.

72

4.3.5 Series Analysis
Although any one sample will give only the bilayer thickness, A, a series of
samples with one bilayer component held fixed will reveal whether systematic or random
errors exist in the thicknesses of each component. First assume the actual thickness of
each material may be difi‘erent from the expected thickness by a linear factor, as would
occur for a low or high fihn thickness monitor reading during sputtering. Ifwe define:
W36, WIL , A = actual SG, IL, and bilayer thicknesses
WSGNr WILN , AN= nominal SG, IL, and bilayer thicknesses

“’50 = C (W SGN) W11. = d (WILN)

then the bilayer A may be rewritten as:
A=WSG +WH. =C(WSGN)+d(Wn.N)
AN"= WILN '1' WSGN
A=d(WIL)+C(AN —WIL)

A=c(A..)+WnN(d-c)

If WILN is constant (usually 30 nm), then plotting A vs. AN gives values for c and d A
similar expression may be found for constant WSGN- A perfect set of samples will give a
straight line of slope 1 and intercept 0, which is often nearly the case. Fluctuations in the
layer thicknesses appear as noise. Since the samples are never sputtered in an order
relating to their thicknesses, any drift in the rate during the run would also appear as noise

in this plot. Figure 4.7 shows a typical line produced by this method.

73

AuFe/Si
Wsi = 7nm

34 r
32 '-
30 l
28 L
26 '_ WSG=(l.OO)WSCN

   

24;
22?
201
18
16~
14;
12;
10;

WIL=(1 .05)WILN

Measured A

 

l

1 1 1 L a l . l

 

1O 12 14 16 18 20 22 24 26 28 30 32
AN

Figure 4.7 A typical plot for individual thickness calculations

74

The AgMn/ Si series gave the only line with significant deviation fiom experiment.
The AgMn/Si slope was 0.87, indicating that the AgMn layers were 13% thinner than

expected, a value supported by the results in Section 4.2.

4.3.6 Step Model for A Reflections

As indicated above, there are three periodicities in the sample, bilayer A and lattice
spacing for each non-amorphous material, dwarf“. The three periodicities cannot be
viewed as independent, as the larger is made from layers of the smaller. A simple, one
dimensional step model, proposed by Segrnuller and Blakesleem, can help to qualitatively
understand the relationships.

In this model, each layer is assumed to have an integer number of atomic planes
having the same lattice constant as in the bulk material. The structure factor, S(q), is

found by summing the contributions from each part of the multilayer:

 

 

sin NA /2 sinna /2 sinna /2 .
S( )____ i q ) 1 .(1 161 )+f2 (2 24 )exp(,Aq/2)
sm(Aq/2) sm(a1q / 2) sm(a2q/ 2)

Thus the diffracted intensity is S‘S,

 

 

 

I~sin2(NAq/2) 2sin2(n,a,q/2)+ psin2(nzazq/2)+
sin2(Aq/2) I sin2(a,q/2) 2 sin2(a2q/2)

sin(n,a,q / 2) sin(n202q / 2)
I 2 sin(a,q/2) sin(a2q/2)

 

cos(Aq / 2 )} . Equation 4.2

Here N is the number of bilayers, q = sine/,1 is momentum transfer, 1. is the x-ray wave

length, and f1 and f2 are the atomic scattering factors for materials 1 and 2. Only one

75

lattice parameter is used per material, since the samples are all highly textured, with only
one orientation parallel to the sample surface (see section 4.3.2).

The term sin2(Aq/2) has zeros at q = ln/ 2A, producing maxima corresponding
to the reflections from A. Successive orders of I produce peaks starting at zero and
reoccurring every 20 = 0.5 to ~ few degrees. The heights of these peaks are modulated

by the terms inside the curly brackets. The atomic form factors, fi, contain the DeBye-

 

Waller factor, exp( '3 ’2": a), which exponentially attenuates the intensity as 0 increases.

As a result the multiple order reflection at low angles fi'om A decrease in height and
generally disappear by 20 = 10°. The intensity decrease is not smooth however; the
faster oscillations occurring from the numerators of the enclosed terms, sin2(n,-a,-q/2),
modulate the intensity in a potentially complex manner. A simplification may be used for
the SG/Si samples, where the form factor for the light Si is so small f5,- may be set to zero.

Equation. 4.2 then becomes

 

 

I ~ sin2(NAq / 2) 2 sin2(nSGaSGq/ 2)
sin2(Aq/2) S sin2(aSGq/2) .

An envelope of period related to 1156 am is superimposed on the A maxima. An example

of this efl‘ect is shown in Figure 4.6. If the minima of this envelope could be accurately
determined, a value for the thickness of the SG layer could be calculated.
The denominators of the enclosed terms, with their small arguments, oscillate

slowly with increasing q, and do not become zero (thus producing a maximum) until 20

2 . .
reaches about 40°. These zeros occur at q i = 7, producing the first order maxima
r

2
from each material's lattice parameter. Superimposed upon these two maxima (or
maximum if a-Si is the second material) are the oscillations fi'om the A reflections, and less

noticeably the oscillations from the numerators of the enclosed terms. If one or both

76

layers of materials are thin enough, their lattice parameters come together and only one
main peak is seen, with satellites on each side fi'om the A reflections. Figure 4.8 shows
two examples of high angle satellites. This scenario repeats itself in the region of the
second order maxima of the material lattice parameters.

The step model considers only a perfect sample. Features in the sample such as
layer thickness fluctuations, layer boundary mixing, and layer roughness, all afi‘ect the x-
ray profile. These effects are discussed firrther in Section 4.3.7.

Log(1ntensity)

Log(lntensity)

 

 

77

33 35 37 39
2 9

b)

Al holder

1 l L A l 1 l A l

30 32 34 36 38
2 9

288-4

41 43 45 47

349-3

40 42 44 46

Figure 4.8 Large angle x-ray scans for a) CuMn/Au 4nm/4nm where a1 is significantly

different fiom a2 b) AuF e 4nm/4nm where a1 ~ a2.

78
4.3.7 Estimating Quality of Layers from X-ray Diffraction

An x-ray difi‘raction scan of a multilayer showing numerous peaks is a good
indication that the sample is layered. But a scan with modest peaks may not mean the
sample is poorly layered, it may be the unavoidable result of the material choice in the
multilayers. Understanding a general set of rules for difi‘raction behavior at low and high
angles can help explain features of a scan. To determine quantitative values of parameters,
such as interface mixing or layer roughness, requires comparison of scans to mathematical
models.

In general, Equation 3.2 indicates that the prominence of the peaks at small angle
(small q) will be determined by the contrast between the scattering factors of the two
materials composing the multilayer. Thus a scan for a CuMn/Au sample should display
better peak structure than that of a CuMn/Al multilayer for otherwise equal samples.
Other efl‘ects however tend to afl‘ect the small angle spectra more. Most notably of import
is the type of roughness at the interfaces. Small angle scans are extremely sensitive to the
long range flatness of the layers. A sample with a cross sectional appearance of Figure 4.9
will have poorly defined low angle dim'action peaks because the x-ray incident at low
angles samples a broader area. Such a sample may exhibit beautifirl large angle structure,
where it is flat on the small horizontal length scale of high angle sampling. This behavior
is observed in the case of columnar growth, where some structural coherency exists
between crystallites of adjoining layers, resulting in a profile of cumulative interface
roughness as shown in Figure 4.9. Thus the spectacular small angle scans observed for a
SG/Si multilayers (eg. see Figure 4.6) are due not only to the high scattering factor
contrast, but also to the long scale layer flatness imposed by using an amorphous IL

incapable of contributing to cumulative roughness.

 

79

 

LARGE ANGLE
SCATTERING

flat layers on

SMALL ANGLE SCATTERING ““5 le“1!“1 sale

layers not flat on this length scale

 
   

:: .X'f.
‘-' (3+ ...... _.._.
" wen-items.
. u...“

 

 

 

Figure 4.9 Length scales sampled by small and large angle x-ray diffraction beam.

 

 

 

 

 

 

 

 

r flaw-rage? wiwwr‘ww' was"'Ws"~'\\e>“'~\rw\:qgg.~"~w~~i

 

Figure 4.10 Small angle x-ray behavior on unmixed and flat mixed interfaces.

 

 

 

80

Interface mixing on the other hand will not dampen the small angle peaks if the
layers and the mixed area are very flat. Thus Figures 4.10 a) and b) will give virtually the
same small angle spectra for the same materials since the mixed region forming the new
"layer" has the same periodicity as the unmixed layers.

The above ideas can aid in analyzing a series of multilayers where the materials are
the same but the layer thicknesses vary. Figure 4.11 shows small angle scans for the
CuMn/Al system as W A] is decreased. The sharp multiple peaks indicate that the layers
are quite flat, not columnar, and do not become columnar even when even at W A1 = 0. 5

nm (~ 2 ML).

Log(1ntenal ty)

Logflntenaity)

 

 

Cuo.aallno.12/Al
4nm / 211m

81

 

 

Cuo.oalno.12/Al
4nm/I nm

 

 

Lofllntenoltyl

Infinite-natty)

Cuoulnon/Al
411m / l .5nm

 

 

1‘23A15073910

104

103:

102

N I."

 

N 0"
. v. vv

Cuo.esllno.rz/Al
him/0.511111

 

 

Y—fYr

 

Figure 4.11 CuMn/Al x-ray scans for decreasing Al thickness.

82

Large angle (large q) scattering is subject to difi‘erent effects. For large q, the
intensity height of the satellites is strongly affected by the contrast in the lattice spacings
d1 and d2. This effect is demonstrated by Figure 4.8, where a) shows CuMn/Au where d1
¢d2 , and b) shows AuFe/Ag, where (11 ~ d2.

Neerinck et. al. determined, through modifying the step model and calculating
resultant intensities, that large angle satellite reflections can be entirely wiped out by a
small amount of a particular type of multilayer imperfection, continuous fluctuation of a
layer thickness, on the order of ~ few Angstroms (independent of the layer thickness). ‘30
Multilayers with two crystalline components can only present discrete roughness; the
variation in a layer thickness is limited to integral steps of the lattice parameter. An
amorphous layer however may possess a continuous distribution of thicknesses. Figure
4.12 shows AuFe/Si, which not only lacks a material lattice parameter peak from the
second material (Si), but is missing the bilayer periodicity satellites, leaving only the
oscillations from the thickness of the SG layer. All the SG/Si systems with W55 > 0.5 nm
(see Section 4.4) lacked large angle satellites, indicating that the Si layers are amorphous

and fluctuate in thickness by at least several Angstroms.

83

104’;

103

IIH’I‘I'

lntesity
N

102

III IT

101

IIII ' I'I

’ 348-3
2 #2 M 1 1 r 1 . 1 1 1 r 1 . 1 . 1

30 32 34 36 38 40 42 44 46
2 9

I I

 

Figure. 4.12 Large angle scan of Au0.97Fe0.03/Si 4 MW rim. Scan lacks A satellites,
but shows thickness modulation.

84

4.4 Analysis of SG/Si multilayers

4.4.1 X-ray Analysis

Si sputters amorphous rather than crystalline layers, and so metal/ Si systems
require difl‘erent stmctural considerations fi'om those in metal/metal multilayers. As
mentioned above, the amorphous nature produces flat, non-columnar layers, and
continuous roughness that wipes out high angle satellites. We now address the issue of
interface mixing and potential silicide formation.

Silicide formation at the interface between metals and Si has been observed for
numerous metals, including Ni, Mo, Co, Cr, and Fe.131o"-"2~133 In Nr/Si multilayers, it was
found that Si will diffuse into the Ni layer prior to silicide formationm. The light Si atom
can diffuse without significantly changing the atomic density of the metal layer. Such
behavior is found by Fullerton et. al.,133 where Fe/Si multilayers with fixed er only slight
changed A as W81 was increased from 0 to 2 nm, after which A increased with the
expected additive dependence (resulting in a A smaller than nominally sputtered). The
authors concluded that the first 2 nm of Si diffused into the metal layer. Large angle
diffraction data fi'om the same study provided evidence for silicide formation in the
diffused region. Large angle scans of multilayers with WSi 2 2 nm resembled that of
Figure 4.12 , indicating an amorphous layer was present, while similar scans of samples
with W81 3 1.5 nm resembled Figure 4.8 b, indicating two crystalline layers with close
lattice parameters. Since room temperature sputtered Si is not crystalline, the crystalline
layer must be a silicide.

A few early CuMn/Si samples from this study also showed a smaller A than
nominally sputtered. It was assumed at the time the discrepancy was due to the use of
crystalline Si parameters to calibrate the FTM, and so to compensate, the FTM readings

were reduced by 8% over what they would have been normally. For the SG/ Si data where

85

“’56 is fixed, this addition of extra Si presents no problem in the magnetic data
interpretation, since the Si acts only as a separator. For CuMn/Si coupling studies, “'86
held fixed WIL thinned, the 8% is not large enough to qualitatively change conclusions
from the magnetic data or the following structural results.

The small angle x-ray scans in Figure 4.14 show the progression in CuMn/Si
multilayers as W5, is decreased. A sudden breakdown occurs between “’81 = 3 and 2 nm,
indicating that at 2 am that the amorphous, flattening layer is no longer present. The large
angle scans, however, indicate the presence of continuous roughness for “'81 2 1 nm (see
Fig 4.15a). For 1 s “'51 s 2 nm, the Si layer is such that cumulative roughness is allowed
to grow, but the Si layer is not crystalline.

Figure 4.15b, the large angle scan for “'81 = 0.5 nm, shows a narrow peak with
small satellites. This value of W5, is much smaller than the silicide thickness of “’81 = 1.5
nm observed in the Fe/ Si system discussed above. Our profile may indicate two things: a)
the layer is no longer amorphous, as would be the case if a crystalline silicide is formed; b)
the Si layer is still amorphous but is not thick enough to provide the ~ few Angstroms of

continuous roughness needed to destroy the satellites (see Section 4.3.7).

 

 

 

 

86

 

 

 

 

 

 

 

 

 

 

 

 

 

10‘;
: 4
’ 3 CuosollnoJo/Si
s » Cuo.solno.ro/Si 2 , 70m/3nrn
7nm/4am A
- ’1 103»
a E
g. 3 ..
I: E 3.
7; ‘33 2
.3 g .3
E 102:
s: ’
2» 4
:1
lo'rééiééiriiiio ,. .-.....--LL
1 2 3 4 5 6 7 B 9 10
20
2 0
61
s» s
4»
3 ' CuomNM-Io/Si 108 Cuoaottnuo/St
2 . 7nm/2nm : 7nm/lam
2 102- 3 "
3 1 3 ..
5 .1 .f.‘
‘3’. 51
3 4_ 3 102:
s- I
s
2- "
s
z x I A I A g. I Ag A I A I A I I I
I0] 1 1 . 1 . 1 g14g1 1 1 1 1 1 2 3 4 5 6 7 a 9 lo
1 2 3 4 6 8 9 10 20
2 0
2.
Cu0.sollno.1o/Si
7nm/0.5nm
,2 102»
n _
r: a
.‘5’ 7
:5 ..
3‘ 5
--1
‘>
31
2 . . ‘
l 2 3 4 6 8 9 10
29

Figure 4.14 Small angle x-ray scans showing the degradation of CuMn/Si layering.

87

 

 

 

 

a)
103 e
s : Cu0.90Mn0.10/Si
4 r 7nm/1nm
3 .-
3 .1
"'m‘ I
5 102 :
ct) .—
5 C
V 5 _
8" 4 *
r—1 3 .
2 e
101 :
5 L- I_ I l n. I L I I I I L I L J
38 39 4O 41 42 43 44 45 46 47
29
b)
2 r .
104 *: Cu0.90Mn0.10/Si
E 7nm/0.5mm
3 2 f
g 103 :
Q) .
*’ C
:8 2 5
3° 102 1,—
-l :
2 .C
101 _-
2 l- L 1 I I I 1 I 1 I I I I 1 I 1 I I I I I 1
38 39 4O 41 42 43 44 45 46 47 48
26

Figure 4.15 Large angle x-ray scans of CuMn/Si showing transition from a) one
amorphous layer, to b) two crystalline layers.

88

4.4.2 Cross Sectional Analysis

In an effort to compare the structural quality of the three 86/ Si systems,
transmission electron microscopy (TEM) and electron difl‘raction were performed on cross
sectional slices from three samples, CUQ88MDOJz/Si, AgaglMflODg/SI and
Auo_97Fe0.o3/Si, all 3 nm/7 nm. The samples were sliced with a 55° diamond knife, to
an electron beam transparent thickness of ~ 70 nm. The TEM was performed at 200 and
120 keV with a beam current of 10 uA. All cross sectional preparation and imaging were
done by DA. Howell at the Dept. of Material Science and Mechanics at Michigan State
University. For more details on this work, see reference 134.

The dark regions of the bright field images in Figure 4.16 correspond to the SGs,
and the lighter layers the amorphous Si. The image cannot be used to determine actual
layer thicknesses in the sample, because their relative ratio in the image is dependent on
the thickness of the cross section when amorphous Si is present.135 We can only state
fi'om these images that the SG/Si samples are well layered.

Electron diffraction operates under the same principles as x-ray diffraction. The
orientation of the instrument with respect to the samples is, however, difl‘erent. Whereas
the x-ray difi‘ractometer could only respond to periodicities perpendicular to the layer,
transmission electron diffraction can only respond to in-plane periodicities. As with x-ray
diffraction, the width of the rings indicate length of coherence. Sharp rings in the pattern
denote large crystallites, the rings becoming broader as the crystallites get smaller. Bright
spots in the pattern result from in-plane orientation of crystallites. The electron
diffraction patterns in Figure 4.17 .for the three samples reveal some differences between

them. The AgMn layer shows the most crystallinity with a narrow ring and the addition of

89

bright difl‘raction spots, while the AuF e layer gives only a difl‘use ring, indicating the least

crystallinity CuMn lies somewhere between these two.

b)

 

 

Figure 4.16 TEM images of cross sections of 3 nm/7 nm of a) Ag0.9an0_09/Si, b)
CuoggMnoln/Si and c) Au0.97Fe0_03/Si.

a)

b)

C)

 

Figure 4.17 Electron diffraction patterns from the samples shown in Figure 4.16.

CHAPTER 5

EXPERIMENTAL PROCEDURES

5.1 Magnetic Measurements

Magnetic measurements were made on one of two commercial SQUID based
magnetometers made by Quantum Design Inc. Two types of measurements were possible;
static, where a static field is applied and the sample is pulled through three counter-wound
pickup coils (see Figure 5.1), and ac, where the measuring field is a small (< SG )
oscillating sine wave, with or without a supplementary static field. The ac. measurements
require the sample to be stationary and located inside and in-plane with one of the pickup
coils. The response of the sample is also a sine wave, but in general lags the input. The
response signal may be separated into in-phase and out-of-phase components, referred to
as real and imaginary susceptibilities. A non-zero imaginary component indicates energy
losses in the sample. The imaginary part of the susceptibility can give valuable information
about the SG freezing process, since the frequency dependence of the SG transition
implies an intrinsic loss in the material“. The behavior of the real part is similar to that
seen in the static measurement, but where the static measurement is done on a time scale
of ~ few minutes per point, the measuring time in the ac. susceptibility is much shorter
(see Section 1.3). All a.c. susceptibilities in this project were taken at a measuring
frequency of 16 Hz, or 0.065 measuring time. This study focuses on the static

magnetization and the real part of the ac. susceptibility.

92

93

The majority of measurements were made on the older of the two SQUIDs, which
had only static field capabilities. This machine had a temperature range of 1.8 K to 350
(7) K, and a sensitivity of ~ 10‘8 emu (cgs units). 200 - 500 nm of total SG ( 50 to 300
layers, depending on the SG layer thickness) was needed to deliver a signal in the 10" emu
range for a good signal to noise ratio. The residual field in the magnet after a magnet
quenching procedure was typically 5-7 G. The quenching was accomplished by setting the
magnet to the largest available field, 50,000 G, and oscillating towards zero using typically
about 10 fields; e.g. 50,000, -30,000, 10,000, -5000, etc.

The newer machine had both static and ac. capabilities, with the same sensitivity
and temperature range. It also possessed a low field option, which allowed reduction of
the residual field to < 0.1 G after quenching. Most static measurements were taken with a
measuring field of 100 G, and the difl‘erence in the residual field between the two machines

did not afl‘ect the measured value of the transition temperature.

 

 

a) b)
. T
ac R) A
I g g 4 cm distance

ac V V V

SQUID response

 

 

 

 

 

 

/\
V

 

sampl I 4 cm

stra

 

Figure 5.1 a) SQUID pickup coil and sample configuration, and b) resulting signal

 

94

The sample was mounted in a soda straw secured to the brass nonmagnetic 12" tip of a
long hollow stainless steel rod. The 0.5 x 0.5 " substrate had to be broken in halfto fit
into the straw, and was held in place in the vertical plane by either a small amount of
plastic or cotton thread sewn through the straw, both materials having negligible signal in
the amounts used. To enter the measuring chamber, an evacuated narrow dewar
containing the pickup coils, thermocouple, and temperature controlling heating elements,
the sample must first pass through an air lock which is flushed with ‘He boil off and
evacuated. Once the sample is lowered to its proper position, the top of the measuring
rod is attached to a stepping motor so the sample may be moved up and down for
measurement. The vacuum integrity is assured by two knife edge seals in the airlock plug
(see Figure 5.2). Ifthese seals are damaged, oxygen (and other gasses) will leak into the
measuring chamber. Oxygen is a particular problem for the weakly magnetic SG system,
as liquid oxygen has a strong susceptibility of 7699 emu/gram below its boiling point of
90.1 K and a peak of 10,200 emu/gram at its melting temperature of 54.3 K.m A leak in
the system could allow oxygen to enter as a gas at the top of the tube, and condense or
fieeze on the sample. For this reason particular care was taken to slide the measuring rod
slowly through the seal, allowing the rod to warm to room temperature so it does not cool

the o-rings and make them brittle.

 

95

sample rod

 

knife edge o-rings

  

 

..............

 

 

 

 

 

 

 

M

Figure 5.2 Sample rod seal to the magnetometer

 

5.2 Determination of Tf

Magnetization vs. temperature curves were taken for all multilayered samples.
The value for Tf is extracted from the zero field cooled (ZFC) curve, where the sample is
cooled fi'om a temperature T 2 2Tf to a temperature T << Tf , where a small measuring
field, typically 100G, is then applied. As the temperature is increased, a peak in the
magnetization appears, the temperature of which is defined as Tf. Rounding of the ZFC
peak limits the determination of Tf to i 0.5K in most cases. The sample displays difl‘erent
behavior when field cooled (FC) from above Tf to below Tf. Below Tf, the FC
magnetization is significantly stronger than the ZF C signal, and joins the ZF C data at T 2
Tf. This joining usually occurs near to the ZFC peak (within the i 0.5K error), but in
some cases, at temperatures much higher. Since the latter behavior tends to diminish as
the sample ages, or is removed from the substrate, strains created during the grth may

be the cause. Aging or substrate removal does not alter the ZFC curve peak location to

 

96

within experimental uncertainties, and for this reason the ZF C curve peak was used for Tf
determination rather that the onset of irreversibility between the FC and ZF C curves. .

Ideally the smallest measuring field (Hm) possible should be used in the low field
static magnetization measurements. Figure 5.3 shows FC and ZF C static magnetization
curves for multilayers with our thinnest value of WSG using Hm = 100 and 10 G. Even in
this most challenging case, the difl‘erence in Tf between Hm = 10 and 100 G was small,
within our 1 0.5 K error. Therefore Hm = 100 G was chosen because it gave better signal
to noise ratio. Notice also that the value of Tf in these data is not strongly dependent on
whether one defines Tf to be the ZF C peak or the onset of separation between FC and
ZFC data.

In Chapter 1, the long relaxations present in the SG state were shown to cause
weak measuring time dependence in the location of the peak in a bulk sputtered
CUO'86MnOJ4 film, and stronger measuring time dependence in a thin, 2D
Cu0.86Mn0.14/Cu sample with “’86 = 3 nm (see Section 1.63.1). Figure 5.4 shows a
typical M vs. T curve taken at ~ 3 minutes per data point and the corresponding peak in
the ac susceptibility at 16 Hz for a multilayer with thin “’86 = 2 nm Cuo_89Mn0.“ layers.
The fast measurement gives only slightly higher Tf than found in the ZF C measurement.
All Tf values used in this thesis are obtained from the ZFC peak, and are listed in
Appendix A. i

2.4 r

2.3 ~

2.2 L

M (3:104 emu)

2.1 >

 

2.0 .

i

 

-0-ZFC
+FC

 

 

 

1111:3106

Ito—4

 

1.34 r
1.32 ~
1.30 >
1.28 >
1.26 >
1.24 r
1.22 r
1.20 r
1.18 .

M (1:10"5 emu)

1.16

1.14 -
1.12 '
1.10 -

L

 

 

 

 

 

Temp(1()
+ ZFC
i —0— PC
‘r I ,
!
I i
I
Hn=1000
:

4+ 1 1

3.4 3.6 3.8 4.0

l _L l

2.0 2.2 2.4 2.8 2.8 3.0 3.2
Temp(l()

97

b)

)4 (x104 emu)

2.0 2.2 2.4 2.8 2.8 3.0 3.2 3.4 3.8 3.8 4.0 4.2

M (110'5 emu)

 

 

 

 

 

 

 

 

 

 

 

 

3.2 r -0— ZFC
I a I —0— re
3.1 *
' I
3.0» I
I
2.9 ~
2.8 > I i
HI=IOG
2.7 >
2.8 r I
2.5 l _ l l A l .A A l A 1 l l l l l
2.0 2.2 2.4 2.8 2.8 3.0 3.2 3.4 3.8 3.8 4.0 4.2
Temp“)
2.10
. + ZFC
e + 7C
2.05- 4 o
I l 1
i
2.00
I
I
1.05 *
mo» “‘00“
1.85 > I
I
1'80 1A1 IALALAA 1-1 1 r 141
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2
Temp“)

Figure 5.3 Comparison between Hm = 100G and Hm =10 G for a) Cu0_39MnO.ll/Cu
0.21 urn/30 nm and b) CUO.89MDO.11/Ag 0.21 nm/30 nm.

IE-S-
1E-5r
lE—5-

1E-5~

M(emu)

 

b)
6E—7—

I

5E-7

x(emu)

4E-7—

3E-7r

 

98

 

O ZFC

 

 

 

0008

o 8

O.

10 20 30 I 40 A 50
Temp(K)

 

1 L A 1 l l L J

 

2E-7

10 20 3O 4O 50
Temp(1()

Figure 5.4 a) Static magnetization and b) ac susceptibility for Cu0.89Mn0.11/Cu

2nm/30nm.

99

5.3 be - CuMn, AgMn, and AuFe

3111K Tfs, Trbs, for Cu0.901‘41‘o.1o, C“o.s9Mno.11. 811d CuessMnarz were taken
fiom the Tf of the target shavings, since there was general agreement between the Tf of

shavings and the Tf fiom thick sputtered films ( 2 500 nm). An error of :th was
assigned to be to reflect the statistical variation in the values of the Tfs for bulk films.

Target shavings of the other SGs proved unsuitable as bes. The transition
temperature for thick films (2 500 nm) of Ag0.92Mn0.03 was found by Stubi et. al.81 to be
~ 40% lower than that found in the shavings. Reasons for this difl‘erence are discussed in
Chapter 4. As a result, be for the A80.91M“0.09 in this study was averaged fi'om the
thick films. The uncertainty on this average is i 1.5K a value reflecting a statistical
variation in the Tfs of AgMn films that is somewhat larger than that found in CuMn. The
result is a larger overall error in Tf/be for these samples.

As with the AgMn, Au0.97Fe0_03 sputtered a considerably lower concentration
than what was found in the target (see Chapter 4), and so also required the use of an
averaged be taken from the thick films in the appropriate mm. The average concentration
for an AuF e film was ~ 3 at.% Fe, as measured by EDX and Tf values taken from
literature. 59 The experimental uncertainty in T? was i 1.5 K, reflecting the spread in Tfs
occurring for the thick films during the run.

The CuMnOAAuom samples were made much later than the CuMn samples. be
was averaged from the thick films to achieve consistency in method of W determination

between different materials.

100

Table 5.1 be values for CuMn, AgMn, and AuF e

 

 

 

SG W (K) Source
CummMan 47.0 i 1 Target shavingi

 

, Cg“ “Mun 12 58.511 Target shavings
m8 24.8115 Film average

A110 97Fe0 m 17.0i0.6 run 1 Film average

 

 

 

AUG 97Fe0 0'; 16.1i0.6 run 2 F111“ average

 

 

 

 

 

CuMno AAuo or 25.3 i 1 Film average

 

5.4 T3) - NiMn

Our first attempt to sputter NiMn films involved a composite sputtering target
made by setting flat Mn chips on top of an ordinary Ni target. Not only was it dificult to
estimate the number of Mn chips needed to produce the desired film concentration, the
sputtered concentration fluctuated widely and decreased with time as the Ni deposited
onto the Mn chips, choking ofl‘ the Mn supply. Alloy targets were then melted as
described in Chapter 3. Target shavings could not be compared to the thick films, because
the transition temperatures are highly sensitive to sample preparation.

The first thick films grown from the alloy targets using usual substrate temperature
(Tsub) control of -30 > Tsub > 10°C produced samples with unacceptable variance in

magnetic behavior. Some films showed a single peak in the susceptibility, and static scans

101

that changed very little when changing the measuring field from 10 to 100 G. Other films

showed behavior seen in Figure 6.13.

8E-7

7E-7

6E-7

X'(emu)

4E-7

3E-7

2E-7
lE-7

0E0

b)

9E—6
8E—6
7E-6
6E-6
5E-6
4E-6

Mkmu)

3E-6
2E-6
1E-6

CEO
0

5E—7

f

I

I

r

I

 

rrfiefi

I

V T f T f T V

 

102

Efiiiiifimiii
Him}

430-14
50 100 150 200 250 300
T(K)

n... o Hm=lOOG
‘. Cl Hm=lOG

.0
. ..:::3.
933..

Begeamae
9389
Q
y'ageee 996.5999Ieeegg

BB
393 430-14

1 I 1 I 1 . M I

50 100 150 200 250 300
T(K)

Figure 6.13 An early NiMn bulk film with unusual magnetic behavior a) double peaked x
vs. T scan with no biasing field (Hb) and b) strong dependence of Tf on measuring field

Hm.

103
500 -
a) 43.62 a=o.3594 nm

400 r

300 r

.4

FWHM = 0.303 33nm

Intesitv

200 -

100 -

 

4O 41 42 43 44 45 46 47
26
b)
900 l 43.76
800 L
700 _ Tsub = +2 C
600 *-

500 r
400 ~-

Intesity

 

300 ~

200 ~
44.50

100 L

 

1 1 1 4 I 1 I 4 1 1 1 . J 1 I

4 0 4 l 4 2 4 3 4 4 4 5 4 6 4 7
2 9
Figure 6.14 X—ray diffraction scans of NiMn 86 sample with a) single peak from sample

grown under good temperature control b) additional peak suspected to be caused by
warmer growth conditions.

104

Many of these samples also displayed a second x-ray difli'action peak at 445° 29,
where only one <111> peak is expected (see Figure 6.14). This second x-ray peak does
not match up with any NiMn crystallographic orientations, but is consistent with a pure Ni
<1 11> peak.

Keeping Tsub under more stringent control of (-20 :1: 5) °C, at times halting the
run to let the sputtering system cool, provided more consistency in film behavior. Some
natural drifi in the concentration still occurred, particularly between runs, resulting in
different average concentrations and be values for each of the two runs. (Both runs were
from the same target.) The first sample fi'om each of two runs were bulk films that gave
concentration readings significantly difi‘erent from the other bulk films in the run (made

every other or third sample), and so the first two samples in each run were not used.

Table 5.2 be values for NiMn

 

 

 

 

 

 

 

SG be (K) Source
Ni“ 71Mn019 71 :t 3 Film averages
N10 figMno 3 1 86.4 i2 Film averages

 

Averaging the thick film values for the two runs gave be = 71i3 and 86.4i2 K.
Actual be values from thick films in these runs are listed in Appendix Al Table Al.9. All
well-cooled samples produced only one x-ray diffraction peak, that shown in Figure 6.14a.
Samples left at room temperature for several weeks, and samples exposed to the electron
beam used for the EDX composition analysis, often displayed magnetic behavior which
resembled Figure 6.13, and developed the second x-ray diffraction peak like that seen in

Figure 6.14b. Whether the x-ray peak is from growth of pure Ni or that of a NiMn

105

compound, it indicates a change in the sample that is likely similar to that which occurred
in the early samples during sputtering. For this reason, and warnings given in literature
about potential grth of ferromagnetic Ni3Mn in samples held at room temperature,60
the samples were kept in liquid nitrogen until measurement.

Both static magnetization and ac susceptibility scans were taken of the SG samples
to verify SG (as opposed to reentrant) behavior. Figure 6.15 shows a SG sample. The
purpose of the biasing field, Hb is explained in the next chapter.

5.5 Errors in Relevant Values

As stated above, the error in determining Tf is i 0.5K. In some cases, at low
temperatures where the peak is better defined or the data are taken closer together, the
error may be as low as i 0.3 K. Tf values and their errors are tabulated in Appendix A.
The experimental uncertainty in the quantity Tfltb is generated by this error on Tf and
the error on the appropriate n”, as stipulated above. These uncertainties may also be
found in Appendix A.

Errors in WSG and WIL are i 5%, as discussed in Chapter 4.

106

2E-5 -

215-5 ~ 04%

2E-5 - O O O O 06) (8%

153-5 -

2 - O Hm = 10G

lE-5 -

lE—5- ©

lE-5 - 9

9E—6 ~ 0

7E—6 -

O

3E-6- O 0 o

lE-6 1 r . l . l 1 r . 1 1 r 1 r

0 20 40 60 80 100 120 140
Temp (K)

M (emu)

 

 

b)

lE—S -
’ ° 0 Hb = 0G
1153-5 f O Hb = 400G

9E-6
A 8E-6 - e
D 1
E 7E-6-
m .
\ V 6E-6 j— .
\ ' e
r“ 5E—65 .
4E—6- ' '
' 00000 e

3E—6+ :é§> O .0 0

2E-6 } , ' O . 0 .

113—6L .nagufiggggp

0E0 I 1 1 1. 1 1 l 1 I 1 I 1 I 1 J

0 20 40 60 80 100 120 140
Temp (K)

 

 

Figure. 6.15 b) Static magnetization and b) a.c. susceptibility SG film with and without
the biasing field (Hb) of a 300 nm Ni0.74Mn0.26.

CHAPTER 6

DATA

6.1 Finite Size Effects - CuMn

As described in Chapter 1, previous studies of the long range metallic SG CuMn
showed significant decreases in Tf with decreasing “'86 down to “’56 = 2 nm. In Section
1.5 it was argued that samples with thinner “'56 were needed to determine the value of Tf
for “'86 = 1 ML, and to distinguish between the Fisher-Huse Droplet model and general

scaling analysis. The following describes the results of such a study.

6.1.1 Host Interlayers

To determine unambiguously whether Tf= OK at WSG = l IVE, CUO.89MI'IO_ 11 and
Cu0_38Mn0.121multilayers were made down to this thickness, (W 86 ~ 0.21 nm). The SG
layers were separated by Cu, Ag, or Au interlayers of 30 nm, a thickness previously shown
sufficient to magnetically decouple CuMn SG layersml’loo These ILs were chosen to
perturb the SG layer the least; Cu, Ag, and Au all have the same electronic structure as
the Cu in the CuMn, the same FCC structure, and Cu has nearly the same lattice
parameter as the CuMn.

The presence of SG characteristics in these thinnest WSG samples is confirmed in

Figure 5.3. Notice that the value of TfIS not 0 K. A test sample made of WSG = 0.21 nm
107

108

and WIL = 60 nm showed no change in the value of Tf fi'orn the WIL = 30 nm case,
confirming that for the quasi- static Tf measurement these samples are magnetically
decoupled by a 30 nm IL.

We showed in Section 1.5 that Tf data from similar samples of Cu 1.anx/Cu with
WSG > 2 nm collapsed nearly upon one another for X = 0.04 to X = 0.14 when
normalized by the appropriate bulk spin freezing temperature, be (see Figure 1.7 ). This
suggests that C%.89WO_11 (be ~ 47 K) and the Cu0_33Mn0.12 (be ~ 58.5 K) data should
be similarly compared to each other and to the older Cu0.36Mno.14 data after
normalization. The uncertainties in the plotted values are discussed in Chapter 5, and are
approximately thesize of the symbols depicted in the following figures. '

From chapter 2, the data will be fit to the general scaling law

 

T W -T” ’“V
f( ) f ~[_14_7] , Equation 2.4

b
Tf W

C

where v is the correlation length exponent, and to the Droplet Model form for thin “'56

-T—f-~W“.
T

C

Equation 2.6

Here a < 2 from the droplet theory, and is estimated through a literature average fiom
experiment and calculation to be 0.3 s a s 0.65, the uncertainties of which are discussed in
Section 2.2.

Figure 6.1 shows the normalized Tf data for CuMn/host multilayers. The
normalized data for Cu0.89Mn0.11 and CuofigMnon do indeed collapse onto a single
curve, and the new data are in good agreement in the overlap region with the previous

data. The data indicate that Tfis still finite at WSG = 1 ML.

109

The solid curve in figure 6.1 represents the scaling equation 2.2, with the values of
v = 1.6 and Wc = 1 nm that allow fitting over the widest possible range. It is now clear
that the generalized scaling law is incapable of fitting data for WSG below ~ 1nm, where
the inflection point occurs.

Figure 6.2 shows the data of Figure 6.1 replotted on a log-log scale for
comparison to Equation 2.3. Straight line behavior, indicative of a power law, is observed
for 0.21 s “'86 s 2 nm. From Chapter 2, Equation 2.4 should be valid for l) Tf << be
and 2) WSG > average impurity spacing. Condition 1) is met through the significant Tf
depression occurring by 2 nm. Condition 2) should limit consideration to WSG > lML,
so the theory may not be directly applicable to the thinnest WSG data. Since the values for
WSG = 0.21 nm are in line with the data for thicker WSG, they were included in the
calculation of the exponent a.

Using a linear regression fit on the log(ng) and log(Tf/be) data for 0.21 nm <
“'56 < 2 nm, the solid line in Figure 5.5 was produced, corresponding to a = 0.8 :t 0.1.
This value is outside the estimate from the literature parameters, but still well below the
rigorous bound of 2.

Since determining when each monolayer is complete is not possible for a sputtering
technique, the thinnest layers and boundaries between layers will not be perfectly planar.
We must thus justify plotting the data as though the layers were "perfect". Figure 6.3a
shows a schematic of the cross section for a SG/host system. When the IL is made of host
material (a material in which the Mn impurity behaves the same as in the SG) a blending
of the SG and IL creates a wider, more dilute SG layer. While this dilution reduces Tf (Tf
~ c0-7 where c is the concentration in the range 0-13 at.% Mn in Cu“), widening the SG
layer increases Tf, (Tf ~ WSGO-S). Since the powers are so similar, these two effects
should approximately cancel each other, yielding a measured value close to that of a true

unmixed layer.

llO

    

 

 

1.1 "
'_ x
10. - V31.6 Wc=lnm
0.9 r
0.8 *-
0.7 r
1: 1 Cur-anx/IL
1': 0'61 x=o.10.o.11.0.12
} 0.5 1 0 1L=Cu(30 nm)
E— 04; UlL=Ag(30nm)
' » V IL=Au(30nm)
0.3 r
0.2 - (B X Cuo.36Mno.14/Cu
0 1 L 60 From Kenning
' 1 U
0.0 —1 1 1 .1 11111111 L111LLL 44111111 111111 11 1111111141111 14L1111 1
10-1 2 3 100 2 3 101 2 3 102 2 3 103

Wsc (nm)

Figure 6.1 CuMn/host multilayers showing scaling law behavior for thick SG layers

 

 

 

100; X X X
7 _ XE
6- 3*
5: X
4E
1 Cur—anx/IL
Q 3; x=o.1o,o.11,o.12
g7 2L 0 lL=Cu(30nm)
E 1 D 1L=Ag(30 nm)
E" . V 1L=Au(30nm)
10“;
7: X Cu0.36Mno.14/Cu
6 ~ From Kenning
5:
4f—
3 11 +141 1 11111114 14111 111111 111 1111 111111 1 1111 1111111 1
10—1 2 3 100 2 3 101 2 3 102 2 3 103

log WSG (nm)

Figure 6.2 Droplet model power law behavior of thin CuMn layers with "host" interlayers.

111

6.1.2 Non-host Interlayers

As mentioned in the previous section, some mixing between layers must inevitably
occur during the sputtering process. We can estimate the degree of mixing by comparing
data for host and non-host ILs.

In the case of the non-host IL, two effects are present. Both effects reduce Tf.
First, mixing at the boundary removes impurities from the SG layer if the IL doesn‘t
support a SG state, resulting in an effectively thinner SG layer (see Figure 6.3b). Second,
the non-host IL may not support the RKKY interaction as well as the host IL, (as is

clearly the case with an insulator), causing some loss of interactions between impurities at

 

 

 

the edge of the SG layer.
a) wso
x X "lost" impurity

7(““"
X

 

 

 

 

 

)9
m
C)
[

KIL

 

{
1

T . good
WSG envrronment

 

Figure 6.3 Comparison of mixing cases for a) host and b) non-host ILs, where WSG =
nominal layer thickness, WSCL' = efi‘ective layer thickness.

 

 

112

The two studies of CuMn multilayers previously done with non-host ILs (reviewed
in Section 1.5) both used insulating ILs (Si and A1203), and produced faster decreases in
Tf than that observed for the CuMn/host samples (see Figure 1.8). To see if this behavior
is mimicked by non-insulating materials, samples were made using several metallic non-
host interlayers of WI]. = 30 nm. Figure 6.4 shows the normalized Tf data plotted next to
a solid curve representing the CuMn/host data of Figure 6.2. The downward pointing
arrows indicate samples for which Tf 5 2K the lower limit on the magnetometer. The
metal IL data fall faster than the host IL curve, but not as quickly as the insulator IL data
previously found. If the CuMn/host data are representative of a nominal thickness SG
layer, subtracting a constant thickness of 0.5 to 1.0 nm from each series accounts for the
observed reduction in Tf, even if no Tf reduction is attributed to some loss of RKKY
interaction through the flanking non-host interlayers. Figure 6.5 illustrates this idea by

replotting the data with the estimated effective thickness, WSG'.

Table 6.] Estimated values of CuMn mixing with non-host metal ILs.

 

 

 

 

 

 

IL WSG - Wsfi' ML mixing
Al 1 nm ~ 5

V 0.75 nm ~ 4
M0 0.5 nm ~ 3

 

 

 

 

Taking these derived reductions in “'56 as a guide, we conclude that mixing at interfaces
must be limited to ~ 2 layers on each side, with the largest mixing (~5 ML total) in the

CuMn/Al system.

113

     
 

 

 

100:
C
6 .—
5 r-
4 r
3?
.6 2L
5: [ . Cu1-anx/IL
} X=O.10, 0.11.0.12
E- O
lO-1~
1:1 IL=AI,W1L=30 nm
6: e <>1L=Mo W11=3o nm
5_ .IL=V Wsc=30nm
4 .-
3 E $ $1 -' IL = Cu,Ag,Au
2 1 1_11E.JLM11111 1111111114L11 1 1111111
10-12345 100 2345 101 2345

log WSG (nm)

Figure 6.4 Tf reduction due to "non-host" interlayers. The solid line represents data for
the CuMn/host IL from Figure 6.2. '

     
 

 

 

root
6:
5 P
4r
3?
.o 2 1
1: : Cur-anx/IL
} , x=o.1o,0.11,o.12
[—
10’1:
- D IL=A1 WSG’=Wsc-l.0 nm
6 : 0 IL: Mo wSc’=Wsc-o.5 nm
5 — . 1L=V WSG’=Wsc-O.75 nm
4:
3,; ¥ — IL=Cu,Ag.Au WSG’=WSG
1
24111111111111111'111 1 111111111111 1111.111
10-1 2 34 100 2 345 101 2 345

log WSG’ (nm)

Figure 6.5 Replotted data for metallic H.s using effective SG layer thickness (WSG').

114

6.2 Coupling -CuMn

In the original studies on CuMn multilayers reviewed in Section 1.5, an unusually
long coupling length of CuMn through Cu and Ag 11.5 was observed, while a shorter
coupling length was found through the insulating IL Si. It is of interest to know whether
other metal ILs exhibit similar long range coupling as do Cu and Ag. To observe the
degree of coupling through a given interlayer, “'86 must be fixed, while wIL is changed
fiom 30 —) 0 nm. A SG thickness must be chosen that is thin enough to show significant
Tf depression, so that the depressed Tf value can be seen to return to its bulk value as WIL
—> 0. The chosen “’56 must also be thick enough that the mixed regions at the
boundaries represent a small portion of the layer. Both conditions are met with “'56 = 4

nm, where Tp’be ~ 0.5 for all metal ILs (see Figure 6.4 ).

6.2.1 Host Interlayers

Measurements on CuMn coupling through Cu and Ag ILs taken by Stubi et.
al.,“mv101 showed coupling out to 2 20 nm in both cases. Since Cu and Ag have FCC
lattice parameters that differ by 13%, this behavior suggests that lattice mismatch at the
boundaries is not an important factor in coupling. The first metal chosen to be tested
against the Cu and Ag IL results was the host metal Au, which behaved similarly to the Cu
and Ag 11.5 in the finite size effect study. Au is a strong spin-orbit coupler, a trait ofien
associated with the ability to provide extra Dyzaloshinki-Moriya anisotropy interaction in
CuMn (see Section 1.3.3). Second, CuGe was selected as a small variation on the Cu IL,
to test the effect of simply reducing the mean free path. Adding 2 and 10 at. % Ge
reduced the mean free path in Cu by a factors of about 10 and 60, respectively‘”, while

causing little disturbance in the electronic or crystallographic structure.

115

 

 

 

0.9 P
Q U Cuo.9oMno.1o/Au
O Cuo.9oMno.10/Cuo.9aGeo.02
_ O Cuo.90Mno.1o/Cuo.9oGeo.ro
0.3 o
A
A CuMno.aeMno.14/Cu
E,“ V CuMno.aeMno.14/Ag
.o 0-7 ' 8 A From Stubi et. al.
[2: m
\ L
r: o 0'3 m
0.6 " U
o ' ‘ A
1
o O ' :1
0.5 _ O 6
T
0.4 1 1 I 1 I 1 1 1 1 1 1 1 I
O 5 IO 15 20 25 30
W1L(nm)

Figure 6.6 CuMn coupling through host interlayers and CuGe ILs.

116

Figure 6.6 shows the coupling of CuMn through Cu, Ag, Au, and CuGe ILs with
WSG = 4 nm. The Au IL data show the same long coupling as Cu and Ag, the effects of
which may be seen out to WIL~20-30 nm, with a more noticeable rise in Tf for Wm < 10
nm. Adding the Ge to the Cu has little efl‘ect on the coupling behavior. Coupling is still
observed out to Wu. ~ 20-30 nm, the onset of faster Tf rising occurring perhaps at a
slightly lower value for the Cu0_9oGeo_lo series than the CuoggGeom series. These
behaviors suggest that neither spin-orbit scattering in the IL nor mean fiee path efl‘ects

play a significant role in the coupling length.

6.2.2 Non-host Interlayers

The non-host IL materials were chosen to have properties which distinguish them
from host materials and fi'om each other. Al has the same FCC crystal structure as the
noble metals, and nearly the same lattice parameter as Ag and Au. It is a nearly fiee
electron, s-band metal, and a weak spin-orbit coupler, but has a different electronic
structure from Cu, Ag, and Au. Nb, Mo, and V are all BCC transition metals with
predominantly d-band electronic states at the Fermi surface. Si is an amorphous insulator.
To make a comparison between metal IL samples and Si IL samples, a series of the latter
was made using a fixed WSG = 7 nm with variable a-Si IL thicknesses. Such samples
correspond to Tp’Ttb ~ 0.5 when decoupled (see Figure 6.10).

Figure 6.7 compares the coupling behavior through five non-host materials with
that for Cu, Ag, and Au. Al, while having many similarities to the hosts, does not allow
the long range coupling of the noble metals. Neither do the transition metals nor Si. All

these materials show significant coupling only when WIL g 2-3 nm.

117

  
     
 

 

 

1.0 ~ CuMnr-anx/IL
, x=o.11, 0.12
0.9 ~ 0 IL=Si
D IL=A1
El 0 lL=Mo
0.3 1 .0 A 1L=Nb
O 1L=V
g: 0 7 _ — Cu1-anx/host
} - x=o.1o,o.14
r— 1 0
° 1
0.6 ~ 6 .9
D
1g 0 11 D ’ ’
0.5 r A A a
O O O .
0.4 1 1 1 1 I 1 I 1 1 1 I 1 I 1 1
0 2 4 6 8 10 12 14

Figure 6.7 CuMn coupling through non-host interlayers

118

The Al and Si series do exhibit a feature different fi'om the other materials, a sharp
rise below WIL ~ 3. For Si ILs, this behavior can be expected fiom the structure analysis
of these samples in Section 4.4, where it is argued that a breakdown in layering occurs
between WIL = 3 nm and WIL = 2 nm. This layering deficiency is likely to cause breaches
in the Si layer where a CuMn layer can be in physical contact with the neighboring layer,
causing the rapid increase in Tf.

The CuMn/Al x-ray difl‘raction structural analysis did not reveal a breakdown of
layering associated with the rapid Tf increase. The finite size effect data fi'om section
6.1.2 do suggest, however, that ~ 0.5 nm of mixing occurs at each CuMn/Al interface,
leaving only a couple of ML of pure Al at Wm = 1.5 nm, which may contain pinholes
through which the CuMn can couple strongly.

6.3 Other SGs

6.3.1 AgMn

A second SG was studied to determine whether the finite size effect behavior
described in the preceding section is unique to CuMn. AgMn was chosen as the SG most
like CuMn, as they are both long-range RKKY Heisenberg metallic SGs, both using noble
metal hosts and the same impurity (Mn). As described in Chapter 1, Stubi et. al.81 made
AgMn/Cu and AgMn/Ag multilayers with 1 nm 5 WSG s = 500 nm to compare with the
CuMn/Cu data of Kenning et. al..79 They found little difi‘erence between the finite size
behavior of the two SGs. As for CuMn, no difference was observed between multilayers
using Cu and those using Ag as the interlayer. To test whether the similarity of AgMn to
CuMn holds when WSG < 1 nm, AgagzMnQog multilayers with WSG as thin as possible

were made to compare to the data in Section 6.1.1. The lower limit was WSG = 2 ML,

119

since the lower be (24.8 K) for these samples caused the Tf of WSG = 1 ML samples to
be below the susceptometesz low temperature limit of 2K.

Figure 6.8 shows the new data for the AgMn/host IL samples, extending the
previous data from Stubi et. al. down to WSG = 0.5 nm. The values for Tf’be of the
AgMn system are slightly lower than those for the CuMn system, but the difi‘erences are

within the total experimental uncertainties.

120

     
 

 

 

100 f
7 i
6 .—
5 r
4 C-
1: 3 7 A Ago.92Mno.03/Cu
g: V Ago.92Mno.oa/Ag
\ 2
E" X Ago.91Mno.09/Cu
From Stubi
-1
10 — Cu1—anx/Cu,Ag
7. ‘1‘ x=o.11,o.12,o.14
6 1-
5 r
1
4 1 1 1 1 1 1 1 1 1 g 1 1_.1 1 1 1 1 1 L 1 I 1 1 L 1 1 1 1 J
3456100 2 3456101 2 345

log Wsc; (nm)

Figure 6.8 Size efl‘ect data for AgMn.
The solid line represents the averaged CuMn/host IL data fiom section 5.2.1 and Figure
6.2 with the concentrations indicated.

121

6.3.2 High Anisotropy SGs, CuMnAu and AuFe

As described in Section 1.4 , Monte Carlo simulations suggest that the lower
critical dimension, d], is affected by the amount of anisotropy present in the sample.
Adding anisotropic interactions in these simulations can allow d, to be lowered from above
to below 3, and lowering d, may well afi‘ect the rate of Tf depression as wSG decreases.
CuMn is believed to be a low anisotropy $6. The anisotropy field (HA), (see Section
1.3.3) is found to be about 300 G as measured by transverse susceptibility and NMR
measurements”. Two SGs with higher anisotropy were tested against CuMn. First,
CuMnAux where X < 0.03, which shows a sharp increase of anisotropy with increasing X.
Prejean et. al.”.41 reported that CuMnAuX with X=0.0015 showed an increase of a factor
of 6 in Honer pure CuMn. Second, Au1_XFeX where X < 0.012, which is widly
believed to be an intrisically high anisotropy SG, with H A ~ SOkG, about 100 times the
strength of that found for CuMn.58 Otherwise CuMn, CuMnAu, and AuFe are similar; all
are long range RKKY type SGs based on noble metal hosts.

The higher anisotropy in CuMnAu comes fi'om the Dyzaloshinski-Moriya
interactions, those caused by the interaction with a third impurity. These interactions are
believed to be particularly prominent when the third impurity is a strong spin-orbit coupler
like Au (see Section 1.3.3). The CuMn0_04Au0_01 samples contain an amount of gold that
should produce an anisotropy field ~ 35 times larger than CuMn alone”.41

The strong anisotropy in AuFe arises from two effects: a) the dipolar interaction,
the interaction between two impurities, is much stronger in AuFe than in CuMn. The
stronger interaction in AuFe arises from an orbital contribution to the Fe moment in Au
(due to spin—orbit coupling), whereas Mn is a good S-state ion in Cu. Levy and Fert
calculated a "pseudo-dipolar" interaction for AuFe that was 40 times the size of the

classical dipolar one.86 b) Dyzaloshinski-Moriya interactions are much stronger for Fe

122

atoms than Mn atoms. Levy and Fert calculated a maximum value of H A > 50kG fi'om a
triangle of Fe atoms, which is enough alone to account for the observed values of H A.“
As was the case with AgMn, WSG for CuMnAu and AuF e had a lower limit due
to lower transition temperatures of these alloys (be for CuMnOAAuom was 25.3 K and
for Au0.97Fe0.03 be ~ 16K). Figure 6.9 shows the data for thin “’56 layers of
CuMnOAAuom with Cu and Ag ILs, and for Au0.97Fe0.03 with Au and Ag ILs. The solid
line indicating the CuMn/host IL data from Figure 6.2 is added for comparison. The data
for both systems follow almost the same curve to within the total experimental
uncertainty. Raising the anisotropy thus did not significantly change the finite size effect

behavior.

123

    

100 2

8 1

7 z

6 I-

5 E

.9 4 E
i 3 O Auo.97Feo.03/Ag
['3 Cl Auo.97Feo.os/Au

V CuMno.04Auo.01/Cu
l CuMno.04Auo.01/Ag

 

 

i — Cur-anx/Cu,Ag

1 X=0.ll,0.12.0.l4
10—1 1 LJ 1 Ag 1 1 1 1 41111 1 11 1 11 I 1 1 1 1 1 1 1 114

7 100 2 3 4 5 6 7 101 2 3 4 5

log WSG (nm)

Figure 6.9 Size effect data for AuFe.
The solid line represents the averaged CuMn/host IL data as indicated.

124
6.4 Finite Size Effects of CuMn, AgMn, and AuFe with Si ILs

The above results for AuFe/host multilayers are clearly quite different from those
reported by Vloeberghs et. al. shown in Figure 1.8 for single AuFe films. Their data fall
faster than even the cold sputtered CuMn/Si data shown in the same figure. Since their
AuFe films were evaporated onto glass with a SiO overlayer, there is a question about
whether AuFe difi‘ers significantly from CuMn when flanked by an insulator.

To investigate this issue, SG/Si systems were made for SG = CuMn, AgMn, and
AuF e with the concentrations described above. The CuMn/Si data reproduced that of
Kenning et. al.” for cooled samples shown in Figure 1.8, with the addition of a “’86 = 1.5
nm point. All samples were sputtered cold, with substrate temperatures between -60 and
0 °C.

The complicated situation of mixing at the boundaries for the SG/Si multilayers is
addressed in Section
4.4 Low angle X-ray diffraction analysis, and low resolution TEM imaging of cross
sections of samples, show beautiful layering for all three systems. Cu, Ag, and Au are all
capable of forming silicides.61 One difference observed, fiom electron diffraction analysis,
is a difference in crystallinity in thin layers of AuF e, CuMn, and AgMn. AuFe was found
to be almost amorphous, with very small crystallites, and AgMn was the most crystalline
of the three (see Section
4.4). Since one way Si may diffuse into the SG layer is along grain boundaries, one may
expect more Si diffusion in the AuFe layers where there are more grain boundaries
present.

Figure 6.10 shows the three SG systems with Si 11.5. There appear to be slight
differences between AgMn, CuMn, and AuFe. The AuFe curve is depressed the most,

and the AgMn curve the least. Since the AuFe layers are believed to encourage Si

125

diffusion the most, and the AgMn layers the least, the difference in the finite size behavior
is most likely due to differences in layer mixing, rather than to magnetic difi‘erences
between these 86 materials. Figure 6.11 shows the data replotted, assuming a fixed

value of boundary mixing for each material, as was done in Section 6.1.2.

Table 6.2 Estimated'interface mixing for SG/ Si multilayers.

 

 

 

 

 

 

 

 

 

SG WSG - wSfi' ML mixing
CuMn 1.6 nm ~ 7
AgMn 1.3 nm ~ 6
AuFe 3.3 nm ~ 10

 

Notice that the value of ng' for CuMn/Si is higher than those found for CuMn with any
of the metallic interlayers. This result is consistent with the results of the coupling study,
which showed a sharp coupling increase through 3 nm of Si, and with the structural
analysis in Section

4.4, which suggested a high degree of interfacial mixing.

Tr/ Tr b

126

 

 

 

 

100 c
6 .-
5 .—
4 :
3 E
2 h-
Is I
2 Cl Cu0.90Mn0.10/Si
2 I O Ago.91Mno.09/Si
4 , 1: O Auo.97Feo.03/Si
3 L
E - Cur-anx/Cu.Ag.Au
2* x=o.1o, 0.11, 0.12
10—21 lJLLJ 1.1111m1111111111 1111111111

456100 2 3456

11. 111
101 2 3 456

log Wsc (nm)

Figure 6.10 Finite size effects of CuMn, AgMn, and AuFe with Si IL.
The solid line represents the averaged CuMn/host IL data as indicated.

Tr/Tr b

 
    

 

 

100 :
6 i
5 >—
4 r
3 5
2 1 E
l H1
10"1 :
6 C C] Cuo.90Mno.io/Si Wsc’ =Wsc-1.6 nm
3 : O Ago.91Mno.09/Si Wsc' =Wsc-1.3 nm
3 E Auo.97Feo.03/Si Wsc’ =Wsc-3.3 nm
i
2 T — Cur-anx/Cu,Ag.Au
’ X=O.10. 0.11.0.12
lo-2 1 111.1111 11-111 1 1 1111441111 1 111111
10-12345 100 2345 101 2345

log WSG (nm)

Figure 6.1 l Replotted data for Si ILs using effective SG layer thickness (WSG').

127

6.5 NiMn- Short Range Interaction and Reentrant SC

The NiMn random alloy offers a significantly difl‘erent system in terms of magnetic
interactions. Unlike CuMn, AgMn, and AuF e alloys, where a dilute magnetic element
communicates via the RKKY exchange interaction, NiMn contains two magnetic
components. All atoms have magnetic neighbors, and the dominating interaction is short
range.””1 Neutron data indicates competition between ferromagnetic and
antiferromagnetic interactions,” with ferromagnetic Ni-Ni and Ni-Mn bonds, and
antiferromagnetic Mn-Mn bond strengths of the following ratio: O.25:1.O:4.0.1“2 As Mn
is added to pure Ni, ferromagnetism persists until enough Mn-Mn interactions occur to
disrupt the order. This disruption leads first to a reentrant SG (RSG) regime, where the
ferromagnetism surrenders to a mixed SG phase at low temperatures, and then to a regular
86 regime, where only paramagnetism and SG exist, as the concentration increases still
further (Figure 6.12).

The phase diagram of Figure 6.12 is based on the 1987 work of Abdul-Razzaq
and Kouvel.‘43 Later Gezalyan and Shul'pekovaI44 qualitatively reproduced this picture,
but with a slightly higher multicritical concentration (the temperature where Tc and ng
come together) of 25 at.% Mn, and the addition of an antiferromagnetic reentrant region
above 30.2 at.% Mn. The Abdul-Razzaq multicritical concentration of 23.9 at. % Mn was
supported by Roshko et. al.,145 who detemiined a 23.6 at.% Mn sample to be reentrant
and a 24 at.% Mn sample to have a single transition to SG. Our study also supports this
value, with sputtered samples above 24 at.% Mn behaving as SGs and those below 23
at.% exhibiting reentrant behavior.

The RSG is expected to display a spontaneous ferromagnetic moment, which has

been experimentally observed.146 Although this readily distinguishes the "pure" 86 from

128

the RSG state, some similarities between the two are reported to exist. Magnetic domain
structures have been observed to exist in both the RSG and SG phases through hysteresis
measurements146 and neutron depolarization”? The neutron data revealed domains of
decreasing size as the Mn concentration decreased, with domains of a few hundred nm in
the SG phase at 25 at.% Mn and 10-50 pm in the RSG phase at 23 at.% Mn. Evidence of
similarity between these two phases also comes from the decay of low field
therrnoremnant magnetization, where the relaxation isotherms display the same
systematics in the RSG and SG phasesm.

The finite size questions then become: a) will the paramagnetic (P) to "pure" SG
transition show the same behavior as observed for RKKY-type alloys; b) will the transition
in the reentrant regime from the F phase to the RSG phase behave the same as the P-SG
transition in the SG regime; and c) will the location of Tc (P to F transition) remain as

resistant to change in thickness as observed in regular ferromagnets?

129

200 ~
180
160
140
120 2
100 r
80 -
60 r ng TI
40 r
20 l

O A l I J A l A l A l A l A I A 1 4L 1 A l

22 23 24 25 26 27 28 29 30 31 32
at. Z Mn

0 Sputtered Films
Tc

l T I fi 1

 

Temp (K)

RSG SG

 

 

Figure 6.12 NiMn magnetic phase diagram, based on Abdul-Razzaq and Kouvel.

130

6.5.1 Pure SG Regime

6.5.1.1 Tr” Values

The data forming the magnetic phase diagram in Figure 6.12 were taken fi'om
needle like, bulk samples that were well annealed at a temperature just below the melting
point, then quickly quenched in an efi‘ort to ensure randomness. The be values for our
sputtered films are also shown in Figure 6.12. The W value for the samples with 29 at.%
Mn agree well with the literature values, but the be for 31 at.% Mn is higher, indicating
be is rising in this region. We can think of two possibilities for this discrepancy: a)
difference in Mn distribution. Since the disorder causing the SG state is dependent on the
Mn-Mn nearest neighbor interaction, a different distribution of numbers of nearest
neighbors could alter the ordering temperature. For example, if n1 indicates the number
of Mn atoms with one Mn nearest neighbor, n2 the number with two nearest neighbors
and so on, the annealing-quenching process may produce one distribution of nl,n2,n3,...
while the sputtering process may create another distribution of n1',n2',n3',... . Thus our
sputtered samples could have a different chemical configuration than the annealed-
quenched samples without necessarily containing short or long range order. No
ferromagnetism in the magnetic measurements was detected in our NiMn SG sputtered
films. b) Difference in atomic spacing. As shown in Chapter 4, sputtered films have a
high degree of structural imperfections. For NiMn, this resulted in a 0.6 to 0.8 % smaller
lattice parameter than expected for a well annealed alloy of the same concentration149 in
the <111> direction, the grth direction normal to the film surface (in-plane directions
were not measured, and might have expanded atomic spacing). It is not unreasonable that
small changes in the atomic spacing could affect the ordering temperature of this short

range interacting system.

131

6.5.1.2 NiMn/Cu Multilayers

Cu was chosen as an IL for the NiMn system, since the nominal host,
ferromagnetic Ni, was inappropriate for a magnetic study. The previous section showed
identical behavior for Cu, Ag, and Au when used as [1.5, so Cu was chosen as the
cheapest. In hindsight, Ag would have made the x-ray analysis easier, having more
contrast in both density and lattice parameter.

The NiMn/Cu system, with its non-host IL, might be expected to display different
behavior than a NiMn/host system, such as the faster decreases in Tf seen for the
CuMn/non-host systems above. Unlike CuMn, there does not appear to be any published
experiment or calculation which indicates the efi‘ect of impurities such as Cu on the Tf of
NiMn, so it is not known whether mixing Cu into the edges of a NiMn layer would drive
Tf up or down. This question might be partly answered by co-depositing some Cu into a
NiMn film, and also testing different ILs, such as Al or an insulator.

The coupling behavior was checked only to be sure that the NiMn layers were
decoupled by 30 nm of Cu. No change was seen between “'56 = 4 nm samples with Wm
= 30 and 10 nm, indicating that 30 nm was sufficient for decoupling. Since the interaction
between layers must in some way be related to the interaction inside a layer, a detailed
coupling study of this material might be a useful comparison to the RKKY systems.

Figure 6.16 shows the normalized Tf data for decoupled NiMn layers. To within
experimental error, the finite size behavior of the NiMn/Cu system is not different than the
CuMn/host systems. This data should probably be interpreted as a lower bound, since the

IL is non-host.

 

132

   
 

 

 

100:
7 +-
6 .—
5 r
4E
3 L
p .
S—
: 2 — CuMn/Cu,Ag,Au
12: O Nil-XMnx/Cu X=O.26,0.27
IO-1
7 ..
6 .—
5 r
l-
4’11L1144111l 1 1 11111111111 1 1 111111
3456100 2 3456101 2 345

log Wso (nm)

Figure 6.16 Finite size effect behavior of NiMn/Cu SG multilayers.

133

6.5.2 Reentrant SG Regime

Reentrant behavior was identified through the use of ac. susceptibility. The
characteristic triple peaked curve may be observed with the help of a static biasing field,
Hb- Figure 6.17 shows the progression fi'om small Hb = 50 G (very similar to the Hb = 0
scan, not pictured), where the ferromagnetic signal dominates, to a high Hb, where all
three peaks are seen. The biasing field in an ac measurement reduces the overall
magnitude of the signal, since the signal is dependent on spins following the ac excitation
and Hb tends to hold the spins in place. This effect is particularly prominent for a
ferromagnetic state, and so the more subtle SG features, hidden by the strong FM signal,
are seen through applying Hb. The highest temperature peak, at T3, shifts to higher
temperatures as Hb is increased, characteristic of a ferromagnetic peak (an external field
aids in the alignment, allowing the FM state to persist to a higher temperature). The two
lowest temperature peaks, at T1 and T2, shift to lower temperature as Hb is increased,
characteristic of SG phenomenon (an external field disrupts a SG state, which requires
spin disorder). A pure 86 film should show only one peak in an ac. x scan, regardless of
the value of Hb. This is the case in Figure 6.15b, where Hb = 400 G is applied to the
single peak and no structure is observed.

T1 and T2 indicate two SG transitions, an observation which agrees with the mean
field model of Gabay and Toulouse”. In this model the reentrant regime has three
transitions with decreasing temperature; a) paramagnetic to ferromagnetic (T3), b)
ferromagnetic to "mixed" ferro-SG (F SG) state with weak irreversibility (T2) c)
crossover to mixed FSG state with strong irreversibility. The FSG state consists of
ferromagnetic ordering with spontaneous magnetization, while the transverse component
of the spins are frozen into SG ordering. Above T2 the transverse order melts, allowing

more conventional ferromagnetism to exist, and above T3 the system is paramagnetic.

134

 

 

o Hb=50G
m— . $131888
0 O ._
7E—5 _ . C ...O Hb-4OOG
,, . ..
6E-5 ~ 154‘“ A A A A O
. C
3‘ 5E-5— A A '
E o ‘
OJ ‘ A
\ V 4E'5 _ .-II.. . A
>< . . ' " I 91
3E-5 * A . AA
. X I I Q:
23—5r '
. g" ' 95
A
13-5-— %5 ' A
OEOL O<><>g isz3CCOOOOOOOOOWA
0 20 40 60 80 100 120 140 160 180 200 220

Temp (K)

Figure 6.17 Susceptibility of a 500 nm NiMn film the reentrant region (21.5 at.% Mn)
with several biasing fields (Hb)-

135

Hb of 200 - 400 G is necessary to observe the triple peaked structure in x vs. T in
our sputtered films, while groups that studied bulk annealed samples have needed only
fields of Hb~ 50 6.1411142’143 Thus, as with the NiMn in the SG region, some significant
difl‘erences are observed between our sputtered samples and the annealed samples
reported in the literature. One possible explanation for the required higher Hb is the
presence of stronger ferromagnetism in the sputtered films, thus more external field is
required to reduce the FM signal to the desired level. Extrapolating the three peak
positions to their values at Hb = 0 (as was done by others'”) proved impossible when the
first points were Hb ~ 200 - 400 G and the peaks were entirely extinguished by Hb ~ 1000
G.

Abdul-Razzaq and Kouvell“l used the low field static magnetization curve to
determine values for the phase diagram in Figure 6.12. ng was taken from the point of
F C-ZF C irreversibility, and Tc was taken from the point of signal drop 03. The sputtered
NiMn films showed a similar ZFC curve to this measurement, but the FC curve did not
rejoin the ZF C curve at the low temperature "comer" (see Figure 6.18). Rather the ZFC
curve rejoins suddenly at a higher temperature. We do not know whether this temperature
is related to the strong to weak irreversibility crossover, or is merely a result of
concentration inhomogeneities in the sample.

The concentration stability was similar in the reentrant NiMn alloys to that found
in NiMn SG alloys, but in the reentrant samples the magnetic behavior was inconsistent
between samples in the same run, even under the best sputtering temperature control.
Thus, continuity could not be guaranteed from one sample to the next, or even from one

NiMn layer to the next in the same sample. More work is needed on this problem.

136

 

0.0057 —
O ZFC

0.0055 ~ ., 0 FC

 

 

 

0.0053” ......
oo 0
0.0051» 0 00000000008.
. O 08

0.0049 - 8

M (emu)

0.0047 1 O 8

0.0045 c 0

0.0043 4 O

. o 0 451-11

0.0041 1 1 l 1 l 1 l 1 I 1 l 1 L 1 J 1 I

O 20 4O 60 80 100 120 I40 160
Temp(K)

 

 

Figure 6.18 Static magnetization for a 300 nm RSG Ni0_77Mn0.23 sputtered film.

X (emu)

X '(eniu)

2E-5

2E-5

1E-5

lE-5

lE-5.
8E-6b
6E-6>
4E-6p

2E-6

0E0

3E-6

2E-6

2E-6

1E-6

lE—6

5E-7

0E0

 

o
oo-Oi.

I J 1 l

137

, 539—3

0

O
O

2000000...

1 L l l A; l A l l l 1 1 J; L

l m

 

 

 

() 20 40 60 80 100 120 140 160 180 200 220

 

NM
3 ._
‘ 1: Hb—O
1
I
‘ 11
‘ t
I J. I 1
I t
t
t
I ‘1‘ ‘
I I
I t
t 539-9
0 20 40 60 80 100 120 140 16 180 200 220

T(K)

Figure 6.19 Two different 1 vs. T (Hb =0) for two RSG NiMn films from the same
sputtering run grown under similar well controlled conditions.

 

 

138

One finite size study has been done with sputtered NiagsMnon/Cu multilayers in
the RSG region, by Abdul-Razzaq and Wu”. Here Tfs/Tfs" for thin “'86 = 10 nm was
0.88, indicating less of a depression than seen in the CuMn and AgMn systems reviewed in
Chapter 1 and the SG systems presented above in this chapter. The triple peak structure
was not shown, the static magnetization of the bulk film was not squarish but had a single
peak which was defined as ng. Reentrant behavior was determined through the
therrnoremanent magnetization, which persisted until a much higher temperature defined
as Tc for the bulk film. The value of T6 for the thin NiMn layer was not reported.

Although the variation in magnetic behavior just described would not allow reliable
comparison between our samples, we did make some RSG NiMn/Cu multilayers.
Surprisingly, all the multilayers with which showed triple peak structure had T3 much
lower than observed in any of the bulk samples (see Figure 6.20 ). Since T3 is associated
with ferromagnetic ordering, it was expected to be the most resistant to changes in layer
thickness. This behavior may be an indication that the bulk films contain large

ferromagnetic clusters that are unable to form when the multilayer is grown.

139

NiMn/Cu 1113:4000

NiMn/Cu
”‘6 ' - lOnm/30nm/10
[3% A 5nm/30nm/20
2E-6 2 AA A A
A
1. A
= 2E-6 ~ A
E 0‘0. . 6
5.1 A ' 0 o 0 .
\ O
l A o
lE—6 - ° A '
_ A
O A .
5E-7 _ A A.
8 5.. .
0E0 b l l m l 4 l 1 I 1 i 1 l 1 l 1 l 1 l 1 l 4 l

 

 

0 2O 40 60 80 100 I20 140 160 180 200 220
Temp (K)

Figure 6.20 1 vs. T with Hb = 400G for RSG NiMn/Cu with 10/30 nm and 5/30 nm.

CHAPTER7

CONCLUSIONS

7.1 Structure of Multilayers

Using UHV sputtering we have produced a wide variety of multilayers. Five SG
alloys and one non-SG alloy were sputtered fi'om home-made targets to produce samples
containing Cu1.anX where X=0.10, 0.11, 0.12, Agoqganoflg, Auo.97Feo.03, M1_anx
where X=O.29 and 0.31, CuMnomAuom, and Cu1.xGex where X=0.02 and 0.10. The
SGs were layered with the following metals: a) CuMn: Cu, Ag, Au, CuMnAu, CuGe, Al,
Mo, Nb, and V; b) AgMn: Cu and Ag; c) AuFe: Au and Ag; (1) Nran Cu. In
addition, CuMn, AgMn, and AuF e were each layered with amorphous Si.

X-ray .difi‘raction analysis was able to confirm layering for all samples. Layering in
the SG/Si systems was also confirmed through TEM imaging of cross sections. The layer
thicknesses were determined through x-ray difi’raction peak analysis and mechanical
thickness determination to be :t 5% of the nominal values in almost every case.
Crystallites in the metal layers are found to be highly textured, with the <111> plane lying
parallel to the sample surface for FCC materials and the <110> plane preferred in the BCC
materials. The perpendicular coherence lengths were on the order of ~ hundreds of nms

for bulk films of each material. The mixing at the layer interfaces was argued from

140

141

magnetic data to be ~ few ML for the SG/metal systems, and 5 to 15 ML in the SG/Si
systems.

The Si layer was determined to be amorphous for W56 2 1 run through the lack of
satellites in large angle x-ray dim'action. Such satellites are seen in CuMn/Si when WSi =
0.5 nm, either because 0.5 nm is the width of a Cu-silicide layer, or 0.5 nm is too thin to
create enough of the continuous roughness that is responsible for the satellite destruction.
Electron dim’action data for each SG/ Si system showed decreasing crystallinity in the SG
layer in 3 MW nm samples for AgMn, CuMn, and AuFe respectively.

7.2 Finite Size Effects

To observe finite size efi‘ects, SG layers were decoupled by 30 nm of the above
metals or 7 nm of Si. Tf was determined through the peak in the low field static ZFC
magnetization curve for all samples. The thinnest of the samples, CuMn layers with WSG
~ 1 ML interlayered with Cu or Ag, showed the characteristic FC and ZF C magnetization
signature indicating non-zero Tf.

For CuMn/IL where IL = Cu, Ag, or Au, the decreases in Tf with decreasing W56
> 2 nm agreed with the results of Kenning et. al. discussed in Chapter 1. In this “’86
range the data fit the generalized scaling law

D’Ub
b

—_ ~ W 0“” V

9
with v = 1.6. The generalized scaling expression, however, is incapable of describing data
below WSG = 2 nm. The data in the extended range of 0.21 < “’86 < 2 nm show power

law behavior, and were fit to the Fisher-Huse Droplet Excitation model for thin WSG:

 

142

T
-Lb- ~ W" where a =—————W3 + W2 V263 .

Tf 1 + V2 W2

The value obtained for the exponent is a = 0.810. 1, which is outside the literature estimate
of 0.3 < a < 0.65, but below the rigorous bound of 2.

AgMn was tested as another SG similar to CuMn to determine if its finite size
behavior was the same for WSG < 2 nm. Within the experimental uncertainty, the finite
size efi‘ect behavior for AgMn/Cu and AgMn/Ag systems was not difi‘erent from that
observed for CuMn.

Two high anisotropy SGs were studied, inspired by theoretical results indicating
that the degree of anisotropy might affect the lower critical dimension d] (Chapter 1).
CuMnomAumm and AuFe with Ag and Au ILs both show behavior indistinguishable
from the equivalent CuMn systems. This suggests that anisotropy does not play a major
role in depression of the quasi-static Tf due to finite size efi‘ects.

The type of interaction is also theoretically predicted to change (11 (Chapter 1),
and so NiMn was chosen as one SG with considerably difi‘erent interactions than the other
SGs studied. The NiMn/Cu system also did not show a significant difference from CuMn
behavior, although this data might represent only a lower bound, because the IL used is so
different fi'om the SG.

The finite size behavior of CuMn/IL where IL is not a noble metal, was also
examined. ILs = A], Mo, and V (and Si) all induce faster decreases in Tf than that found
for the noble metal ILs. This behavior could be attributed largely to mixing at the
interfaces.

CuMn, AgMn, and AuFe were each layered with Si, and some differences resulted

between the three curves, with AgMn/Si depressed the least and AuFe the most. This

 

143

behavior is also explained as an interface mixing efi‘ect, using the structural results

concerning the crystallinity fi'om x-ray and TEM studies.

7.3 Coupling

The Tf of CuMn with a fixed “’86 = 4 nm was studied as a fimction of decreasing
WIL. The same unusually long range coupling (out to WIL ~ 20-30 nm) previously seen
for Cu and Ag ILs (Chapter 1) was found for Au and CuGe lLs. Since Au is a strong
spin-orbit scatterer, and CuGe has high resistivity, it is concluded that these two efi‘ects do
not affect the coupling length. All other materials tested- A], Mo, V, Nb, and Si gave
much shorter coupling lengths of ~ 2-5 nm, indicating that the long coupling length is

dictated by the electronic structure of the IL.

APPENDIX

Appendix A1

Tf VALUES

All Tf values in this appendix carry an error of i 0.5 K unless otherwise specified.
Table Al.l Finite size effect data for CuMn/X and AgMn/X X = Cu, Ag, Au

a. Cu0.3 Mno 12/Cu, where Wm is fixed at 30 nm. be = 58.5 from shavings

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WmOlIh) TL Te’T 1"
0.6 8.6 0.15 i 0.01
1.0 13.1 0.22 :1: 0.01
2.0 21.4 0.37 i 0.01
4.0 34.0 0.58 :I: 0.01
b. Cum; n/Cuflhere WIL is fixed at 30 nm. be = 49.5 from shavings
. “’59 (um) Tr (10 TN)
0.21 2.9 i 0.3 0.059 t 0.006
0.21 2.6 i 0.3 0.053 i 0.006
0.42 4.7 0.095 t .01
0.42 4.6 i 0.3 0.093 3: .006
0.42 4.5 0.091 :t .01
0.63 6.4 0.13 i 0.01
0.63 6.8 0.14 :l: 0.01
0.84 8.7 0.18 i 0.01
1.0 9.3 0.19 i 0.01
1.0 9.50 0.19 :t 0.01
2.0 18.1 0.37 i 0.01
2.0 16.7 0.34 i 0.01
4.0 25.9 0.52 i 0.01
10.0 36.8 0.74 :1: 0.02
0.21/60 2.4 i 0.3 0.055 i 0.006

 

 

 

 

1114

 

 

 

 

 

 

145
c. Cuoxm where WIL is fixed at 30 nm. be = 49.5 from shavings
W301!!!) Tf (K) Tf/Ttb
0.21 2.9 :t 0.3 0.059 :I: 0.006
0.42 5.1 0.10 i 0.01
0.63 7.2 0.14 i 0.01
2.0 16.8 0.34 :t 0.01

 

 

 

 

 

d. CUO_00MHO m/Au, where WIL is fixed at 30 nm. be = 47.0 fi'om shavings

 

 

 

 

 

 

 

 

W 1 (nm) T1(K) Ts’Tr"
0.42 3.5 i 0.3 0.074 :t 0.007
0.63 6.5 :1: 0.3 0.14 :1: 0.01

1.0 10.3 0.22 i 0.01
1.5 14.1 0.30 :t 0.01
2.0 17.8 i 0.4 0.38 :1 0.01
4.0 24.3 i 1 0.52 i 0.02
4.0 27.7 0.59 :l: 0.02

 

 

 

 

 

e- A809

 

 

 

 

 

 

 

 

 

 

A where Wm is fixed at 30 nm. be = 24.8
I WISE: (um) Tr (K) Tm” ‘
0.24 < 2 < 0.08
0.42 < 2 < 0.08
0.47 < 2 < 0.08
0.71 2.9103 0.121001
0.94 3.5 10.3 0.14:0.01
2.0 7.3 0.29 1: 1.03

 

 

f. Agog Mno 09/Cu, where WJLis fixed at 30 nm.Ttb= 24.8

 

 

 

 

 

 

 

 

W (In) Tr (K) Trr’T 1b
0.47 ~ 2.5 ~0.097
0.71 3.4103 0.141001
0.94 4.2 :1: 0.3 0.17 i 0.02
2.0 7.3 0.29 i 0.03

 

 

lama
fl. ..‘_
'A

146

Table Al.2 Finite size data for CuMn/X, X= Al, Mo, and V

a. 6103st 12011, W fixed at 30 nm be = 58.5 fi'om shavings

 

 

 

 

 

 

 

1w (um) T100 1418
2.0 13.4 0.23 i 0.01
4.0 28.7 i 0.3 0.49 :l: 0.01
7.0 39.4 0.67 i 0.01
50.0 56.4 0.96 i 0.02

 

 

 

€110.91 m/Al, where W11 is fixed at 30 nm. ij = 47.0 from shavings

 

 

 

 

 

 

WIL (Hm) T1119 Tfl?’
1.0 < 2 < 0.043
1.5 4,810.3 01010.01
2.0 10.0 1; 0.3 0.21 :1: 0.01

 

 

 

 

 

b. Cuomenn 12/Mo, where WIL is fixed at 30 nm or 8.0 nm be = 58.5 from shavings

 

 

 

 

 

 

 

 

w (um) Tr (K) T1015
0.6/8.0 < 2 < 0.034
1.0/8.0 6.5 0.11 i 0.01
2.0/80 15.8 0.271 :t 0.01
4.0/30 27.7 0.474 d: 0.01

50.0/30 51.0 0.871 i 0.02

 

 

c. Cuoi 9Mn0 “N, where Wm is fixed at 30 nm. be = 49.5 from shavings

 

 

 

 

 

 

 

, Wsfi (nm) 1400 m?
1.0 3.3 i 0.3 0.067 i 0.006
1.5 7.5 0.15 i 0.01
2.0 11.9 0.24 :1: 0.01
4.0 24.3 0.49 :1: 0.02
10.0 33.9 0.69 i 0.02
30.0 34.7 0.88 i 0.02

 

 

 

 

 

147

Table A1.3 Finite size effect data for CuMnAu/X and AuFe/X X = Cu,Ag, and Au

/A where wIL is fixed at 30 run. be = 23.5 i 1 fi'om run

 

 

 

 

a. Mn0_ A
W (mu) Tf(K) T1“?
1.0 5.7 0.23 :l: 0.02
5.0 14.6 0.58 :1: 0.04
12.5 20.2 :1: l 0.86 :1: 0.05

 

 

 

 

 

b. CUMMAUQ m/Cu,

where W111 is fixed at 30 nm. T1

b=25.3 i 1 from run

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, “'59 (nm) Tr (K) T8’T 1"
4.0 10.2 0.40 20.03
2.0 7.4 0.29 :1; 0.03
0.8 3.7203 0.15 10.01
c. Auoe F /A , where Wm is fixed at 30 nm. be = 16.1 :1: 0.6 fiom run
w) Tr(K) Tfi’TF’
1.0 3.0103 0.191002
1.5 4.0 0.25 :1: 0.03
2.0 4.7 0.29 i 0.03
4.0 8.4 0.52 :1: 0.04
d. 1411103213n m/Ag, where wIL is fixed at 30 nm. be = 17.0 i 0.6 from run
._Wso (nm) Tr (K) Tf/T'fb
2.0 6.3 0.37 s: 0.03
4.0 9.4 0.55 i 0.04
7.0 11.3 0.67 :l: 0.04
25.0 14.7 0.86 i 0.04

 

 

 

 

 

e. AuomFeO m/Au, where WIL is fixed at 30 nm. be =, 17.0 i 0.6 from run

 

 

 

 

 

 

 

, ng(nm) TMK) T1774" |
4.0 8.5 0501003 |
25.0 14.2 0841004 |

148

Table Al.4 Finite size effect data for N iMn/Cu

6- Ni0.7

Table ALS Coupling data for CuMn/X X = An, CuGe

a. Cuo.

Mno 29/Cu, where Wm is fixed at 30 nm. be = 71 :1: 3 from run

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. W59 (run) Tr (K) Ti” 11’
0.6 12.4 0.17 i 0.01
1.0 (19) ac 0.26 :t 0.01
2.0 31.4 0.44 :1: 0.0
4.0 43.4 0.61 i 0.02
7.0 56.3 0.79 :1: 0.02
‘ Cu, where Wm is fixed at 30 nm. be = 86.4 i 2 fiom run
W3: (mu) Tr(K) Tfi’T 41’
0.6 16.1 0.19 i 0.01
1.0 21.8 0.25 i 0.01
2.0 37.9 0.44 :1: 0.01
4.0 55.0 0.64 20.02
7.0 68.0 0.79 :t 0.02

 

m/Au, where W39 is fixed at 4 nm. T413 = 47 .0 from shavings

 

 

 

 

 

 

 

 

 

 

 

 

we (run) T100 MP
1.0 40.3 i 1 0.86 i 0.03
2.0 33.5 0.71 i 0.02
3.0 32.3 i 0.3 0.69 i 0.02
4.0 31.3 0.67 i 0.02
7.0 28.7 0.61 :t 0.02
10.0 28.9 i 0.3 0.62 :t 0.02
30.0 27.7 0.59 i 0.02
30.0 24.3 :t 1 0.52 i 0.02

 

 

 

 

 

m/Cuo 91 Geo 02, where W59 is fixed at 4 nm. be = 47 .0 fi'om shavings

149

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table Al.6 Coupling data for CuMn/X X=Al, Mo, v, and Si

a. C110. Mno 1201.1, where wsfi is fixed at 4 nm. nb = 58.5 from shavings

 

b. Cuo.
Wn. (um) Tf(K) UT 11’
3.0 33.0 0.70 :1: 0.02
5.0 29.5 0.63 i 0.01
7.0 28.7 0.61 :l: 0.01
10.0 25.1 0.53 i 0.01
30.0 22.5 0.48 :l: 0.01
c 'Cuo 2M 1010.3 39% 10: where
W1L(nm) Tf(K)
1.0 37.2 0.79 :1: 0.02
3.0 29.6 0.63 i 0.01
7.0 24.6 0.52 :l: 0.01
5.0 26.8 0.57 i 0.01
10.0 23.6 0.50 i 0.01
30.0 22.9 0.49 :i: 0.01

 

 

 

 

 

 

 

 

 

 

 

 

 

 

wIL (nm) Tf 11715
0.5 49.2 0.84 i 0.02
1.0 44.4 0.76 i 0.02
1.5 38.7 0.66 i 0.01
2.0 32.2 0.55 i 0.01
3.0 32.8 0.56 :l: 0.01
5.0 31.7 0.54:1:0.01
10.0 29.5 0.50 :l: 0.01
30.0 28.7 i 0.3 0.49 :1: 0.01

 

 

W is fixed at 4 nm. be = 47.0 from shavings
T1773;

 

 

b. Cuo. Mno lz/Mo, where “’50 is fixed at 4 nm. ij = 58.5 from shavings

150

 

 

 

 

 

 

 

 

 

Wn. (mu) Tr(K) Tfl 1"
0.5 46.4 0.79 i 0.02
1.5 33.7 0.58 :1 0.01
2.0 30.4 0.52 :1 0.01
4.0 36.6 0.63 :1 0.01
5.0 27.8 0.48 :1: 0.01

10.0 27.3 0.47 s 0.01
30.0 27.7 0.47 :1: 0.01

 

 

 

9- C008

9MnO ”N, where wSfi is fixed at 4 nm. be = 49.5 from shavings

 

 

 

 

 

 

 

 

d. CuomMno m/Si, where W35; is fixed at 7 nm. T}: = 47.0 from shavings

 

 

Wmimn) Tr(K) Tim"
1.0 27.6 0.56 :1: 0.01
2.0 26.5 0.54 s 0.01
4.0 23.6 0.48 1 0.01
7.0 23.4 0.47 :1 0.01
10.0 24.4 0.49 :1: 0.01
30.0 24.3 0.49 s; 0.01

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Wm (um) T109 MP
0.5 42.5 0.90 1: 0.02
1.0 37.6 :t 0.3 0.80 :t 0.02
1.5 34.5 0.73 _+. 0.02
2.0 28.3 0.60 :t 0.01
3.0 24.8 0.53 s: 0.01
4.0 24.8 i 0.3 0.53 :l: 0.01
4.0 24.4 0.52 i 0.01
7.0 25.3 s 0.3 0.54 i 0.01
10.0 25.5 s 0.6 0.54 :1: 0.01
10.0 24.7 0.53 i 0.01

 

 

 

 

Table Al.7 Coupling data for AuFe/Ag

151

a. AuoflFgQ m/Ag, where W59 is fixed at 4 nm. be = 15.6 :t 0.5 fiom run

 

 

 

 

 

 

 

“’0 (nm) TfCK) T1”?
1.0 12.7 0.81 :l: 0.04
2.0 11.5 0.74 i 0.04
4.0 10.4 0.67 :l: 0.04
10.0 8.7 :l: 0.3 0.56 :l: 0.03
60.0 7.2 O 0.46 i 0.04

 

 

 

 

Table Al.8 Finite size effect data for X/Si X= CuMn, AgMn, AuFe

a. CuMn(10)/Si, where wIL is fixed at 7 nm. be = fi'om shavings

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, “’59 (nm) TrOQ m?
1.5 < 2 < 0.04
2.0 3.9 0.08 i 0.01
3.0 7.7103 0.16 3:00]
4.0 13.8 0.29 i 0.02
7.0 25.3 :1: 0.3 0.54 i 0.02
10.0 27.0 0.57 :l: 0.02
b. Cuo MnO 15/Si, where WJL is fixed at 4 11m. T19 =7 65.4 i 0.5 from run
w wee 1am) Tf(K) Tf/Tib I
3.0 14.2 0.217 |
7.0 37.4 :r 1 0.571 |
c. Agoeanimg/Si, where Wm is fixed at 7 nm. be = 25 i 2 from run
w (um) Tr(K) Tie/Tili
2.0 2.4 i 0.4 0.10 i 0.02
3.0 5.3 i 0.3 0.21 :l: 0.03
4.0 9.2 i 0.4 0.37 i 0.03
7.0 11.8 0.47 :l: 0.04
10.0 15.4 0.61

 

 

 

 

 

152

93Mn0 og/Si, where Wm is fixed at 7 nm. be é 22.7 i 0.5 from run

 

 

 

 

 

 

ng 0w) Tr(K) Tim" I
7.0 14.4 0.634 |
3.0 6.7 :l: 0.3 0.30 l

 

e. Ana‘s-fie“ m/Si, where Wm is fixed at 7 nm. be = 16.2, :1: 0.5, 16.1 i 0.6 from run

 

 

 

 

 

 

 

 

 

 

W51; (urn) Tr(K) T177 11’
40 < 2 < 0.123
4.0 2.5 :l: 0.03 0.16 :t 0.02
7.0 6.3 0.39 :t 0.03
7.0 5.4 3: 0.03 0.33 i 0.02
10.0 8.1 0.50 i 0.03
10.0 8.8 0.55 :1: 0.04
25.0 12.5 0.78 :l: 0.04

 

 

 

r. Au0.97FeQm/Si, where wIL is fixed at 7 run. "rib = 15.6 :t 0.2 from run

 

 

 

 

W (nth) Tf(K) T871" I
5.0 3.9 i 0.3 0.25 s: 0.02 J
| 15.0 10.7 0.69 s 0.03 I

 

 

Table Al.9 T45 of NiMn films grown under stringent temperature control.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

samrile Tr (K)
525-3 66 :l: 1
525-5 70 i 1
525-7 74 i 1
525-14 73 i 1
sample Tf (K)
526-3 84 i 1
525-5 87 i 1
525-10 88 i 1
525-14 87 i l

 

 

 

 

LIST OF REFERENCES

REFERENCES

 

lV. Cannella, J.A. Mydosh, and J1. Budnick, J. Appl. Phys. 42, 1689 (1971); V. Cannella
and J .A. Mydosh, Phys. Rev. B6, 4220 (1972).

21L. Tholence and R. Toumier, J. Phys. (Paris) 35, C4-229 (1974); H. Bouchiat and P.
Monod, J. Mag. Mag. Mat. 30, 175 (1983).

3K. Binder and AP. Young, Rev. Mod. Phys. 58, 801 (1986).

4P. Monod, J.J. Prejean, and B. Tissier, J. Appl. Phys. 50, 7324 (1979).

51.]. Prejean, M.J. Ioliere, and P. Monod, J. Phys. (Paris) 41, 427 (1980).

6LE. Wenger and PH. Keesom, Phys. Rev. B11, 3497 (1975).

7C.A.M. Mulder,A.J. van Duyneveldt, and IA. Mydosh, Phys. Rev. B23, 1384 (1981).

8D. Sherrington and S. Kirkpatrik, Phys. Rev. Lett. 35, 1792 (1975).

9G. Parisi, Phys. Rev. Lett. 43, 1754 (1979); ibid, J. Phys. A13, L115,1101, and 1887
(1980)

10P. Monod and H. Bouchiat, J. Physique Lett. 43, L45 (1982), R. Omari, J. J. Prejean, and
J. Soulitie, J. Physique 44,1069(1986).

1' L. P. Levy and A. T. Ogielski, Phys. Rev. Lett. 57, 3288 (1986).

”S. Kirkpatrick, Lecture Notes in Physics, Vol. 149, 280 (1981) Springer, Berlin.

l3S. Kirkpatrick, C.D. Gelatt, and MP. Vecci, Science 220, 671 (1983); S. Kirkpatrick, J.
Stat. Phys. 34, 975 (1984).

14].]. Hopfield, Proc. Natl. Acad. Sci. USA. 79, 2554 (1982); Ibid, 81, 3088 (1984); I
Guyon and G. Dreyfus, J. Phys. Lett. 46, L359 (1985).

15A. Arrot, J. Appl. Phys. 36, 1093 (1965).

15].W. Cable, S.A. Werner, G.P. Felcher, and N. Wakabayashi, Phys. Rev. B29,1268
(1984)

17IL. Tholence and R. Toumier, J. Phys. (Paris) 35, C4-229 (1974). H. Bouchiat and P.
Monod, JMMM 30, 175 (1983).

18AP. Malozemoff and Y. Imrg, Phys. Rev. 824, 489 (1981).

19F. Mezei and AP. Murani, J. Mag. Mag. Mat. 14, 211 (1979); F. Mezel, Recent
Developments in Condensed Matter Physics, Vol. 1, Plenum Press, 679 (1981).

20G]. Nieuwenhuys and F .R. Hoekstra, Mag. Resonance Rev. 12, 137 (1987).

21Y.J. Uemura and T. Yamazaki, Physica 109,110B, 1915 (1982).

22RH. Heffner, M. Leon, and DE. MacLaughlin, Hyperfine Interactions, 18, 457 (1984).

23PA. Beck, Prog. Mater. Sci. 23, 1 (1978)

2“ J.J. Prejean, M.J. joliere, and P. Monod, J. Phys. (Paris) 41, 427 (1980).

2518. Kouvel, Recent Progress in Random Magnets, ed. DH. Ryan,World Sci. Press
(1992)

153

154

 

26L. Sandlund, P. Granberg, L. Lundgren, P. Nordblad, P. Svedlindh, J .A. Cowen and G.G.
Kenning, Phys. Rev. B40, 869 (1989).

2"K. Gunnarsson, P. Svedlindh, P. Nordblad, L. Lundgren, H. Aruga, and A. Ito, Phys. Rev.
Lett. 61, 754 (1988); L. Levy, Phys. Rev. B38, 4963 (1988).

28D. Sherrington, Proc. of Heidolber Col. on Glass Dynamics and Optimization, (1986).

291. Kondor, Science Prog. 71, 145 (1987).

30H. Maletta and W. Felsch, Phys Rev. B20, 1245 (1979); H.G. Bohn, W. Zinn, B. Domer,
and A. Kollmar, Phys. REV. B22, 5447 (1980).

3‘G.N. Parker and W.M. Saslow, Phys. Rev. B38, 11718 (1988).

32W. Abdul-Razzaq and JS. Kouvel, Phys. Rev. B35, 1764 (1987).

33AD. Gezalyan nad s. V. Shul'pekova, JETP Lett. 54, 47 (1991).

34M. Gabay and G. Toulouse, Phys. Rev. Lett. 47, 201 (1981).

35MA. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954).

36T. Kasuya, Prog. Theoret. Phys. 16, 45 (1956).

3"K. Yosida, Phys. Rev. 106, 893 (1957).

38C. Kittel, Solid State Physics, V0122, ed. F. Seitz, D. Tumbull, an H.Ehrenreich.

39]. Souletie and R. Toumier, J. Low Temp. Phys. 1, 95 (1969).

“DC. Vier and S. Schultz, Phys. Rev. Lett. 54, 150 (1985).

4'K. H. Fisher, landolt-Bornstien: Numerical Data and Functional Relationships in
Science and Technology, Springer-Verlag Press, III/15a, 289 (1982).

42LR. Walker and RE. Walstedt, Phys. Rev. B22, 3816 (1980); U. Larsen, Sol. St.
Comm. 22, 311 (1977); W. Kinzel and KR. Fisher, J. Phys. F7, 2163 (1977).

43U. Larsen, Phys. Rev. B33, 4803 (1986).

44PG. deGennes, J. Phys. Radium 23, 28 (1981).

45A. Jagannathan, E. Abrahams, and M.J. Stephen, Phys. Rev. B37, 436 ( 1988).

45A.Y. Zyuzin and B1. Spivak, JETP Lett. 43, 234 (1986); L.N. Bulaevskii and S.V.
Panyukov, JETP Lett. 43, 240 (1986); U. Larsen, Solid State Commun. 22, 311 (1977);
M. Hitzfeld and P. Ziemann, Phys. Rev. B32, 3026 (1985); J.A. Cowen, C.L. Foiles, and
J. Shell, J. Mag. Mag. Mater. 31-34, 1357 (1983).

“Q. Zhang and PM. Levy, Phys. Rev. B34, 1884 (1986).

4“W3. Carr, Jr., Phys. Rev. 85, 590 (1952).

49].W. Cable and JR. Child, Phys. Rev. B10, 4607 (1974); T]. Hicks and O. Moze, J.
Phys. F43, 2633 (1981).

50LE. Dzyaloshinski, J. Phys. Chem. Sol. 4, 241 (1958).

51T. Moriya, Phys. Rev. Lett. 4, 51 (1960).

52PM. Levy and A. Fert, Phys. Rev. B23, 4667 (1981).

53G. Kotliar and H. Somploinsky, Phys. Rev. Lett. 54, 150 (1985).

54S. Schultz, EM. Gulliksen, D.R. Fredkin, and M. Tovar, Phys. Rev. Lett. 45, 1508
(1980); K. Okuda and M. Data, .1. Phys. Soc. Jpn. 27, 839 (1969).

55P. Monod and Y. Berthier, J. Mag. Mag. Mat. 15-18, 149 (1980).

55A. Fert and P. M. Levy, Phys. Rev. B44, 1538 (1980).

155

 

5"H. Alloul, J. Appl. Phys. 50, 7330 (1979); H. Alloul and F. I-Iippert, J. Physique Lett. 41,
L-201 (1980).

58H. Bouchiat and E. Daryge, J. Physique 43, 1699 (1982).

59Zibold, Landolt-Bomstien: Numerical Data and Functional Relationships in Science and
Technology, New Series, Springer-Verlag Press, III/19b, 111.

60M. Hansen, Constitution of Binary Alloys, McGraw-Hill Book Co. Inc., (1958).

H. Kunkel, R.M. Roshko, W. Ruan, and G. Williams, Phil. Mag. B63, 1213 (1990).

61SA. Werner, Comments Cond. Mat. Phys. 15, 55 (1990).

62J.A. Mydosh JMMM 73, 247 ( 1988).

63 1960 overhauser, fi'om Fawcett?, A.W. Overhauser, Phys. Rev. 128, 1437 (1962).

64R. Fisch and AB. Harris, Phys. Rev. Lett. 38, 785 (1977); R.V. Ditzian and LP.
Kadanofl‘, Phys. Rev. B19, 4631 (1979).

65R. Fisch and AB. Harris, Phys. Rev. Lett. 47, 520 (1981); KG. Palmer and F .T. Bantilan
Jr., J. Phys. C18, 171 (1985).

“I. Morgenstern and K. Binder, Phys. Rev. Lett. 43, 1615 (1979); Ibid, Phys. Rev. B22,
288 (1980); Ibid, Z. Phys. B39, 227 (1980).

6"RN. Bhatt, Phys. Rev. Lett. 54, 924 (1985); AT Ogielski and I. Morgenstern, Phys.
Rev. Lett. 54, 928 (1985); AT Ogielski and Nishimori, J. Phys. Soc. (Japan) 56, 1568
(1987); AP. Young, Phys. Rev. Lett. 50, 917 (1983).

68W.L. McMillian, Phys Rev. B31, 342 (1985); Morris J. Physics C19, 1157 (1986); S.
Olive, A.P. Young, and D. Sherrington, Phys. Rev. B34, 6341 (1986); A.J. Bray and
MA. Moore, J. Phys. C15, 3897 (1982); F. Matsubara, T. Iyota, and S. Inawashiro,
Phys Rev. Lett. 67, 1458 (1991).

591D. Reger and AP. Young, Phys. Rev. B37, 5493 (1988).

7°A.J. Bray, M.A. Moore, and AP. Young, Phys Rev. Lett. 56, 2641 (1986).

71see for eg. W. Dfirr, M. Tavorell, 0. Paul, R. Gerrnar, W. Gudat, D. Pescia, and M.
Landolt, Phys. Rev. Lett. 62, 206 (1989); CA. Ballentine, R.L. Fink, J. Araya-Pochet,
and J.L. Erskine, Phys. Rev. B41, 2631 (1990); Yi Li and K. Baberschke, Phys. Rev.
Lett. 68, 1208 (1992); F. Huang, M.T. Kief, G.J. Mankey, and RF. Williams, Phys. Rev.
B49, 3962 (1994).

72K. Binder and AP. Young, Rev. Mod. Phys. 58, 801 (1986).

73D.A. Huse and I. Morgenstern, Phys. Rev. B32, 3032 (1985).

“G.G. Kenning, J .M. Slaugher, and J.A. Cowen, Phys. Rev. Lett. 59, 2596 (1987).

75 J.A. Cowen, G.G. Kenning, and J. Bass. J. Appl. Phys. 64, 5781 (1988);

76 R. Stubi, J .A. Cowen, d. Leslie-Pelecky, and J. Bass, Physica B 165-166, 459 (1990).

77MN. Barber, Phase Transitions and Critical Phenomena, 8, ed. C. Domb and J .L.
Lebowitz, 145 (1983), Academic Press.

73R. Omari, J.J. Prejean, and J. Souletie, J. Physique, 44, 1069 (1983). The authors actually
reported values for critical exponents y and B, the hyperscaling relation dv = y + 213 (d=3)
was used as in reference [11] to find v.

79G.G. Kenning, J. Bass, W.P. Pratt, Jr., D. Leslie-Pelecky, L. Hoines, W. Leach, ML.
Wilson, R. Stubi, and J .A. Cowen, Phys. Rev. B42, 2393 (1990).

156

 

80G.G. Kenning, thesis (1988).

81R. Stubi, J.A. Cowen, L. Hoines, M.L. Wilson, W.A. Fowler, and J. Bass, Phys. Rev.
B44, 5073 (1991).

82A. Gavrin, J.R. Childress, C.L. Chien, B. Martinez, and MB. Salamon, Phys. Rev. Lett.
64, 2438 (1990).

33 BS. Fisher and DA Huse, Phys. Rev. Lett. 56, 1601 (1986); Ibid, Phys. Rev. B36,
8937 (1987)

84J. Vranken, C. Van Haesendonck, H. Vloeberghs, and Y. Bruynseraede, Phys. Scr. T25,
348 (1989); H Vloeberghs, J. Vranken, C. Van Haesendonclg and Y. Bruynseraede,
Euro. Phys. Lett. 12, 557 (1990).

”RM. Levy and A. Fert, J. Appl. Phys. 52, 1718 (1981).

85D.S. Fisher and DA. Huse, Phys. Rev. B36, 8937 (1987); ibid., B38, 386 (1988); ibid,
B38, 373 (1988).

37$. Geschwind, DA Huse, and GE. Devlin, Phys. Rev. B41, 2650 (1990).

88G. Williams, Can. J. Phys. 65, 1251 (1987).

89J. Mattson, P. Granberg, L. Lundren, P. Nordblad, G. Kenning, and J .A. Cowen, JMMM
104-107, 1621 (1992).

9°C. Dekker, A.F.M. Arts, and H.W. de Mjn, J. Appl. Phys. 63, 4334 (1988); Ibid, Phys.
Rev. B38, 8985 (1988).

91P. Svedlindh, P. Granberg, P. Norblad, L. Lundgren, H.S. Chen, Phys. Rev. B35, 268
(1987) .

92P. Granberg, P. Nordblad, P. Svedlindh, L. Lundgren, R. Stubi, G.G. Kenning, D.L.
Leslie-Pelecky, and J.A. Cowen, J. Appl. Phys. 67, 5252 (1990).

931 . Mattsson, P. Granberg, P. Nordblad, L. Lundgren, R. Loloee, R Stubi, J. Bass, and
J.A. Cowen, JMMM 104-107, 1623 (1992).

94]. Mattsson, P. Granberg, P. Nordblad, L. Lundgren, R. Stubi, D.L. Leslie-Pelecky, J.
Bass, and J. Cowen, Physica B165-166, 461 (1990).

95C. Dekker, A.F.M. Arts, H.W. de Mjn, A.J. ban Duyneveldt, and J.A. Mydosh, Phys.
Rev. Lett. 61, 1780 (1988); ibid., Phys. Rev. B40, 11243 (1989); J.A. Mysosh, JMMM
90&91, 318 (1990).

96DD. Awschalom, J.M. Hong, LL. Chang, and G. Grinstein, Phys. Rev. Lett. 59, 1733
(1987)

”AG. Schins, A.F.M. Arts, H.W. de Wijn, L. Leylekian, B. Vincent, C. Paulsen and J.
Hammann, J. Appl. Phys. 69, 5237 (1991).

98J.A. Cowen, G.G. Kenning, and J .M. Slaughter, J. Appl. Phys. 61, 4080 (1987).

99R. Stubi, D.L. Leslie-Pelecky, and J .A. Cowen, J. Appl. Phys. 67, 5970 (1990).

100R. Stubi, L. Hoines, R. Loloee, I. Kraus, J.A. Cowen, and J. Bass, Europhys. Lett. 19,
235 (1992). Part of the work in this paper is part of this thesis.

101R. Stubi, J. Bass, and J.A. Cowen, J. Appl. Phys. 69, 5054 (1991).

102S.S.P. Parkin, N. More, and KP. Roche, Phys. Rev. Lett. 64, 2304 (1990); W.R.
Bennet, W. Schwarzacher, and W.F. Egelhoff, Jr., Phys. Rev. Lett. 65, 3169 (1990); P.

157

 

Grflnberg, R. Schreiber, Y. Pang, M.B. Brodsky, and J. Sowers, Phys. Rev. Lett. 57, 2442
(1986)

103MB. Salamon, S. Sinha, J.J. Rhyne, J.E. Cunningham, R.W. Erwin, J. Borchers, and
GP. Flynn, Phys. Rev. Lett. 56, 259 (1986) and references within.

l"4C.P. Flynn, F. Tsui, M.B. Salamon, R.W. Erwin, an 1.]. Rhyne

l05P. Granberg, J. Mattsson, P. Nordblad, L. Lundgren, R. Stubi, J. Bass, D.L. Leslie-
Pelecky, and J.A. Cowen, Phys. Rev. B44, 4410 (1991); J. Mattsson, P. Granberg, P.
Nordblad, L. Lundgren, R. Stubi, J. Bass, R. Loloee, and 1A Cowen, JMMM 104-107,
1619 (1992).

1“SF. Edwards and P.W. Anderson, J. Phys. F6, 1923 (1976); Ibid, F5, 965 (1975).

107D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 62, 1972 (1975).

1"3K Binder and AP. Young, Rev. Mod. Phys. 58, 801 (1986).

10”LR. Walker and RE. Walstead, JMMM 31-34, 1289 ( 1983).

110A. Chakrabarti and C. Dasgupta. Phys. Rev. Lett. 56, 1404 (1986).

“1MB. Fisher, Advanced Courseon Critical Phenomena, (1982).

112ME. Fisher, in "Critical Phenomena", Proceedings of the 51st Enrico Fermi Summer
School, Varenna, Italy (M.S. Green, ed.), Academic Press, New York.

113B. \Vrdom, "Fundamental Problems in Statistical Mechanics", Vol. III, Ed. E.V.G.
Cohen, North Holland (1975).

“‘AE. Ferdinand and ME. Fisher, Phys. Rev. 185, 832 (1969).

115W. Kinzel and K. Binder, Phys. Rev. B29, 1300 (1984); AP. Young, Phys. Rev. Lett.
50, 917 (1983).

116L. Sandlund, P. Granberg, L. Lundgren, P. Nordblad, P. Svendlindh, J.A. Cowen, and
G.G. Kenning, Phys. Rev. B40, 869 (1989); P. Granberg, P. Nordblad, P. Svendlindh, L.
Lundgren, R. Stubi, G.G. Kenning, D.L. Leslie-Pelecky, J. Bass, and J.A. Cowen, J. Appl.
Phys. 67, (1990).

117C. Dekker, A.F.M. Arts, H.W. deWijn, A.J. van Duyneveldt, and J.A. Mydosh, Phys.
Rev. Lett. 61, 1789 (1988); J.A. Mydosh, JMMM 908191, 318 (1990).

“3 J .M. Slaughter, W.P. Pratt, Jr. and RA. Schroeder, Rev. Sci. Instrum. 60, 127 (1989).

J.M. Slaughter, Ph.D. Thesis

“9 Angstrom Sciences, PO. Box 18116, Pittsburgh, PA 15236.

‘20 Tosoh SMD Inc. 3515 Grove City Rd, Grove City OH 43123-3099 (Formerly Varian)

12‘ Demetron Inc. 235 Tenant Ave. Morgan Hill, CA 95037 (old address)

122 J ohnson-Mathey Electronics E. Euclid Ave, Spokane WA 99216 (Formerly Cominco)

‘23 Signum Cohn Corp. 121 8. Columbus Ave. Mount Vernon, NY 10553

‘24 Silicon Quest International, 2904 Scott Blvd, Santa Clara, CA 95054

125 Martin Mastovich, Noran Instruments, private communication, (608) 831-6511

126See E.W. Nuffield, X-ray Diffraction Methods, John Wiley and Sons Inc, NY pg. 148
(1966)

127W.B. Pearson, A Handbook of Lattice Spacing and Structures of Metals and Alloys
Pergamon Press Inc. (1958).

128RF. Miceli, D.A. Neumann, and H. Zabel, Appl. Phys. Lett. 48, 24 (1986).

158

 

129A. Segmuller and AB. Blakeslee, J. Appl. Cryst. 6, 19 (1973).

130D. Neerinck, H. Vanderstaeten, L. Stockman, J.P. Locquet, Y. Bruynseraede, and Ivan
K. Schuller, J. Phys: Cond. Mat. 2, 4111 (1990).

131CV. Thompson, LA Clevenger, r. DeAbillea, E. Ma, and H. Miura, Mat. Res. Soc.
Symp. Proc. 187, 61 (1990).

132D.G. Stearns, M.B. Stearns and Y. Cheng, 1H. Stith, and NM. Ceglio, J. Appl. Phys.
67, 2415 (1990); R. Pretorius, Vacuum, 41, 1038 (1990).

133L. Slaughter, P.A. Kearney, D.W. Schulze, C.M. Falco, CR Hills, E.B. Soloman, and
RN. Watts, Proc. SPIE 73, 1343 (1990); E. Fullerton, J.E. Mattson, S.R. Lee, C.H.
Sowers, Y.Y. Huang, G. Felcher, S.D. Bader, and RT. Parker, JMMM 117, L301 (1992).

l34D.A. Howell, L. Hoines, M.A. Crimp, J. Bass, and J.W. Heckman, Proc. 51st Annual
Meeting of the Microscopy Society of America, eds. G.W. Bailey and CL. Rieder, 1098
(1993)

135]. Liu et. al., Ultramicropscopy, 40, 352 (1992); P. Donovan et. al., J. Appl. Phys. 69,
1371 (1991).

136see e.g. L. Lundgren, P. Svedlindh, and O. Beckman, JMMM 25, 33 (1981);

137Handbook of Chemistry and Physics, ed. R.C. Weast, CRC Press Inc. (1986-7).

1331 Bass, Landolt-Bornstien: Numerical Data and Functional Relationships in Science
and Technology, Springer-Vedag Press, III/151, (1982)

13918. Kouvel, C.D. Graham, and LS. Jacobs, J. Phys. Radium 20, 198 (1952).

l‘“’G.N. Parker and W.M. Saslow, Phys. Rev. B38, 11718 (1988).

1“W. Abdul-Razzaq and J.S. Kouvel, Phys. Rev. B35, 1764 (1987).

142AD. Gezalyan and S.V. Shul'pekova, JETP Lett., 54, 47 (1991).

1”RM. Roshko and W. Ruan, J. Phys. I France, 1, 1809 (1991). H. Kunkel, R.M. Roshko,
W. Ruan, and G. Williams, Phil. Mag. B63, 1213 (1991).

144J.S. Kouvel, W. Abdul-Razzaq, and Kh. Ziq, Phys. Rev. B35, 1768 (1987).

145 I. Mirebeau, S. Itoh, S. Mitsuda, T. Watanabe, Y. Endoh, M. Hennion, and P.
Calmettes, Phys. Rev. B44, 5120 (1991).

l45R.M. Roshko and W. Ruan, J. Phys: Condensed Matter, 4, 6451 (1992).

147W. Koster and W. Rauscher, Z. Metallik. 39, 178 (1948).

148W. Abdul-Razzaq and M. Wu, J. Appl. Phys. 69, 5078 (1991).

   

"11111111111111