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This is to certify that the

dissertation entitled

The Structural Changes and
Their Effects upon the
Magnetic Properties of
Ultrathin Fe Layers

presented by

Heekyung Sung

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Physic s

 

Uta/1,42”. {0444/

Major professor

 

Date December 21, 1990

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MSU I: An Affirmative Action/Equal Opportunity Institution

chM-DJ

 

STRUCTURAL CHANGES AND THEIR
EFFECTS UPON
THE MAGNETIC PROPERTIES OF
ULTRATHIN Fe LAYERS

By
Heekyung Sung

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1990

ABSTRACT
STRUCTURAL CHANGES AND THEIR EFFECTS UPON
THE MAGNETIC PROPERTIES OF ULTRATHIN Fe LAYERS
By
Heekyung Sung

Ultrathin Fe/ Si, Fe/Mo, Fe/ V and Fe/ Cr metallic multilayers have been pre-
pared with a UHV sputtering system. The individual layer thickness is between 3
monolayers(ML) and 40 ML. Sputtered Si is amorphous while the lattice parameter
mismatches between bulk crystalline constituents are 9%, 5% and 0.6% in Fe/Mo,
Fe/ V and Fe/ Cr respectively.

Standard reflection X-ray difi'raction(XRD), transmission electron diffrac-
tion(TED) and limited EXAFS data were used for structural studies. Fe layers in
Fe/ Si are structurally isolated(non-coherent). For layer thickness of 3 10A, amor-
phous Fe layers were observed in Fe / Si and these amorphous Fe layers were non-
magnetic. Fe/ Mo, Fe/ V and Fe/ Cr systems form coherent structures with a perpen-
dicular coherence length of at about ~ 200A. Strained layer superlattices(SLS) have
been directly observed in Fe/ V and Fe/Mo for the first time using TED. The double
BCC to single BCC transition in the layer planes occurred at bilayer thickness ~
32ML in Fe/V and ~16ML in Fe/Mo. XRD data were consistent with TED data
but suggested that the strain was unisxial.

The saturation magnetizations of Fe multilayers at thin layer thicknesses were
closely related to the lattice mismatches. Fe/Mo lost its magnetism abruptly at a
layer thickness between 3ML and 6ML while the reduction in Fe/V was gradual.
Fe/ Cr retained bulk-like magnetism over all the thickness range indicating little
structural change in the Fe layers.

Anomalously large saturation fields and magnetic anisotropy have been ob-
served in Fe/ Cr. The antiferromagnetic coupling between magnetic Fe layers, known
to exist in Fe/ Cr, is believed to be responsible for these large saturation fields and

anisotropy.

To my mother and father

iii

Acknowledgements

I wish to thank Professor Carl Foiles for his support and patient guidance through
my thesis work. Without his help it would not have been possible to finish this
thesis.

I would like to thank Professors J. Cowen, T. Kaplan, J. Linnemann and
W. Lynch and for their service as my Ph. D guidance committee and Professor J.
S. Kovacs for his warm encouragement during my initial stage at Michigan State
University.

I am also indebted to W. Abdul-Razzaq, C. Fierz and R. Loloee for helping
me in operation of the sputtering system.

Most of all I would like to thank my wife, Hyeran, for her loving and patient
support during the course of my thesis work.

The support of the Michigan State University Center for Fundamental Ma-
terials Research is gratefully acknowledged.

iv

Contents

1 Introduction

1.1 Motivation .................................
1.2 Basic structure ..............................
1.3 Experimental environments .......................

2 Sample preparation

2.1 Introduction ................................
2.2 Substrates and samples ..........................
- 2.3 Sputtering sources and gun parameters .................

3 Structural studies with XRD and TED
3.1 Experimental method ...........................
3.2 X-ray model calculations .........................
3.2.1 Ideal superlattices .........................
3.2.2 Nonideal superlattices ......................
3.3 Experimental data(X-ray and TED) ...................
3.3.1 Measurements of basic sample parameters ...........
3.3.2 Fe/a-Si system (Crystalline/ Amorphous) ............
3.3.3 Fe/ transition metal systems (Crystalline/ Crystalline) .....
3.3.4 Observation of metallic SLS ...................

4 Magnetic properties

4.1 Measurements of magnetic data .....................
4.2 Saturation magnetization of Fe multilayers ...............

ll

16
17
19
19
27
33
33
38
44
48

4.2.1 Fe/ Si system ........................... 70

4.2.2 Fe/ transition metal system .................... 73
4.3 Saturation magnetic fields and magnetic interlayer coupling ...... 77
EXAFS studies 89
5.1 Introduction ................................ 89
5.2 Experimental techniques ......................... 93
5.3 EXAFS analysis .............................. 94
5.3.1 Background removal ....................... 95
5.3.2 Fourier transform filtering .................... 95
5.3.3 Curve fitting ............................ 97
5.4 Structural changes observed by EXAFS in metallic multilayers . . . . 101
5.4.1 EXAFS data of Fe/ Si multilayers ................ 102
5.4.2 EXAFS data of 3ML Fe/ t ML Mo systems ....... I . . . . 105
Summary and recommendations ' 115
6.1 Structure and magnetism ......................... 115
6.2 Magnetic interlayer interaction in Fe/Cr ................ 117
6.3 Recommendations ............................. 118

vi

List of Tables

2.1

3.1

4.1
4.2

5.1

5.2

Gun parameters for each constituent of the Fe multilayers. ...... 14

Structural parameters of elements used for the metallic multilayers in

this thesis and their magnetic properties. From the CRC Handbook

of Chemistry and Physics 66th ed. 1985. ................ 47
The magnetic data of Fe/ V samples. H ,4 = 41M; is well satisfied. . . 80
The magnetic data of Fe/Mo samples ................... 80

The number of Fe atoms and Mo atoms in the first 4 nearest neighbor
shells of the Fe atoms in an ideal 3 ML Fe(110)i layer with thick Mo
layersonbothsides. ............ 113

The optimum fitting parameters of the EXAFS data for the Fe/Mo
systems considering only the first 2 Fe atomic shells ........... 113

vii

List of Figures

1.1 Basic structure of an ideal multilayer. The unit cell consists of N 4
atomic layers of element A and N 3 atomic layers of element B with
the lattice spacings d; and d3 respectively ................ 3
1.2 Structural orders inherent in multilayers. Reflection XRD is sensitive

to the PSCL. After Fujii[2] ........................ 5

2.1 Schematic block diagram of the MSU sputtering system. After J .M.
Slaughter, Ph. D. thesis, Michigan State University, 1987 ....... 10

2.2 Atomic flux control in the MSU sputtering system. Far separation
between sputtering sources and collimation of each atomic flux ensure .

no intermixing between the two fluxes at the substrate. ........ 12

3.1 The geometry of the standard reflection X-ray diffraction . The scat-
tering vector is perpendicular to the sample plane ............ 18
3.2 One dimensional ideal superlattice model with a perfectly periodic
structure. (a) step model (b) trapezoidal composition and d-spacing
modulation model. ............................ 20
3.3 Step model calculation of (15ML Fe/15ML V)20. In (a) the Laue
function LNU) is drawn (b) is the structure factor squared of a bilayer
and (c) is the X-ray intensity. ...................... 23
3.4 Step model calculation demonstrating the effect of the layer thickness . 25
3.5 Step model calculations of (15ML Fe/15ML Mo)20 demonstrating the

effect of the relative difference in lattice spacings, 6 ........... ‘26

viii

3.6

3.7

3.8

3.9

3.10

3.11

3.12

3.13

3.14

3.15

3.16
3.17

3.18

Trapezoidal composition model(solid line) and step model(dotted line).
N4 = N5=10 ML, Np = NR=5 ML. Intermixing reduces the intensi-
ties of the satellites ............................. 28
Model calculations with continuously distributed amorphous layer

thicknesses. a is the width of the Gaussian distribution and c is

the thickness of the a-Si layer. (20ML Fe/50A a-Si)10. ........ 30
The effect of the discrete fluctuation of layer thickness on high angle
X-ray diffraction of (15ML Fe/15ML Mo)20. ..... - ......... 32

Evolution of simulated high-angle spectra of (15ML Fe/15ML Mo)20
for crystalline layers having a continuous distribution of interface dis-
tances. The half width 0 is given in units of the d-spacing of Mo
layer ..................................... 34

Experimental diffraction spectra of a sample with nominal parameters

(15ML Fe/15ML Mo)28 (a)harmonics (b)satellites. The average line

is denoted by a vertical line. ....................... 35
The plot of satellite data for sample #199-1 as q versus at. The slope
1s21r/A ........ 37
(a)low angle and (b)high angle X-ray diffraction of a sample ,#187~2,
with a nominal thickness of 462A ..................... 39
Plot of the small oscillation data of sample #187-2; 03,. vs. (m + k)“.
The slope is A/4t’. ............................ 40
The low angle harmonics of (18AFe/50ASi)40 which verify the com-
positional modulation. .......................... 42
The high XRD of Fe/SOA Si. No satellites are visible and the finite

size broadening is evident. Sapphire Bragg lines are seen at about 42°. 43

Data plot of the intensities of Fe(110) lines versus Fe thickness squared. 45

TED data of Fe/ Si multilayer systems. The Fe layer thicknesses are
20 ML(a) 12 ML(b) and 4 ML(c). After C. L. Foiles ...... '. . . . 46
Low angle harmonics of (3 ML Fe/tMo Mo)N samples. (a)tM,:12 ML
(b)tM.=8 ML (c)tM.=3 ML ........................ 49

ix

3.19 High angle reflection lines of (3 ML Fe/tu. Mo)M samples. (a)tu.=12
ML (b)tu.=8 ML (c)tu.=3 ML. ....................

3.20 High angle reflection lines of samples having equally thick of Fe and
Mo layers. .................................

3.21 Measured d-spacings from the average Bragg lines of each multilayer.

The horizontal lines near each data set denote the average d-spacings
using the bulk values of d(110) for each metal ..............

3.22 The linear relation of the average d-spacing, J, and the fraction of Fe
in a bilayer for Fe/ V systems. ......................
3.23 A cubic object. ..............................

3.24 The structure factor squared and the Laue functions of three step
models. ..................................

3.25 The ratios [0/ 1+ of three step models versus A. (a)Fe/Mo system (b)
Fe/ V system. ...............................

3.26 The TED data for a A =15 ML Fe/V sample. The Bragg peaks are
_ identified as those of a single BCC lattice. ...............

3.27 The TED data for two Fe/ V samples having different A’s (a) for A =60
ML (b)for A =12 ML. ..........................

3.28 The TED data for Fe/Mo samples having different A’s (a) for A =30
ML (b)for A =12 ML. ..........................

3.29 The relative differences of the two lattices parameters versus 1/ A in

Fe/ V and Fe/Mo samples using TED data ................

4.1 The magnetization curves in parallel and perpendicular magnetic fields
for a Fe/ V multilayer. Extrapolating the high field part to zero field
gives the value of M3 = 1600ernu/cm3 at 5K for Fe ...........

4.2 The saturation magnetizations for various Fe multilayers as a function
of Fe thickness at 5 K. As the Fe layer thickness increases, the value
of bulk Fe, 1740 emu/m3, is approached. ...............

51

52

55
56

60

62

65

68

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10
4.11

5.1

5.2

Magnetically dead layers in a Fe/ Si model system. The Fe layers at

the interface with a-Si have a thickness 24 and are assumed to be
nonmagnetic. ............................... 71
Data plot of (Mo — M) /Mo versus l/tp. of Fe/ Si for multilayers. The
slope is the thickness of nonmagnetic Fe layers in the magnetic dead

layer model; 34 = 10.2.4 in this plot. .................. 72
Saturation magnetization of 3 ML Fe layer samples as functions of

the nonmagnetic layer thickness ...................... 75
Average atomic moments of binary alloys of the elements in the Fe
group. (Bozorth.) ............................. 76
The magnetization curves in parallel and perpendicular fields for (a)5ML
Fe/5ML Cr and (b) 5ML Fe/20ML Cr superlattices ........... 81
The magnetization curves of 7ML Fe/ t ML Cr samples in parallel field.

The saturation field H5 decreases systematically as the Cr thickness
increases. ................................. 82
The systematic change of saturation field H5 as a function of the Cr
thickness. Data for samples with different Fe thickness are plotted
separately .................................. 83
Plot of AH = HA — 41M; versus the Cr layer thickness. ....... 86
Plot of AH versus H5. The high degree of linear correlation between

the two parameters is clear for positive values. Note also that negative

. AH is always associated with very low H5 values. ........... 87

Total electron yield spectrum of a polycrystalline Fe foil. The sharp
rise in yield near 7112 eV is the Fe K edge and the modulation above
the edge is the EXAFS. ......................... 90
The origin of the EXAFS. The outgoing photoelectron wave(solid
lines) and backseattered photoelectron wave(dashed lines) interfere
at the center of the absorbing atom and thereby modulates the ab-
sorption cross-section. After T.M. Hayes and J .B. Boyce[2] ....... 92

5.3 Standard experimental geometry of EXAFS experiments. ....... 96
5.4 k’ch) derived from fig. 5.1 by removing smooth backgrounds using

a polynomial spline fit. The photon energy he: has been converted to

the photoelectron momentum k ...................... 98
5.5 The magnitude of the Fourier transform of the curve in fig. 5.4. The

dashed line denotes a window function used to isolate the EXAFS

signal of the first peak. The 4 arrows indicate the actual positions of

the first 4 nearest neighbors ................... ' ..... 99
5.6 Inverse transform of Fourier transformed data in fig. 5.4 after multi-

plication by the window function shown in fig. 5.5. The dotted curve

is the simulated EXAFS using only the first 2 Fe neighboring shells. . 100
5.7 X-ray absorption spectra of two Fe/ Si multilayers measured by the

fluorescence detection method ....................... 103
5.8 Extracted EXAFS spectra k3x(k) for two Fe/ Si multilayers after re-
moving backgrounds. ......................... ~ . . 104

5.9 Fourier transform magnitudes of k3x(lc) in fig.5.8. The FT magnitude .
of 30A Fe layers clearly shows higher order peaks indicating BCC

crystalline structure. ........................... 106
5.10 Observed(solid lines) and calculated(dotted lines) EXAFS data. The
fitting parameters for the simulated curves are given in the text. . . . 107

5.11 Pure EXAFS spectra of 3/t Fe/Mo samples. Note the difference in
the period and envelope function of the EXAFS of the 3/3 system
compared to the other spectra ....................... 108
5.12 FT magnitudes of the EXAFS data of 3/ t Fe/Mo samples in fig.5.11.
The first peak in the FT magnitude of the 3/3 samples is shifted
toward shorter distances relative to the others .............. 109
5.13 Observed(solid line) and calculated EXAFS spectra for 3/t Fe/Mo
systems. (a)3/3 (b)3/4 (c)3/8 (d)3/12. The 3/3 system is not fitted
very well by the 2 Fe shell model. .................... l I l

xii

Chapter 1

Introduction

1.1 Motivation

The fabrication of ultrathin metallic films and multilayers is an expanding research
area that has produced exciting results associated with elastic anomalies[1], magnetic
properties[2][3], superconductivity[4] , transport properties[l] and X—ray reflectivities
of sufficient strength~ to produce mirrors[5]. .

The main research field of this thesis lies within the area of magnetic prop-
erties of ultra thin metallic layers. The magnetic properties of ultrathin magnetic
layers are interesting from both the fundamental and applied point of view. Funda-
mental properties which can be studied with ultrathin magnetic layers include two
dimensional magnetism, surface and interface magnetism and new magnetic struc-
ture from artificially layered structures involving antiferromagnetic coupling between
ultrathin magnetic layers. Magnetic mass data storage offers a possible application
of this field.

For the purpose of this thesis ultrathin denotes layers with thicknesses be-
tween 3 and 40 atomic monolayers(ML). Investigation of ultrathin magnetic layers
can be devided into three basic approaches. In one approach the layer of interest
maintains a free surface and is grown upon a substrate chosen to control the struc-
ture of the layer. Surface science techniques and theoretical consideration of broken

symmetry are essential in this approach. The second approach is similar to the first

and continues on to study effects as a controlled overlayer is added to the previ-
ously free surface. The third approach involves numerous ultrathin magnetic layers
and incorporates them into some type of periodic multilayered structure. Controlled
symmetries can be produced and the possibility of interactions between magnetic
layers must be considered.

This thesis uses the third approach, multilayers. The advantages of this ap-
proach are as follows: (i) Structural change in the magnetic layers can be induced
by combining the magnetic layers with various materials having difl'erent structures.
(ii) Due to the multilayered structure, a large number of magnetic layers are in-
volved giving strong magnetic signal for easier measurements. (iii) The multilayered
structure also offers an opportunity to observe the possible magnetic interlayer in-
teraction between magnetic layers. The difficulty in obtaining suficiently detailed
structural information for a multilayered structure and its buried interfaces is one of
the disadvantages of this approach. Solving this difficulty is a main subject in this

thesis.

1.2 Basic structure

A metallic multilayer is made by depositing two elements alternatively on a proper
substrate. The building block of a multilayer is a bilayer which consists of N 4
atomic monolayers(ML) of element A and N3 atomic monolayers of element B as
shown in fig.1.l. Our typical multilayers repeat the bilayer for M cycles to give
a total thickness of approximately 1800.4. The periodicity (or the compositional
modulation wavelength) A is given by

A=(NA-1)d,,+(N3-1)d3+2¢l (1.1)

where JA and d3 are the lattice spacing of element A and B, and J is their average
value which we take as the spacing between two unlike atoms at interface. We will
denote a multilayer by (N ,4 ML A / N3 ML B)M. This one has N A monolayers of A
and N3 monolayers of B in a bilayer and it is repeated M times. The resulting struc-

ture is referred to as an artificial superlattice. The distinction between superlattice

 

 

 

 

 

------._-_—---—-

 

 

 

Figure 1.1: Basic structure of an ideal multilayer. The unit cell consists of N 4 atomic
layers of element A and N3 atomic layers of element B with the lattice spacings (1,,

and «13 respectively.

4

and multilayer varies with different authors but, generally, a multilayered structure
with a high order of structural coherence is called a superlattice.

An artificial superlattice is an inherently metastable structure and relies for its
existence on slow intraplane kinetics(during the growth process) and slow interplane.
diffusion(during and after the growth process). The metastable nature of artificial
superlattices suggests that they may be engineered to have material properties which
might not be otherwise attainable. This is a major motivation for the large current
interest in these materials.

An understanding of the physical properties (magnetic properties in this the-
sis) requires careful measurements of both the crystalline structures involved and
the extent of their commensurateness. We define two coherence lengths in describ-
ing the structural order. PSCL is the perpendicular structural coherence length and
is associated with the multilayer structure perpendicular to the substrate surface
while TSCL is the transverse structural coherence length and is associated with the
structure in planes parallel to the substrate surface. In fig.1.2 some possible struc-
tural disorders related to 9301. or TSCL are illustrated. Disordered interfaces due
to lattice mismatch, intermixing and irregular periodicity reduce the PSCL and the
formation of many randomly oriented grains reduces the TSCL.

1.3 Experimental environments

Fe is the magnetic layer of interest in this thesis and we have made Fe/ Si ,Fe/ Mo,Fe/ V
and Fe/ Cr multilayers in an effort to systematically change the environments of the
Fe layers. Sputtered Si is amorphous. The transition metals used for our metallic
multilayers have BCC crystal structure as their natural bulk structure. Bulk Mo,V
and Cr have the lattice parameter mismatches with bulk Fe of about 9%, 5% and
0.6% respectively. Recently the Fe/ Cr system has attracted special interest. Antifer-
romagnetic interlayer coupling between the ultrathin magnetic Fe layers across the
Cr interlayer has been observed by various groups.[6] [7] [8] The rare earth magnetic

superlattice Gd/ Y is another example of magnetic interlayer coupling; coupling be-

 

Degree of Order

Low High

 

 

     
     

 

 

 

 

 

 

 

 

 

 

 

1,” COMDOSIIIOH I l l I I
ill 1 Nil: 6...... I I I I
Graded Sharp
.5. ‘ Layer
PSCL {:34 Structure
Amorptmus Crystalline
Irregular Perlect

 

           

 

   

 

dflW/fi'

TSCL "“ ”(W ' Domain {1’ llllfl
7 unm'um .
PO'Y' Sungle-X'tal

 

 

 

 

Figure 1.2: Structural orders inherent in multilayers. Reflection XRD is sensitive to

the PSCL. After Fujii[2]

tween the Gd layers can be made ferromagnetic or antiferromagnetic by varying the
Y layer thickness .[9] Since the combinations of bulk Fe and Cr, and bulk Cd and
Y have BCC and HCP structure respectively with nearly identical lattice parame-
ters, these systems have produced a belief that large coherence lengths are crucial
in controlling magnetic coupling.

In this thesis magnetic properties(saturation magnetization and magnetic
anisotropy) of ultrathin Fe layers in various multilayer systems will be tested. Chap-
ter 2 describes the sample preparation conditions and procedures with the MSU
sputtering system. Chapter 3 discusses the structural characterization of the metal-
lic multilayers using standard reflection X-ray diffraction(XRD) and transmission
electron diffraction(TED). In chapter 4 the magnetic properties of Fe multilayers
are presented and in chapter 5 some limited EXAFS(extended X-ray absorption fine
structure) data for Fe multilayers is discussed. EXAFS data provide measurements

of local order that can be important in understanding magnetic behavior.

Bibliography

[1] R. C. Cammarata, Scripta Metallur. Q, 479 (1986)

[2] T. Shinjo and T. Takada, Metallic superlattices (Elsevier Science Publishers
B.V., 1987)

[3] B. Y. Jin and J. B. Ketterson, Advances in Physics E, 189 (1989)
[4] S. T. Ruggiero, Superlattices and Microstructures l, 441 (1985)

[5] Troy W. Barbee, Jr. , in Synthetic Modulated Structures, edited by L.L. Chang
- and B.C. Giessen ( Academic Press, 1985)

[6] S.S.P. Parkin, N. More and K.P. Roche, Phys. Rev. Lett., 93, 2304 (1990)

[7] M.N. Baibich, J .M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Eitenne,
A. Friederich, and J. Chazelas, Phys. Rev. Lett., 3;, 2472 (1988)

[8] C. Carbone and S. F. Salvarado, Phys. Rev. B. 36, 2433 (1987)

[9] C.F. Majkrzak, J.W. Cable, J. Kwo, M. Hong, D.B. McWhan, Y. Yafet, J.V.
Waszczak, and C. Vettier, Phys. Rev. Lett., Q6, 2700 (1986)

Chapter 2

Sample preparation

2.1 Introduction

There are numerous epitaxial methods available nowadays for preparation of arti-
ficial metallic superlattices; MBE (Molecular Beam Epitaxy), vacuum evaporation
and sputtering have been most widely used. A system to prepare a superlattice
might be broken down into the following components or functions.[1]

(1) Sources to produce atomic fluxes of the desired constituents of the superlattices.
(2) Means to position the substrates alternatively over the sources.

(3) Methods to mount the substrates and maintain the substrate temperature.

(4) A deposition chamber to establish the desired ambient background conditions
such as high vacuum or inert gas.

(5) Methods to control and monitor the fluxes.

With regard to the method of producing atomic fluxes we distinguish three
modes
(i)physical vapor deposition (PVD)
(ii)chernical vapor deposition (CVD)
(iii)electrodeposition
MBE, vacuum deposition and sputtering methods are categorized as PVD. PVD

has been carried out with thermal evaporation, electron beam heating and dc or rf

sputtering being the most commonly used techniques. A resistively heated crucible
containing a tight fitting cover with a small hole to allow the vapor to escape is
called an effusion cell.[2] The process 'of growing epitaxial films using an effusion
cell is referred to as MBE. Electron gun evaporation is accomplished by impacting a
beam of high energy( greater than 3 Kev) electrons on the material to be evaporated.
Sputtering is a very powerful method for depositing metallic superlattices. In the
sputtering process a plasma discharge is created by ionization of an inert gas(e.g. Ar)
and maintained above the target (source) when an” appropriate negative potential is
applied to the target. Target material is sputtered by the impact of energetic ions.
For a given power applied to the sputtering gun, the atomic flux is generally quite
stable with time until a substantial part of the target material has eroded. The
amount of fluxes and the kinetic energy of the sputtered atoms can be controlled by
adjusting the applied potential, the plasma current, the pressure of the sputtering
gas and the target-to-substrate distance.

All samples in this thesis were made with the MSU sputtering system and fig
.2.1.shows a schematic diagram of the MSU sputtering system. Although detailed
descriptions of this system have been presented by J .M. Slaughter and G. Kenning
[3][4][5] a brief review of them will be attempted in the next sections.

2.2 Substrates and samples

Substrates were mounted on the Substrate Positioning and Monitoring Apparatus
(SPAMA). Each substrate had a covering shutter. The SPAMA can accommodate 16
substrates so that 16 different samples could be made without breaking vacuum. To
make multilayered films the SPAMA was positioned alternatively over two sputtering
sources by a stepping motor which is controlled by an IBM-PC. Typically, two sets
of samples having the same nominal number of atomic planes per layer but different
sample total thicknesses were prepared. One set was prepared on polished c-axis
oriented sapphire (A1203) crystal substrates and had the bilayer thickness repeated
until a total sample thickness was about 1800A. This set was used for reflection X-

10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I®H€W€fl

 

 

 

I

 

 

 

 

1. Stepping motor

3. Rotary teedtnrough

S. Ionization gauge

7. wobble stick

9. Cold-trap gas purifier
11. Gas flow controller
13. Residual gas analyzer
15. Cats valve

17. Bellows sealed valve

19. Shutter assembly

 

12.
In.
16.
18.

20.

. Rotary teedthrough
. Heissner trap

. Convectron gauge

. UH? Ar tank

. Hydrox gas purifier

Rotary teedthrough
Cryopunp
Mechanical pump
SPAMA

Sputtering source

Figure 2.1: Schematic block diagram of the MSU sputtering system. After J .M.
Slaughter, Ph. D. thesis, Michigan State University, 1987

11

ray studies, EXAFS data collections and magnetic measurements. The second set
of samples was deposited on freshly cleaved NaCl substrates. These samples had
at least 5 bilayer distances and gave the total thickness of between 400.21 to 50021.
After reflection X-ray measurements the thinner samples were floated off the N 9.01

onto Cu grids to provide free standing films for TED studies.

2.3 Sputtering sources and gun parameters

Sputtering is the emission of the surface atoms of a target material by bombarding
it with energetic ions. We use Ar+ ions to bombard the targets. Sputtering is
done in a cylindrical stainless steel chamber of height 48 cm and radius 23 cm. The
sputtering chamber was pumped to S 0.5 torr with a mechanical pump and then
further pumped down to < l x 10" torr with a CTI cryopump and a Meissner trap.
Then ultra-high purity Ar gas was introduced into the chamber giving a pressure of
2.5 x 10‘3 torr.

Four Simard ”Tri-Mag” sputtering guns are mounted 90° from each other on
a circle of radius 14 cm. Targets with 99.9 % purity are mounted on each gun and
the target to substrate distance is 10 cm. About 50 ev energy electrons are passed
through the Ar flowing over the target to produce a plasma discharge. A negative
potential is applied to the target and the positive Ar+ ions are accelerated to the
target and bombard it .

Fig.2.2 is a schematic cross-sectional diagram to demonstrate the control of
the atomic fluxes. Atomic beams from the sputtering sources reach the substrate
after passing through a hole in the chimney top and then through a shutter mounted
on the SPAMA. If the deposition rate is measured as a function of angular displace-
ment from the center of the target it is found to drop to zero between 20 and 35
degrees depending on the size of the hole.[3] Considering that the sources are sepa-
rated by 90° and that the time between sources is approximately 0.2 sec it is clear
that the intermixing of two atomic fluxes is negligible. With the completion of a

given sample, its shutter is closed.

12

 

stepping motor _

 

 

 

 

 

 

 

SPAMA -———L 1
L.T‘ 1'

3' ll

chimn' ey———:IlTl :"l
i'i: '1'“

I';. I'll

Sputtering sources A 1 I B

 

 

 

 

Figure 2.2: Atomic flux control in the MSU sputtering system. Far separation
between sputtering sources and collimation of each atomic flux ensure no ,intermixing

between the two fluxes at the substrate.

13

The deposition rate can be changed by adjusting the Ar pressure, target-to -
substrate distance, the target potential and the plasma current. The gun parameters
used in this work were determined by trial and error with the constraint that the
substrate temperature should not be too hot. Too large Ar energies or total flux of
sputtered atoms cause thermal interdifl'usion and poor layering in samples.[5]

Temescal FTM-3000 quartz crystal film thickness monitors (FTM) are used
to determine the deposition rates prior to and directly after making samples. Desired
layer thicknesses in the samples are programmed into the computer which controls
the stepping motor attached to the SPAMA plate.

The gun parameters and the deposition rates of each constituent for the
multilayers in this thesis are summarized in table 2.1. For the all cases the Ar

pressure was kept at 2.5 x 10'3torr and the target to substrate distance was 10 cm.

14

 

 

 

Substance Target potential Plasma current Deposition rate
Fe 525 V 1.0 A 7.0 A/sec
Or 500 V 0.8 A 6.9 A/sec
v 725 v 1.1 A 7.3 A/sec
M. 320 V 1.1 A 7.9 Mac
Si 300 V 0.8 A 2.0 A/sec

 

 

 

 

Table 2.1: Gun parameters for each constituent of the Fe multilayers.

Bibliography

[1] B.Y. Jin and J .B. Ketterson, Advances in Physics, 18, 189 (1989)

[2] F. Reif,'Fundamentals of Statistical and Thermal Physics (McGraw-Hill Book
Company,1965)

[3] J .M. Slaughter, Ph. D. thesis , Michigan State University, 1987

[4] J .M. Slaughter, W.P. Pratt,Jr. and RA. Schroeder, Rev. Sci. Instrum. @, 127
(1989)

[5] G. Kenning, Ph. D. thesis, Michigan State University, 1988

15

Chapter 3

Structural studies with XRD and
TED

When we fabricate multilayers, in most cases a structural characterization is neces-
sary to confirm the successful growth of the desired samples. X-ray diffraction(XRD)
provides the most easily interpreted structural data characterizing a broad range of
multilayers. This technique is a nondestructive and readily available method, and
most of the measurements can be done in a standard reflection geometry while leav-
ing the sample on the substrate. The evolution of one-dimensional order along the
growth direction can be studied on a standard diffractometer.

X-rays scattered by individual atoms give rise to interference depending upon
the positions of the scatterers. The structural information from XRD includes
(i) the positions of the average Bragg lines and the surrounding satellite lines are used
to calculate the average lattice spacings and the average modulation wavelength.

(ii) the FWHM of the average Bragg line gives a perpendicular structural coherence
length (PSCL). For PSCL the Scherrer formula

_ 0.9A
- FWHAI cos 0M,

 

{l (3.1)

is used where A is the wavelength of X-ray and 0,4,“, is the position of the average
Bragg line.

(iii) The relative intensities of the satellites can give additional information about a

16

17

unit bilayer if the uniqueness of the bilayer model can be established.

In this chapter we describe the experimental setup for the X-ray diffraction
measurements, present the results of calculations based on various models of chemi-
cal and structural environments to demonstrate how diffraction patterns reflect the
structural characteristics of multilayers, and then analyze the data of actual samples.

Complementary data from TED studies are also discussed.

3.1 Experimental method

A Rigaku 0-20 diffractometer with Cu-K a radiation is used for all XRD measure-
ments. The wavelength(A) of Cu-Ka line is 1.540624.

Since multilayers are compositionally modulated in the growth direction(i.e .
perpendicular to the surface of the substrate), knowledge of the structure along this
direction is of primary interest. This knowledge can be achieved using a standard
reflection geometry which is shown in fig. 3.1. X-rays specularly reflected by mul-
tilayer film plane give rise to interference depending on the position of the atoms.

The scattering vector is perpendicular to the sample plane in this geometry and is

defined as

.7 = IE} — IE.- (3.2)
q = Icfl = 2k sin0
1;; and k; are the wave vectors of the incident and reflected X-rays respectively
and the magnitude is unchanged for elastic scattering with value I: = 21r/A. If
the lattice constant of the c-axis is chosen to be the modulation period A, we have

the reciprocal lattice constant C = 21r / A along this axis. A constructive interference

occurs whenever the scattering vector is an integral multiple of the reciprocal vector.
q = On = 21rn/A,n = integer (3.3)

Combining eq.3.2 and eq.3.3 leads to the well known Bragg’s law in kinematical

18

 

 

 

 

 

>CD>CD>

 

Figure 3.1: The geometry of the standard reflection X-ray diffraction . The scattering

vector is perpendicular to the sample plane.

19

diffraction
2A sin 0 = 1:) (3.4)

When our multilayer is grown successfully, the first order Bragg reflection (001) due
to the compositional modulation period appears at the scattering vector q = 21r / A,
or at the scattering angle given by 20 = 2 sin'l(A/2A). Higher order reflections
(00n) appear at positions expressed by integral multiples of G, q=nG.

3.2 X-ray model calculations

3.2.1 Ideal superlattices

For direct structural information it is necessary to know both the amplitude and
the phase of the scattered waves; unfortunately, only the intensity(the square of the
amplitude) is observed experimentally. Therefore one often has to make some model
calculations which yield only part of the information on the multilayer structures.
The model calculation is quite straightforward for a number of idealized geometries.
The ideal diffraction models which are most frequently used can be categorized as
follows.

(i) the step model : atomically sharp interface, bulk structural properties for indi-
vidual layers and no fluctuation in the modulation period.

(ii) the strain model : same assumptions as in the step model except different lattice
spacings from the bulk values arise due to the coherency strain.

(iii) the composition modulation model : intermixing over some region at interfaces

First we discuss the step model which shows the characteristic features of
difl'ractions of superlattices. The X-ray scattering amplitude of an ideally stacked

superlattice is just the sum of the atomic form factor over their relative distances.

PC = Lf(17)ezp(ié-F)d3r (3.5)
21rli
A

 

6:

20

 

 

 

 

 

A \l
NA IVs—4
eeeeeeeee d4

 

 

on
.S
U
('3
Q.
U)
L.
G)
>
to
._]
0000
0 A atoms
0 B atoms
A
co _ NA—a
C:
'8 eeeeeeeeeeee— d4
63 O
Q. 9 e
m e
3 .° °
>~ go o
‘3 o
"3 0000 ooocooo
*— F —" *R ”8—“

 

 

 

 

Layer number (n) ——r

 

ioooooooool—da

_d8

(8)

'(b)

Figure 3.2: One dimensional ideal superlattice model with a perfectly periodic struc-

ture. (a) step model (b) trapezoidal composition and d-spacing modulation model.

21

where (3 is the reciprocal vector of the superlattice with period A. In standard
reflection geometry, the scattering vector is along the growth direction so that the

eq.8.5 can be simplified as

 

 

 

M A
F, = gezfiiq(j—1)A)/; f(z)ecp(iqz)dz
sin(NqA/2) . _ n sin(quNA/2)
sin(qA/.2) waQMN 1V2" Af‘ sin(qu/2)
mi. "$1221: 72/)”cam/znnpliquzv. - mm (3.6)

The square of the scattering amplitude is the intensity of the reflected X-ray, and
for perfectly stacked superlattice with modulation period A and total thickness NA,
it is calculated as

Mr) = |F(«1)|’ = Li:(«1)|~‘5(¢1)l2 (3.7)

where
Lu(q) = sin'(<1AM/2)/sin’(¢1A/2) (3-8)
|S(q)|2 = nifi sin2 NAa/ sin2 a + ngffi sin2 Ngfi/ sin2 [3 . (3.9)

+2n4ngf4f3 cos(NAa + Ngfl) sin NAa sin Ngfi/ sin a sinfi

Here in and as are the atomic area densities, f4 and f3 are the atomic form factors
of metal A and B respectively, a = qu/Z and fl = qda/ 2.

In an actual experiment the measured intensity is not the same as eq. 3.6. A
number of correction factors affect the actual intensities. They are the Lorentz
factor 1/ sin(20),the polarization factor 1 + cos'(20), the absorption factor 1'—
erp(-2i1t/ sin 0) and the Debye-Waller factor ezp[(—23 sin’ 0/A’)]. Here ii and B
are the average absorption and Debye-Waller coefficients, respectively. A discussion
of these corrections can be found in the book by Cullity.[1] Including the above

corrections, the experimental diffraction intensity is given by

I(r1) = 1001)1 2:322:30)

The Laue function LM(q) is obtained by summing over the number of the bilayer

 

ezp(—ZB sin2 0/A2)[1 — erp(2flt/ sin0)]‘1 (3.10)

cycles and has its maximum M 2 at equally-distant positions given by integral multi-

ples of G = 21r/ A and its width is proportional to 1/MA in momentum space. This

22

function is shown in fig.3.3 The function 5 (q) is a layer structure factor reflecting
the structure within a bilayer. At low angles the structure factor has large value
due to the forward scattering . At high angles the Bragg reflections by individual
atomic spacings and their interference enhance the structure factor. The convolution
of the Lane function and the square of the structure factor produces reflection X-ray
peaks that are characteristic of superlattices. The Laue function, the square of the
structure factor and the final X-ray diffraction pattern of (15ML Fe/15ML V)20 are
shown in fig.3.3

For more understanding of the step model, we will check the effect of individ- V
ual layer thickness within a bilayer on the reflection pattern. The first two terms in
eq.3.9 are the diffraction functions of layer A and layer B, and the resulting pattern
consists of two broad peaks(the width or 1/N,-d,-,i = A, B) located at angles 04 and
03 which satisfy the Bragg conditions

2d4 sin 04 = ml (3.11)

ZdB sin 03 = m\

where m and n are integers. The third term in eq.3.9 is an interference term which
comes from the overlap of the diffraction peaks at 0,4 and 03 in the angular region
between these two angles. If NA and N3 are small as in fig.3.4 (a), the A and B
peaks are broad and there will be considerable overlap, and a single average peak
will appear at an angle between 04 and 03. In contrast, if N A and N3 are large
the line widths of peaks A and B are small and the overlap will be negligible. The
calculated diffraction patterns in fig. 3.4 clearly show this trend. In this calculation,
Fe and Mo are chosen as two constituents and equal numbers of atomic layers of two
metals are taken. The lattice spacings are dp. = 2.026821 and (134., = 2.2250131, and
their Bragg angles are 20;. = 44.67° and 20", = 40.51° respectively.

Now we consider the effect of the difference in the individual lattice spacings
on the X-ray diffraction pattern. If the difference is large the Bragg angles 0A and
03 are well separated as we see in eqs. 3.9 and 3.11; the function in eq.3.9 gives

individual Bragg lines with small overlap between them. On the other hand, if d A

23

 

400
300
200
100

(a)

IIIIIIIIIIIIIIIIIII1

 

 

 

 

 

 

 

 

 

 

 

 

 

400 *
300
200
100

1I1IIII1I|IIIIIIIII

 

 

 

100 *
80
60

40 f
2: All.
0

5 4 45 5O
26 (deg)

(C)

 

 

I"IIIIIIIIIIIIHIIIIIIII

 

 

00

Figure 3.3: Step model calculation of (15ML Fe/15ML V)20. In (a) the Laue function
Lu(l) is drawn (b) is the structure factor squared of a bilayer and (c) is the X-ray

intensity.

24

and d5 are very close, essentially only one Bragg line appears. As a result, a large
lattice spacing difference enhances the intensities of the satellites surrounding a weak
average line, and a small difference develops a strong average line and suppresses the
developments of the satellites as shown in fig.3.5 where 6 = (dA — dB)/maz(d4,d3)
is the lattice spacing difference and 15 ML of Fe, 15 ML Mo and 20 cycles of bilayers
are used.

Until now we have assumed an atomically sharp and abrupt interface. Now,
as the final ideal model calculation, we will consider the effects of interdiffusion at
the interfaces. The intermixing of atoms at interfaces is quite realistic when two
constituent elements are miscible or if the interfaces are atomically rough. Just for
the convenience of the calculation we assume a trapezoidal compositional modulation
where the atomic concentration and lattice spacing vary linearly over some region
of the interfaces. No fluctuation in the period is assumed. The structure factor
is calculated by summing up all atoms in the unit bilayer which is divided into 4
regions.(see fig.3.2)

The structure factor is obtained using Eq.3.2

S = S, + einpdSA + cMdi-f-NAJ‘)SR + eMNpJ+N‘d‘+Ngd)SB (3.12)

where S’s are the structure factors of the four regions, «I is the average lattice spacing,
N ,- and N n are the number of atomic layers with linear composition and the number
of atomic layers of pure metals A and B are denoted by N A and NB respectively.

The structure factors of each region are

Sp z : fpnp(z)e‘°" (3.13)
s. = f: mm“
53 = : fann(z)eiq"

53 = Zfsnseiq“

25

 

300 '-

200 (a) (sin. P's/3K1. Mo)100

I V l V U I I

100 *-

oil L

150

 

 

 

fr

I U

100 - (5) (ram. ire/ism. no)2o

50

'j—Tj 1 U

 

 

 

l A

 

 

 

E
125 r
100 r (c) (room. F's/100m. was

75:-

 

50E-

25E-

 

 

 

 

0 : h
35 40 45 50
26 (deg)

Figure 3.4: Step model calculation demonstrating the effect of the layer thickness .

26

 

150

6-20 x
100

50

 

 

 

150 _
' 6-10 3

rr

100 _-

 

 

 

 

I
300 :- “a

'I'

200 :-

TU.

 

100 r

.5 -1-

35 40 45 50
20 (deg)

Figure 3.5: Step model calculations of (15ML Fe/15ML Mo)20 demonstrating the

 

 

 

effect of the relative difference in lattice spacings, 6.

27

where the atomic scattering factors in each region are

 

 

fr = (fa - falN’: 1 + fa (3-14)
f4 = f4

fa = (fs — 1:.) N3, + f.

fs = fs

unnn are linear functions of the atomic area density at the interface regions and z.
is the position of the x-th atomic plane within each region. The square of eq.3.12 .
gives the intensity for a unit bilayer ;this function becomes the new IS (q)|’ in eq.3.8.
Results for a step model and a trapezoidal model of interfaces are compared in fig.
3.6. The major effect of interdiffusion at the interface is a reduction in satellite

intensities.

3.2.2 Nonideal superlattices

The previous results given for composition models have had very sharp reflection
lines because perfect periodicity has been assumed and thus the total thickness MA
was the coherence length. But in most metallic superlattices, the experimentally
observed high angle reflection lines are much broader than those predicted by simple
one dimensional models, such as the ”step” and the ”strain” model. Typical perpen-
dicular structural coherence lengths(PSCL) in the growth direction of our metallic
superlattice samples are about 200A, ranging from a few A’s to nearly 10A’s. The
PSCL is much shorter than the total sample thickness of ~ 1800.4, indicating that
some mechanisms are decreasing the long range order. Several mechanisms which
can cause this decrease are

(l) imperfections in the deposition process

(2) geometric constraints at the interfaces due to the difference in the lattice param-
eter and symmetry

(3) variations in growth mode and wetting

(4) interdiffusion and alloying

Practically all these mechanisms would limit the accurate control over the thick-

28

 

j

I

I '

 

 

 

 

 

 

 

 

 

 

 

35 40 45 5O
26 (deg)

Figure 3.6: Trapezoidal composition model(solid line) and step model(dotted line).
NA = N5=10 ML, N;- = Nn=5 ML. Intermixing reduces the intensities of the

satellites.

29

nesses of the individual layers by at least a few percent.

Recently X-ray model calculations assuming imperfect periodicity have been done by
two groups. Structural imperfections can be modeled as (i) a continuous layer thick-
ness distribution associated with the amorphous layer in a Crystalline/ Amorphous
system[2][3] (ii)a discrete distribution for the number of atomic planes in the layers of
a Crystalline/ Crystalline system[3] [5] and (iii) a continuous fluctuation of the inter—
face distance(the distance between unlike atoms) due to the lattice mismatch.[4][5]
Clemens and Gay[3] assumed fluctuations of a Gaussian type, continuous thickness
fluctuations for amorphous layers and discrete thickness fluctuations in crystalline

layers, and made kinematical X-ray diffraction calculations. The intensity is

1(9) = |D(¢1)I'IS(¢1)|2 (3-15)
5 (q) is the layer structure factor which is the same as in eq.3.2, D(q) is the Fourier
transform of the layer distribution function. For amorphous layers having a contin-
uous layer thickness distribution described by a Gaussian distribution of half-width
a about the average thickness c,

|D(q)|2 = N + ZERN - n) cos(n(NAdA + c)q)ezfl—na’q’fl) (3.16)

n=1

For a discrete thickness distribution where one of the layer thicknesses differs from
the average c by md with a probability e:1:p(—m’d2 / a”) and m is a integer,

N—l
|D(q)|2 = N + 2 221(N — n) cos(n(NAdA + c)q) (3.17)

x [1 + 2 : ezp(—m2d’/naz) cos(mdq)]

Calculated intensities using eq.3.16 are illustrated in fig. 3.7 for a 20ML Fe layer and
a 50.4 multilayer system. Sharp reflection lines are developed(fig. 3.7 (a)) with zero
fluctuation and as the distribution width 0 increases the lines rapidly become broad.
With a cr of 4% for the amorphous layer thicknesses only the finite thickness Fe layer

broadened line occurs and there is no trace of superstructure. We will see this kind

30

 

 

 

 

 

 

 

 

25:
20:— «=0
15E—

10E-

.oi‘———s + L an
2.5 E-
2.0 E- a=o.ozc
1.5 E-

1.0 _:_—
as g—
as ‘
2.0 a=o.04c
1.5

1.0
0.5
0.0 — A IL—l

 

40 42 44 46 48 50
26 (deg)
Figure 3.7: Model calculations with continuously distributed amorphous layer thick-
nesses. a is the width of the Gaussian distribution and c is the thickness of the a-Si

layer. (20ML Fe/SOA a-Si)10.

31

of behavior in our Fe/ Si system which will be discussed in the next section. On the
other hand, the diffraction intensity for a discrete fluctuation of layer thicknesses
shows superlattice peaks due to the superlattice structure image in eq.3.18. Fig.3.8
illustrates the calculation of ( 15 ML Fe/15ML Mo)20 for 3 values of the discrete
distribution width 0 where a is given in units of the lattice spacing of M0. The
reflection peaks remain rather sharp even for a considerable discrete distribution
width. This is the case for Crystalline/ Crystalline multilayers such as Fe/Mo and
Fe/ V systems in next section.

Locquet et al.[4] assumed that the distance at the interface between unlike
atoms fluctuates around an average value «1 following a continuous, Gaussian distri-
bution of width 0. They state, ”The origin of this fluctuation can be the perpen-
dicular lattice mismatch 6 = («14 — d3)/maz(d4,dg), with «1,4 and dB the lattice
spacings of the constituents, which is correlated with the in-plane lattice parameter
difference. The geometric conditions imposed by the latter create a ”rough” inter-
face, with large (atoms A forced on top of atoms B) and small (atoms A ”falling”
in between atoms B) interface distances, assumed to follow a Gaussian distribution
around an average value :1.” They note that this assumption is strictly correct for
incommensurate systems and only approximately correct for systems that have a
long-distance commensurate relationship. Incommensurate is understood to mean a
small PSCL. The total intensity is given by

Io(q) = N[Aa + B3 + ZABezfi—q’a'fl) cos(qA/Z)
+2 IVE-1(N — m)((A2 + B’)ezp(-2mq’a"/4) cos(2qu/2)
+A,B-elzp[—(2m + 1)q'a’] cos[(2m + 1)qA/ 2]
+ABezp[—(2m — 1)qzaz/4] cos[(2m — 1)qA/2)]) (3.18)

with

A = fA sin(NAqu/2)/ sin(qu/2)
= f3 sin(NBqu/2)/ sin(qd3/2)

For a' = 0, eq.3.18 reduces to the step model, while for a' z 00 it reduces to the

32

 

150 .
125
100

era-0.01:1

'U'l'nrii'I

50%-
'25;—

 

 

 

0 .
300,
250 :-
200
150
100
1000 A ‘ *
800 :' 17-2 :1
600 :-
400
200

UIU'U

owl-0.64

U'U'IWUIVUU

 

 

 

 

 

 

 

 

sssrlssrqsss

 

_lin

35 4O 45 5O
26 (deg)

Figure 3.8: The effect of the distrete fluctuation of layer thickness in high angle
X-ray diffraction of (15ML Fe/15ML Mo)20.

 

33

scattering of two independent blocks of materials A and B without any trace of
superstructure. Using eq.3.18, the high angle X-ray diffraction patterns of a (15ML
Fe/15ML Mo)20 multilayer was calculated for different values of distribution width 0.
A drastic decrease of the peak intensities together with an increase of the linewidths

occurred with increasing a and is shown in fig.3.9.

3.3 Experimental data(X-ray and TED)

3.3.1 Measurements of basic sample parameters

Among the structural parameters potentially available from standard reflection XRD,
two basic sample parameters are most easily obtained. They are the modulation pe-
riod A, and the average lattice spacing dAvg. As we discussed in section 3.3 the
positions of the reflection lines from the superstructure are determined by the Laue
function sin’(qAM/2)/ sin’(qA / 2) which has sharp peaks when the Bragg condition
for the modulation period A is satisfied.

2A sin6 = nA (3.19)

n = 1,2,3,- --

We can rewrite this equation as

q = EAL. (3.20)

where q = 9f- sin0 is the magnitude of the scattering vector. We get the modulation
period from eq.3.20. The average lattice spacing Java is

NAdA-f-Ngdg _ A
NA'i'NB —NA+NB

 

4...; = (3.21)

so the average Bragg line occurs when n = NA + N3 in eq.3.19 or eq.3.20. In fig.3.10.
experimental X-ray diffraction data are shown, (a)low angle harmonics (b)an average
line at 26 = 42.32° with satellites surrounding the average line. Hereafter the term
harmonics denotes reflection lines at low angle and satellites denote the high angle
peaks surrounding the average Bragg peak. The nominal parameters of this sample

are (30.4.4Fe/33.4.4Mo)28 which were intended to make a (15ML Fe/15ML Mo)28

34

 

150
125
100

""

III

UU'III

 

 

 

 

 

N
O 01
rrr I'Il' lmli
P

 

HH

.0!“

001
1'1
2:

0-0.25d

 

 

S"
O
I r ['7 Iii

.0
o

 

 

H
O

o-OAd

ITII'I

 

 

 

 

35 40 45 5O
26 (deg)

Figure 3.9: Evolution of simulatedhigh-angle spectra of (15ML Fe/15ML Mo)20 for
crystalline layers having a continuous distribution of interface distances. The half

width 0 is given in units of the d-spacing of Mo layer.

35

 

 

 

 

 

 

 

 

 

 

104
103
103
101 .
100 in“ ”I fill il‘ I ,q
0 5 10 15
. I
3000 :- A i
E I
2000 E- I
.. I
: l
1000 r '
E 1
o - l
35 40 45 5o
26 (deg)

Figure 3.10: Experimental diffraction spectra of a sample with nominal parameters

(15ML Fe/15ML Mo)28 (a)harmonics (b)satellites. The average line is denoted by

a vertical line.

36

sample with BCC(110) texture. The high angle spectrum of this sample is very close
to the pattern of step model calculation (see fig.3.4(b)) where we used the lattice
parameters of bulk Fe and bulk Mo assuming (110) texture in growth direction.
The closeness of experimental spectra and model calculation confirms the successful
growth of multilayers as designed. The observed average lattice spacing from the
position of the average line is J... = 2134.4, whereas the bulk value is if“), = 2126.4
with d,.(110) = 2.020814 and dM.(110) = 2225.1. [6]

It is often convenient to index the high angle satellites with respect to the
average line. instead of the absolute index as in eq.3.20. Let m be the satellite index
such that m=0 for the average line which is n = N A + Na in eq.3.20. Then eq.3.20

can be rewritten as

21rm

q = T + QAVG (3.22)

In fig.3.11, we plot the experimental data of fig.3.10 as q versus 111. The plot is
linear as expected and the slope is 21r/ A if the sample is adequately layered. The
measured modulation period A from the slope is A... = 63.6:l:0.5.4 and the same plot
with low angle harmonics gives the value A... = 64.7 :i: 0.524. The nominal value is
An = 63.8.4. In most our samples, values of A determined from harmonics, satellites
and nominal preparation parameters agree to within 5% or less with the exception
of several times when the crystal thickness monitor was miscalibrated. '

We will demonstrate the accuracy of A’s obtained from the above methods
by obtaining the total film thickness using another, independent method. As noted
earlier, the samples prepared for TED are very thin (~ 500.4) on a N aCl substrate.
Due to the interference between the X-rays reflected at the outer surface of film and
the X-rays scattered by the surface of substrate, fine oscillations are observed in very
thin films at low angles. Fig.3.12(a) shows the fine oscillation from the total thickness
of a very thin sample on a NaCl substrate. The pronounced peak at 26 = 4.2° is the
first order Bragg line of A.

For the small oscillations the following relation holds. [7]

A2
03,, = 26+(m+k)2227 (3.23)

37

 

q(A"‘)

 

 

 

-2 -1 0 1 2 3

Figure 3.11: The plot of satellite data for- sample #199-1 as q versus m. The slope
is 21r/ A.

38

where 6", is the position of the m-th peak in units of radians, 6 = Re(l — n), n is the
refractive index of the film, k=0 or % for minima or maxima, respectively, and t is
the thickness of the film. The data points of the small oscillations of sample #187-2
are plotted as 63” versus (m + k)2 in fig.3.13. The slope of the linear line is ”/49
according to eq.3.23. The film thickness from the slope is t = 507.4.

The nominal parameters of the sample (sample number #187-2 and it is
sputtered on NaCl for the TED study) are (6.1.4 Fe/13.4}1 Mo)23 and produce
the nominal total thickness of 462.4. High angle diffraction-data for this sample
in fig.3.12(b), are rather weak due to the small sample volume, but clearly show.
the average peak and a satellite. The measured period using eq.3.22 is A". = 21.521.
Using the measured period A... and the number of cycles produces t = 50814 including
a 13.4.4 Mo overlayer on top. Two independent methods of obtaining the total
thickness give excellent agreement. In this particular sample, the nominal thickness
(t = 462.4) differs from the actual thickness by 9%. This relatively large discrepancy
is typical of samples having a few ML individual layers, and suggests the difficulty

of accurate thickness control with such thin layers.

3.3.2 Fe/a-Si system (Crystalline/ Amorphous)

In all F e/ Si multilayers the thickness of the Si layer is. fixed either at 5021 or at 30/4.
The low angle XRD data clearly show a number of harmonics, ranging from 3 to 6,
which indicate that our samples are compositionally modulated.(fig.3.l4). But when
we look at the high angle XRD data in fig.3.15 there are no satellites at all, only a
broad Fe(110) Bragg line appears in all Fe/ Si multilayers. The peaks at about 42°
are the Bragg lines from sapphire substrates. The lack of Bragg peaks for crystalline
Si, even though the Si layer is relatively thick indicates Si is amorphous in our F e/ Si
multilayers.

Another special feature inFe/ Si multilayer systems is the fact that the mea-
sured period A". is always smaller than the nominal period An by 10% in samples
with nominal Si thickness of 3014, and 15% in samples with nominal Si thickness of
50.4. This fact is special because the opposite behavior, i.e. A... > A", is observed

39

 

 

 

 

 

 

 

 

 

105
104
103
1o2
101
0 2 4 6
26 (deg)
E b
300 :- ( )
200 E-
100 E-
O W
35 40 45 50
26 (deg)

Figure 3.12: (a)low angle and (b)high angle X-ray diffraction of a sample ,#187-2.
with a nominal thickness of 462A.

40

 

 

 

 

8!-
6E-
L
‘ ..
o _
H ..
35, .
.. 2:—
8 .
<5 .
0.11.1.L.nl.14.l.
0 100 200 300

(m+k)z

Figure 3.13: plot of the data point of small oscillation of sample #187-2 as 6,2fl vs.
(m + It)“. The slope is li/4t'.

41

for all other Fe/ metal multilayer systems due to the extra exposure of substrates
to the atomic beam during the motion of the SPAMA plate. Since the densities of
crystalline materials were used for crystal thickness monitor, it is expected that the
density of amorphous Si is larger than that of crystalline Si.

The Fe(110) lines are evident and become systematically broader and weaker
as the Fe thickness decreases. The structural coherence length from the FWHM
of these peaks is always less than but comparable to the Fe layer thickness. The
disappearance of satellites in the Fe/ Si systems can be explained by a continuous
distribution of the amorphous Si layer thicknesses. As we saw in section 3.3 fig.3.7,
a Gaussian type layer thickness fluctuation with a distribution width of 5% of the
layer thickness completely wiped out the high angle satellites and left only a broad
Fe(110) line.

Suppose we have M Fe layers, the positions of layers are randomly located
and each individual layer has n atOmic monolayers. This system can be a rough
model for our Fe/ Si multilayer. If the amplitude of X-rays scattered by an atomic
layer is A, then the X-ray intensity from a Fe layer is proportional to 113A2 because
n atomic layers within individual Fe layer are stacked regularly and constructive
interference occurs at the Bragg angle. But the Fe planes in one layer are not
arranged in a regular fashion relative to the planes in neighboring layers and thus
the X-rays scattered by them would have random phases. Then the intensity of the

waves scattered by the whole system is proportional to M (upeAY.
I = Maire/1’ + B (3.24)

where B is a background signal. In fig.3.16 the integrated intensities of the F e(110)
Bragg lines in fig.3.15 are plotted versus the Fe thickness squared. They are quite.
linear indicating eq. 3.24 explains the systematic change of the intensities. 7 Near
Fe layer thickness of 12ML this Fe(110) peak is lost in the background signal but
TED data indicate that the Fe is still crystalline. The TED data of Fe/ Si samples
that illustrate behavior as the Fe thickness decreases are given in fig.3.17.[8] For 20

ML Fe layers a BCC pattern with a strong Fe(110) Bragg line is evident. As the Fe.

42

 

 

 

 

 

 

105 b l
104
103
'102
101
0 2 4 6 a

26 (deg)

Figure 3.14: The low angle harmonics of (18AFe/ 50145040 which indicate the com-

positional modulation.

43

 

400

 

 

 

 

40 42 44 46 48 50
26 (deg)

Figure 3.15: The high XRD of Fe/50A Si. No satellites are visible and the finite size

broadening is evident. Sapphire Bragg lines are seen at about 42°.

44

layer thickness decreases while the Si thickness remains constant the higher-index
Bragg lines broaden, merge and finally disappear. This systematic variation clearly
indicates that long range order is lost as Fe thickness decreases. All these data are
consistent with the formation of structurally isolated, crystalline Fe layers in our
Fe/ Si multilayers. But TED data suggest a crystalline to amorphous transition as
the Fe thickness decreases to about 5 ML.

This structural change is crucial in understanding the loss of magnetism in
Fe/ Si multilayers which occur at a Fe layer thickness of 5 ML. We will discuss this
loss of magnetism in Chapter 4.

3.3.3 Fe/transition metal systems (Crystalline/ Crystalline)

Three transition metals, X = M0, V and Cr, are used with Fe to prepare Fe / X
multilayers in an attempt to produce systematic structural changes in the Fe layers.
All four transition metals, including Fe itself, have BCC structure in bulk with
different lattice parameters. The structural and magnetic properties of elements
used in this thesis are summarized in table 3.1.

To more fully explore possible structural changes in the Fe layer we prepared
2 sets of samples for each Fe/X system. In the first set the thicknesses of two
constituents are equal and the modulation period is changed; in the second set the Fe
thickness is fixed at 3 ML and the thickness of the X layer is changed. In this section
some selected experimental XRD data of each system will be presented. Initial
interpretation focuses upon the achievement of adequate compositional modulation,
and then an interpretation of high angle satellites for the presence of coherency strain
will be given. Finally the direct observations of strained layer superlattices(SLS)
using TED data are given.

In fig.3.18 and fig.3.19 the low angle and high angle XRD data for (3ML
Fe/tM,)M are illustrated. (tM,=3 ML, 8 ML and 12 ML ) At least two harmonics
are seen at low angles(the second order harmonic of 3 ML Fe/3ML M0 is out of
range in fig.3.18) and a strong average line plus satellites are observed at high angle.

Note that even the 3 ML Fe/3 ML Mo sample has both harmonics and satellites

.45

 

 

 

 

300
250 —
: O
200}- o 0
.d I
g 150 {- °
5‘ j °
.. '2‘ P
a, 100 f-
4.3
.9. I
50 —
O .n.+lr...ir...l...m
0 10 20 30 40
M(tFe)zx103(Az)

Figure 3.16: Data plot of the intensities of Fe(110) lines versus Fe thickness squared.

46

:2)

mp \[1
L; ‘

 

// ‘\

j K

Figure 3.17: TED data of Fe/ Si multilayer systems. The Fe layer thickness are 20
ML(a) 12 ML(b) and 4 ML(c). After C. L. Foiles

47

 

 

 

Element —Stmcture a(1°1) d(110)(.4) 6 Magnetic property
Fe BCC 2.8663 2.0268 0 Ferromagnetic

Mo BCC 3.1467 2.2250 8.91% Paramagnetic

V BCC 3.0281 2.1412 5.34% Paramagnetic

Cr - BCC 2.8844 2.0396 0.6% Antiferromagnetic
Si Amorp. . . . Diamagnetic(Cryst.)

 

 

 

 

 

 

 

 

Table 3.1: Structural parameters of elements used for the metallic multilayers in this
thesis and their magnetic properties. From the CRC Handbook of Chemistry and
Physics 66th ed. 1985.

48

indicating strong compositional modulation. The systematic shift in the positions
of average lines toward low angle indicates an increase of the average lattice spacing
as the Mo thickness increases.

The high angle XRD data in fig.3.20 are from three equal layer F e/ Mo samples
(a) (15 ML Fe/15 ML Mo)28 (b) (11 ML Fe/ll ML Mo)38 and (c) (3 ML Fe/3 ML
Mo)140 respectively. More satellites are developed as the layer thickness increases
consistent with the model calculation results given in fig.3.4. Note that the positions
of the average lines are almost constant at 26 : 42.3° for all samples. XRD data of
the Fe/Mo systems, in both the locations of average lines and the systematic shifts
in peak locations, are all consistent with expectations of Crystalline/ Crystalline
metallic multilayers. BCC structure with (110) texture along growth direction in
each ultrathin metallic layer is confirmed by the XRD data. XRD data of the Fe/ V
and Mo/V(made for a superconductivity study) systems showed similar behavior to
that of the Fe/Mo systems and will not be given separately. The average d-spacings
calculated from the average Bragg lines of various metallic multilayers are plotted as
functions of the unit bilayer thickness in fig.3.21. Samples with equal ML thicknesses
of each constituent were used in this plot. The horizontal lines near each data sets
denote the average spacings from the tabulated bulk lattice parameters assuming
(110) texture in all layers. The observed average spacings of the systems are very
close to the bulk average d(110) spacings indicating (1.10) texture in individual layers.
Generally the observed points lie a little higher than the bulk values and this can be
explained by the strains in the ultrathin layers which will be discussed in the next

section.

3.3.4 Observation of metallic SLS

A more detailed characterization of ultrathin layers is needed. It is expected that
individual layers in multilayers with large modulation period would have their own
bulk structural properties. But if the layer thicknesses become ultrathin (a few tens
of A) one anticipates strains in the layers due to the lattice mismatch between the

two constituents. Very thin metallic layers grown on a substrate have been reported

 

15000

TU

 

'l

l I U r

 

125003-
: “0
10000 Jk—

 

 

 

 

 

7500 _
E as
5000 r ‘5
2500 E
i l l
O
0 2 <1 5 s 10

26 (deg)

Figure 3.18: Low angle harmonics of (3 ML Fe/tM. Mo)N samples. (a)tM.,:12 Ml.
(b)tu.=8 ML (c)tM.=3 ML.

50

 

 

 

 

 

 

 

 

 

 

 

10000.
5000 E
6000 L
4000 E
i 00
2000 f
- (b)
o - to
35 40 45 50

26 (deg)

Figure 3.19: High angle reflection lines of (3 ML Fe/tMo Mo)M samples. (a)tMo: 12
ML (b)tM.,=8 ML (c)tM.,=3 ML. '

51

 

6000
5000 -

4000 -

 

3000 _—

 

2000 :—

1000:

 

 

 

 

35 40 45 50
' 26 (deg)

Figure 3.20: High angle reflection lines of samples having equally thick of Fe and

Mo layers.

g 52

 

 

 

 

 

 

 

2025 'fi 0 U l V T U I I I 17" r I I I I U I r I U V d
.- J
r- .,
2.20 — “-1
4 .. .
OB - It
I)
E; 2215 - x x .*T
a h x 5 X x x x x- Fe/Mo ‘
a l- l X '1
a" ' ,
D " d
h L ‘
1110 L— -+
Fe V
g " o 5 o o 2 / i
n. .
" o
2.05 l L J_l L I I l l l l L l L I l J l I L l l l I

10 20 so 40 50
Bilayer Distance in ML

Figure 3.21: Measured d-spacings from the average Bragg lines of each multilayer.
The horizontal lines near each data set denote the average d-spacings using the bulk

values of d(110) for each metal.

53

to simulate the structure of the substrate up to a few monolayers. [9] In a multilayer
which consists of many number of ultrathin layers, the strain is expected to reside
throughout the whole sample making a SLS (Strained Layered Superlattice).

It is easily shown that the average lattice spacings of superlattices can be

expressed as a linear function of the chemical composition.

11".; = A: + 4.. (3.25)
where
N3

is the fraction of material A in a unit bilayer and
A = d; - d; (3.27)

is the difference of the two lattice spacings. In standard reflection XRD the average
lattice spacing 64w; satisfies the Bragg condition dAva sin 641:3 = A. In fig.3.22
the average lattice spacings of Fe/ V samples are plotted versus x, the fraction of
Fe in'a bilayer. The results for both types of sample; i.e. samples with equal layer
thicknesses of Fe and V (x~ 0.5), and samples with 3 ML Fe and varying V layer
thicknesses, were used in plotting fig.3.22. Data points from the literature[10] are
also included. The continuous straight line is the plot of eq.3.25 using the bulk
lattice spacings of Fe and V and the individual data points are measured values.
Two differences between the data points and the solid line can be pointed out. (i)
apparently, there are two regions for the data points; the linearly changing region
below a: = 0.4 and the cluster of data points above the solid line near a: = 0.5. (ii)the
slope from the linear region of data points is larger than the slope of the solid line
by about 30%. According to eq.3.25 the slope of the line is just the difference of
the two lattice spacings A. If a coherency strain really exists, one would anticipate
a contracted V lattice and an expanded Fe lattice for the in-plane direction of a
strained layered Fe/V superlattice. This contraction and expansion would be a
maximum for a common in-plane lattice. Indeed we will see the TED data provide

direct evidence of a common in-plane lattice. But the 30% difference in slopes from

54

fig.3.22 suggest the opposite sense of changes in the growth direction, i.e. a larger V
lattice spacing becoming larger and a smaller Fe lattice spacing becoming smaller.

The preceding unian'al strain is consistent with a very familiar phenomenon
in metallurgy and is related to the Poisson’s ratio. Consider a cubic object with a
lateral length a as in fig. 3.23. If this object is expanded in z-direction by strain 6
(e < 1), then the initial and the final volume can be written

V. = a3 (3.23)’
V, = a3(1+e)(1—¢re)2 (3.29)

If the parameter a' = 1/2 the volume is not changed to the order of e’.
v, = Vi + 0(8) (3.30)

Indeed the observed a of rubber which is very flexible is 1 / 2. This parameter a' is
called the Poisson’s ratio and is defined by

u" = ecu” (3.31)

where u” is the displacement in the strained direction and u... is the displacement
of the other two direction. A typical value of a for metals is 1 / 3. i
Since two individual lattice planes with different lattice parameters contact
each other in a SLS, the coherency strain apparently lies in the x-y plane in contrast
to the definition of the conventional Poisson’s ratio where the strain is produced
in the z-direction by tension or compression. Consider the cubic object again and
assume a strain 6 in x-direction and y-direction, planar strain, then the final volume
is
V, = a3(1 + e)'(1 - as) (3.32)
The ratio of the strain in the z-direction to the strain in plane is newly defined as 11

to distinguish it from (7. With 11 = 2, V, = V.- + 0(e’) so that
,1 = 4a (3.33)
The in-plane strain in the Fe and V layers of a Fe/V SLS may have the relation

Ep.tp.6p. = —Evtv€v (3.34)

55

 

 

 

 

 

2.150 _
,, X on A1203
1 0 on Kapton
2'125 7 “xi 0 Endoh et a1.
" 0
2.100 -—
3 I
'U l-
. 2.075 f
i.
2.050 _—
I :1
3025",..11....1....1....1..1.
0.0 0.2 0.4 0.6 0.8 1.0
x=ML(Fe)/ML(A)

Figure 3.22: The linear relation of the average d-spacing, d, and the fraction of Fe

in a bilayer for Fe/ V systems.

56

 

 

 

1———-—-—
\

 

|.__

 

 

Figure 3.23: A cubic object.

57

where E’s are the Young’s moduli, t’s are the layer thicknesses and 6’s are the strains

of each metal. Since the lattice mismatch of Fe and V is 5.34% we have
61.". — 61/ = 5.34% (3.35)

From eq.3.34 and eq.3.35 and assuming tr. = tv we get

 

Evtv
. = X 5.34 = 2.0
“' Evtv + Ehth % 7°

Finally the lattice spacings of fully strained layers are

d3.

415/ = Wh(1+4WI€vl)

dir‘fi"(l — 4dr.|£p.l) (3.36)

and the average spacing of the SL8 is
diva = 412% + 2(dbyh0'levl " diruiha'hlehl) (337)

The amount of increase in the spacing estimated using known values of d,o and e is
0.02814. And this explains a little larger observed spacings than the bulk values at
a: = 0.5 in fig.3.22.

With this uniaxial strain in mind let us examine the experimental high angle
XRD data for effects related to the strain in individual layers. As we saw in section 3
(fig.3.5), the intensities of high angle reflection lines are very sensitive to the relative
difference of two lattice spacings. When the diflerence is large the intensity of the
average line (Io) decreases rapidly while the intensities of nearby satellites increase.
Reflection X-ray intensities are calculated using the step model for a system (12
ML Fe/ 12 ML V)20 with three different lattice parameter conditions: (i)with bulk
lattice spacings (ii) with lattice spacings of uniaxial strain (eq.3.36) (iii) with lattice
spacings of symmetric strain where the sign of strain is the same in any direction. In
fig.3.24 the structure factor squared and the Laue function of the three calculations
are shown: the convolution of these functions produces stronger satellites in the

uniaxial strain model and a diminishing of satellites in the symmetric strain model.

58

In fig.3.25 the ratios Io/L. (Io is the intensity of the average line and 1+ is the
intensity of the satellite at higher angle) are plotted for both Fe/V and Fe/Mo
systems. In both plots the experimental data points deviate from the bulk model
toward the uniaxial strain model. The strains in Fe/ V and Fe/Mo SLS are uniaxial
but the values are smaller than the values predicted by eq.3.25. The data points
for the Fe/Mo system abruptly join the bulk step model for a modulation period
of about A = 16M L while the data points of the Fe/V system do not join up to
A = 32M L which is plausible if we consider the lattice mismatches in these two
systems.

Direct evidence of SLS are provided by TED. Fig.3.26 is the TED data for a
Fe/ V superlattice having A =15 ML and illustrates a large number of Bragg lines.
These Bragg lines are identified as those of a single BCC lattice. A number of
samples with equal numbers of monolayers of Fe and V and systematically varying
A were prepared. Fig. 3.27(a) is the TED data for a A =60 ML sample and fig.
3.27(b) is for a A =12 ML sample. The first two rings in fig.3.27(a),t< 110 > and
< 200 > lines, are wider than the counterparts of fig.3.27(b) but resolution into
two rings is not possible. But the third ring in fig.3.27(a), < 211 > line, is clearly
a doublet. Numerous higher index lines for this sample are also doublets. These
doublets are consistent with two BCC lattices, one for Fe and the other for V is an
obvious interpretation. Systematic TED data show that the onset of the single BCC
lattice plane for Fe/ V occurs when the modulation period is 32 ML or less.

Fig.3.28 shows the TED data of two Fe/Mo samples with equal number of
monolayers of Fe and Mo. Fig.3.28(a) is TED data for a A =30 ML sample and
the first ring is clearly a doublet. A careful inspection of the positions of the rings
indicates they are are from two BCC lattices. TED data of Fe/Mo samples of A =60
ML and 20 ML also show double BCC lattices while a sample of A =12 ML has a.
single BCC lattice plane. Fig.3.28(b) shows the TED data of a A =12 ML sample
and the ring pattern is consistent with a single BCC lattice. From this fact it can
be claimed that the onset of the single BCC lattice in Fe/Mo system occurs when .\
is between 20 ML and 12 ML. This claim is consistent with the suggested onset at

 

59

12ML Fe/12ML v

 

5000_

— bulk A
4000 1.. uniaxial strain I" i
L '“ symmetric strain; \

3000 -
a 2000 -

1000 9

 

 

 

35 37.5 40 42.5 45 47.5 50
26 (deg) '

Figure 3.24: The structure factor squared and the Laue functions of three step

models.

60

 

 

 

 

 

 

 

 

 

100 .
I + 0 measurements
80:- + bulk
I x uniaxial strain
60 E- o symmetric strain
b O 0
J +0000
\. _ o
- 40 : 0 0 0 0 0 O
' x
. + a
20 :_ ( )
0 i ‘
40
I +
_ :1 measurements
30_- + bulk
I + o uniaxial strain
~ :1
i 20 -
.2 :_ +
: 0 +
10 :- 0 + + (b)
C o + t
. 00 n +++Iil
0 . . . 11 . . 9
O 10 20 30 40
11011.)

Figure 3.25: The ratios Io/ I1. of three step models versus A. (a)Fe/Mo system (b)
Fe/V system.

61

A =16 ML by the XRD data in fig.3.25(a).

Since the wavelength of the electrons used in TED is small(0.037.4 with 100
Kev) and therefore the Bragg angles are also small(within few tens of mrad), the
relative difference of the lattice parameters of the two BCC lattices can be estimated
by using the large number of the difl'raction ring radii from the TED data. Fig.3.29
depicts the lattice parameter differences of the double BCC lattice planes, Aa, nor-
malized by the larger lattice parameter so as a function of modulation period A. A
smooth transition from double lattice to single lattice is evident for Fe/ V samples ,
while a rather abrupt transition occur between A =20 ML and 12 ML for Fe/Mo

samples. As previously noted, this behavior is consistent with the results of the

XRD data in fig.3.25.

62

 

 

 

 

 

L...

.— (320

 

 

 

 

(516,431)

Figure 3.26: The TED data for a A =15 ML Fe/V sample. The Bragg peaks are
identified as those of a single BCC lattice.

63

 

 

 

 

 

Figure 3.27: The TED data for two Fe/V samples having different A’s (a) for A :60
ML (b)for A =12 ML.

64

 

Figure 3.28: The TED data for Fe/Mo samples having different A’s (a) for A :30
ML (b)for A =12 ML.

65

 

0.10
l- D FB/MO
0.08 '- U 0 Fe/V

0.06 '-
0.04 _

0.02 :-

0

0.00'....1....11...1...1fi9__._._._1
0 0.02 0.04 0.06 0.08 0.1

1/A(ML"‘)

 

 

 

Figure 3.29: The relative differences of the two lattices parameters versus l/.\ in

Fe/ V and Fe/Mo samples using TED data.

Bibliography

[1] B. D. Cullity Elements of X-ray Diffraction, Addison-Wesley Publishing Read- .
ing, MA (1956 )

[2] W. Sevenhans, M. Gijs, Y Bruynseraede, H. Homma and Ivan K. Schuller, Phys.
Rev. B. 34, 5955 (1986)

[3] B. M. Clemens and J. G. Gay, Phys. Rev. B. 35, 9337 (1987)

[4] J.-P. Locquet,D. Neerinck, L. Stockmann, Y. Bruynseraede and Ivan K.
. Schuller, Phys. Rev. B. 38, 3572 (1988)

[5] J.-P. Locquet,D. Neerinck, L. Stockmann, Y. Bruynseraede and Ivan K.
Schuller, Phys. Rev. B. 39, 13338 (1989)

[6] The CRC Handbook of Chemistry and Physics, 66th ed. 1985

[7] A. Segmuller and M. Murakami in ”Thin films from Free atoms and Particles”
ed. K. J. Klabunde, Academic Press NY (1985)

[8] C. L. Foiles Ultramicroscopy, 29, 80 (1989)
[9] U. Gradmann and G. Waller Surface Science _11_6, 539 (1982)

[10] Y. Endoh, K. Kawaguchi, N. Hosoito, T. Shinjo, T. Takada, Y. Fujii and T.
Ohnish,J. of Phys. Soc. Japan, _5_3, 3481 (1984)

66

Chapter 4
Magnetic properties

4.1 Measurements of magnetic data

The magnetization of the samples was measured at 5K on a Quantum Design MPMS
magnetometer having a maximum field of 55 KOe. Samples remained on their sub-
strates and were mounted in a plastic tube in a manner that aligned the field parallel
or perpendicular to the layers. Fig.4.1 shows a magnetization curve of one of our
Fe/ V samples. The magnetization in parallel fields rises rapidly at low fields and sat-
urates at about 4 KOe; in perpendicular fields the magnetization increases linearly
and saturates at a field about 18 KOe eventually joining the parallel curve. The
negative linear slope at high field in both curves is due to the diamagnetic sapphire
substrate, the plastic tube and the spacer for sample mounting. Extrapolation of
the of the linear portion of this plot to zero field gives the saturation magnetization
M5. The volume of Fe in the layered sample, determined by sample area, individ-
ual layer thickness and the total number of layers, was used to obtain an absolute
value for M3. Tests with pure Fe films provided a separate absolute calibration and
established our error limits as 5%, most of which is from the errors in sample area.

measurements and Fe layer thickness measurements.

67

68

 

2000
- (17.8A Fe/iO.“ V140
. + // field

1500 1:1 .1. field

1000

 

500 J

M (emu/cm:5 Fe)

 

 

o jenlnssslaasslmme

 

AIL. All;

0 5 1 0 15 20 25
H(K0e)

I A

Figure 4.1: The magnetization curves in parallel and perpendicular magnetic fields

for a Fe/ V multilayer. Extrapolating the high field part to zero field gives the value
of M5 = 1600emu/cm3 at 5K for Fe.

69

 

 

 

 

 

2000
1500
? .
a. .
es 1000' Q
8 .
a 1 g
i” . XFe/Cr
3 ”e °F9/V
:2; 500 - '1' Ere/gin
. OFe/VWong et a1.
0 p..g.l....l..r.l....lL...l.r..
0, 5 10 15 20 25 30

t’li'e (ML)

Figure 4.2: The saturation magnetizations for various Fe multilayers as a function
of Fe thickness at 5 K. As the Fe layer thickness increases, the value of bulk Fe, 1740

emu/61113, is approached.

70

4.2 Saturation magnetization of Fe multilayers

Fig.4.2 summarizes the saturation magnetizations at a temperature of 5 K for our
Fe multilayers (Fe/ Si, Fe/Mo, Fe/V and Fe/Cr systems) as functions of Fe layer
thickness The thickness of the two constituents in each system are the same with

the exception of Fe/ Si multilayers where the Si layer thickness is fixed at 50.4.

4.2.1 ' Fe/Si system

The Fe layers in Fe/ Si systems show a rapid reduction of their magnetism and
become nonmagnetic at a Fe layer thickness of about 5ML(~ 10.4). Data points for
Fe/ Si multilayers in this plot can be well fitted by assuming that a region of the Fe
layers at the interface is magnetically dead. In chapter 3 we showed that the Fe(110)
Bragg line in Fe/ Si samples becomes systematically broader and weaker as Fe layer
thickness decreases. TED data indicated that the long range order in Fe layers is
lost when the thickness is less than about 1014 suggesting crystalline to amorphous
transition. ’

As noted earlier, sputtered Si is amorphous in our Fe/ Si systems. And seme-
how, probably due to the disordered surface structure of the a-Si layers, sputtered Fe
atoms may not form their stable BCC structure up to a thickness of about 10.4 and
after that they may form a BCC structure. Suppose a-Fe in our Fe/ Si multilayers is
nonmagnetic and let tr. be the individual Fe layer thickness and 24 be the thickness
of the magnetically dead layer in each Fe layer as shown in fig. 4.3 Then we have
the following relation

Mth.A = M0N(tp. — WM (4.1)

where M is the magnetization per unit volume for all Fe in the sample, Mo is the
magnetization of crystalline bulk Fe, N is the number of Fe layers in the sample and
A is the sample area. Rearranging the above equation we have

Mo — M __ x,

—-——— — 4 .2
Mo t... l ’

In fig.4.4 data points for Fe/ Si samples are plotted as (Mo — M )/Mo versus 1 / t p..

71

 

 

 

////.:.F../// 3:

 

A ////:-F°//Z i):

l ‘M."._.'.'a-Si.'.

 

 

Figure 4.3: Magnetically dead layers in a Fe/ Si model system. The Fe layers at the

interface with a-Si have a thickness :4 and are assumed to be nonmagnetic.

.72

 

1.0

I I I I

0.8

I I 1 I I

0.6

I I I I

0.4 '-

(“o-ll)/Ho

 

0.2 _-

 

 

0.0 ..il...ll....l..4.l....
0 20 40 60 80 100

l/tF.(A"‘) x1000

Figure 4.4: Data plot of (Mo — M )/ Mo versus l/tp, of Fe/ Si for multilayers. The
slope is the thickness of nonmagnetic Fe layers in the magnetic dead layer model;

34 = 10.2.4 in this plot.

73

According to eq.4.2, the slope of this plot is just the thickness of the nonmagnetic
Fe region :4. Linear regression of 6 data points gives 234 = 10.2.4.

In chapter 5 we will describe the EXAFS data which confirm the presence
amorphous Fe layers in Fe/ Si multilayers as the Fe layer thickness decreases.

4.2.2 Fe/transition metal system

A consideration of the loss (or reduction) in magnetization as Fe layers become
thinner with different transition metals produces an interesting pattern. In the
Fe/Mo system the Fe layers retain their saturation magnetizations, which is quite
close to the value of bulk Fe, until they are about 6 ML thick and then lose the
magnetism as the Fe layers become thinner. The sample with nominal parameters
3ML Fe/3ML M0 is nonmagnetic (or at least substantially reduced). The Fe/V
system also loses its magnetism as the Fe layer thickness decreases. However the loss
occurs at a rather gradual pace and Fe layers with thickness less than 3ML still retain
about 50% of the bulk saturation magnetization. The saturation magnetizations of
the Fe/Cr system are essentially independent of the Fe thickness down to 3ML Fe.

Surveying the the magnetic behavior in thin Fe multilayers, it seems that the
lattice mismatches between Fe and the associated transition metals are systemati-
cally related to the reduction of the saturation magnetization. The Fe/Mo system
with a 9% mismatch loses magnetism rapidly below 6 ML Fe thickness while the
Fe/Cr system with only a 0.6% mismatch does not show a significant reduction in
saturation magnetization down to a 3ML Fe thickness.

At this point, however, it is not clear whether the structural disorder in Fe
layers caused by lattice mismatch is responsible for the different behaviors in the loss
of magnetism or whether the increased number of non-magnetic nearest neighbors
due to intermixing plays some role. For the possibility of intermixing at interfaces
the phase diagrams of each binary alloys were surveyed. [1][2]

(l) Fe-V
Up to 23 atomic % of V is soluble in Fe at room temperature and BCC structure is

retained. The saturation magnetization drops to about half that of bulk Fe at 25 %

74

V and then drops even more rapidly at higher V concentrations.

(2) Fe-Mo

Only 3 atomic % of M0 is soluble in BCC Fe at 600°C. The saturation magnetization
falls to zero at about 50 % Mo.

(3) Fe-Cr

Up to 20 % of Or is soluble in BCC Fe at 400°C. The saturation magnetization
drops to half that of bulk Fe at about 30 % Cr.

The effect of interdiffusion at the interfaces would be pronounced when the
Fe layers are very thin. Let us look at fig.4.5 where the saturation magnetizations of
samples with Fe layers 3ML thick and varying nonmagnetic layer thickness are shown.
Again the Fe/Cr system does not show any significant change as the Cr thickness
changes. The Fe/ V system may have a gradual increase of magnetization as the V
layer thickness increases but the magnetizations stays below 70 % that of bulk Fe.
The 3ML Fe/ t ML Mo system shows the most interesting magnetic behavior. While
the 3ML Fe/3ML Mo sample is nonmagnetic, the saturation magnetizations increase
rather abruptly as the Mo thickness increases and approach the value of bulk Fe at a
5ML Mo thickness. As noted above Fe and Mo are insoluble. Moreover, if the loss of
magnetism is caused by an increased number of Mo nearest atoms due to intermixing,
it is difficult to explain the strong magnetism for thicker Mo layer samples. Structural
change in the Fe layers caused by lattice mismatch seems to be the most plausible
explanation for the loss of magnetism in 3ML Fe/3ML Mo samples. With only 3
atomic layers of each metal and 9% mismatch, it may be more difficult to retain
their individual bulk structure than to have some structural disorder. But thick Mo
layers would retain the BCC structure to dominate the thinner Fe layers to form
an ordered structure. More study is needed to clearly establish a structural change.
and EXAF S data in chapter 5 will provide some evidence.

The changes of magnetism in the Fe/ V system seem to be explained by in-
termixing. N MR and Mossbauer measurements indicate a mixed interface range of

about 3ML for Fe/V samples.[3] In fig. 4.5 the lower value of saturation magne-

75

 

 

 

 

 

2000
Battle
1500 ll]

? n
.5" 1...; i i
B .

S i - i xro/cr
g _g Ol'e/V
V 500 r' Dre/Ito
m . .

a

_ m
....LL.L.l.lllL..Lrlrl.ll.LL.

 

0
0 5 10 15 20 25 30
interlayer thickness(ML) ‘

Figure 4.5: Saturation magnetization of 3 ML Fe layer samples as functions of the

nonmagnetic layer thickness.

76

3.0

 

 

2.3 W‘\

9.. fwxi"
//

 

 

 

 

 

/

0.5 ff if ’
a M 4
Cr Mn Fe Co Ni Cu

6 7 8 9 10 l 1
Electron concentration

 

 

4!

Atontcuaouneafllohr-egaetons)
+
XODdOdQDDeoe
5
<

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.6: Average atomic moments of binary alloys of the elements in the Fe group.

(Bozorth.)

.77

tization in 3ML Fe/ t ML V systems also suggests intermixing of Fe and V at the
interfaces. The Fe layers in Fe/ Cr system, on the other hand, retain their bulk
magnetization for all samples. N 0 direct data for Fe/ Cr interfaces are available but
fortunately, the magnetic data of Fe -V and Fe-Cr binary alloys are available in the
literature[10] and shown in fig.4.6. The reduction of magnetization for both alloys
have almost identical linear dependences on the composition of V or Cr. Combining
these facts, the saturation magnetizations of 3 ML Fe layers and the magnetic data of
alloys, suggests that the intermixing in Fe/Cr samples is considerably more limited
than in Fe/V samples for our sputtered samples. Moreover with almost identical
lattice parameters of Fe and Or, the structural disorder should be much smaller in 3
ML Fe/ 3 ML Cr samples than in 3 ML Fe/ 3 ML Mo samples. Less intermixing and
structural disorder are consistent with the bulk-like saturation magnetization of 3
ML Fe/ 3 ML Cr samples.

In summary, structural change caused by insolubility and the large lattice
mismatch of Fe and M0 is responsible for the loss of magnetism in the Fe/ Mo system.
In‘equal thickness Fe/Mo samples the saturation magnetization drops rapidly when
the layer thickness is less than 6ML. At 8ML uniaxially strained layers are observed
by XRD and at 6ML the onset of a single lattice is observed by TED. Non-magnetic
3 ML Fe layers in 3 ML Fe/ 3 ML Mo system recover the magnetism of bulk Fe
when the Mo layers become thicker than 5 ML. The Fe layers in Fe/Cr system seem
to retain their bulk structure and and there is no evidence for interdiffusion at the
interfaces. No loss of magnetism was observed down to a 3 ML Fe layer thickness

in Fe/Cr. Both intermixing and some structural change may have occurred in the

Fe/ V samples.

4.3 Saturation magnetic fields and magnetic interlayer cou-
pfins

Numerous magnetic interactions are known in magnetic multilayers. [4] They are

(i) Demagnetizing energy (Shape anisotropy)

78

(ii) Anisotropy energy

Crystalline anisotropy, Stress anisotropy, Growth anisotropy etc.

(iii) Magnetic field energy with local magnetic field

(iv) Exchange energy between magnetic layers

Recently magnetic interlayer interactions has been reported in some rare earth

superlattices[5] and Fe/ Cr systems.[6] [7][8][9]

Magnetization curves for parallel and perpendicular fields provide some mea-.
sure of magnetic anisotropy. Consider a single magnetic thin film. In a thin film
there is no interlayer coupling and only various anisotropies could be involved. If
the film is very broad compared to the thickness, there is an extra energy per unit
volume, ED = 21ng, when the magnetization is oriented normal to the film plane.
This is the shape anisotropy and if a magnetic field H is applied perpendicular to
the film, H = 41rMs is needed to overcome the demagnetization energy and align
the magnetization perpendicular to the film.

In fig.4.l we have the magnetization curves of a (9ML Fe/9ML V)40 sample in
parallel and perpendicular magnetic fields. In parallel fields the magnetization rises
quickly at low field and saturates at about 4 KOe. In perpendicular fields, on the
other hand, the magnetization shows a slower and linear increase, saturates at about
18 KOe and joins the parallel magnetization curve at higher fields. Extrapolation
to zero field gives the saturation magnetization M; = 1600emu/cm3 Fe. From now
on we designate the parallel saturation field as H3 and the perpendicular saturation

field as H A. If there is only shape anisotropy H A and M5 should be related by
H .4 = 41rM5 (4.3)

For (9ML Fe/9ML V)40 the observed values of H A and Ms satisfy eq.4.3 within
experimental error suggesting any other anisotropies are very small compared to the
shape anisotropy. Indeed the crystalline anisotropy of an Fe single crystal has a
very small effect on the saturation field H5 giving only for 0.4KOe difference in H 5
between the easy axis (100) and the hard axis (111).[10] All Fe/V and Fe/Mo samples

79

tested in this thesis give results consistent with eq.4.3. Currently available data for
perpendicular measurements of the Fe/V and Fe/Mo systems are summarized in
table 4.1 and table 4.2, respectively.

Fe/Cr systems show magnetization curves much difl'erent from those of Fe / V
or Fe/Mo systems. The magnetization curves for fields parallel and perpendicular to
the sample planes of 2 Fe/ Cr superlattices are shown in fig.4.7 (a) for 5ML Fe/5ML
Cr and (b) for 5ML Fe/20ML Cr. The magnetization of sample 5ML Fe/5ML Cr-
increases very slowly in both directions saturating at 26KOe in a parallel field and at
38KOe in a perpendicular field; from parallel field data M5 = 1800emu/cm3Fe. The
saturation fields in both directions are much higher than that of Fe/V and Fe/Mo
samples for which H5 ~ 3K 0e and HA ~ 41rM5. Sample 5ML Fe/20ML Cr has
another interesting feature in its magnetization curve: H3 = 3K 0e which is typical
in the case of Fe/V or Fe/Mo systems but H .4 = 14K 0e which is smaller than the
demagnetizing field 41M; = 22.6K0e by8.6KOe ! The saturation field H5 changes
systematically with the change of Cr interlayer thickness as shown in fig. 4.8 for
7ML Fe thickness samples. The magnetization of the sample with 3ML Cr layers
saturates at H3 = 19K0e and H5 systematically decreases as the Cr layer thickness
increases. Near and above 10ML Cr thicknesses, H5 is approximately constant at
6KOe.

Fig.4.9 summarizes the systematic dependence of H 5 on the Cr layer thickness
in our Fe/Cr superlattices. One immediately notices that the strength of change in
H3 also depends on the Fe layer thickness; 3ML Fe samples have a strong change in
H 5 while samples with thicker Fe layer have a very weak dependence of H 5 upon Cr
layer thickness.

Ultrathin Fe layers are known to have antiferromagnetic coupling across Cr
layers. Recently Grunberg et al. studied evaporated Fe/ Cr/ Fe sandwich samples
using light scattering from spin waves, and claimed antiferromagnetic coupling of
magnetic Fe layers across the Cr interlayer.[9] They also found that in a small ex-
ternal field the double Fe layers order antiparallel with their magnetizations perpen-

dicular to the external field in analogy to the spin- flop phase of antiferromagnets.

80

 

ID No. ML Fe/MLV H5(K06) M5 4«M.(Koe) mums)

 

 

 

 

 

 

 

 

#1349 17/17 3 1710 21.5 22
#134-3 15/15 3 1700 21.4 22
#1342 9/9 4 1500 18.8 18
#69-13 3/3 4 900 11.3 12
#151-13 3/9 4 1530 19.2 20

Table 4.1: The magnetic data of Fe/ V samples. H .4 = 41rM5 is well satisfied.

 

 

 

ID.No. ML Fe/ML Mo [lb-(K06) M3 41rM5(KOe) HA(K0e)
#1993 8/8 6 1800 22.6 22
#199-8 3/8 5 1800 22.6 22
#1999 3/12 4 1700 21.4 18

 

 

 

 

 

Table 4.2: The magnetic data of Fe/ Mo samples.

81

 

(10.21 J's/10.21 cuss

 

 

M (emu/cm° Fe)

 

 

 

M (emu/cma Fe)

 

Figure 4.7: The magnetization curves in parallel and perpendicular fields for (a)51\l L
Fe/5ML Cr and (b) 5ML Fe/20ML Cr superlattices.

82

2000

 

1500

   

+(14.21 Fe/6.1A Cr)89

x(14.21 Fe/10.2A Cr)74
0(14.211 Fe/14.3A Cr)63
004.21 Fe/18.4A Cr)55
«14.21 Fe/28.5A Cr)44

1000. .-

500

 

M (emu/cma Fe)

 

 

O ' 1..1....1....L....1....1....
0 5 10 15 20 25 30
H (KOe)

Figure 4.8: The magnetization curves of 7ML Fe/ t ML Cr samples in parallel field.

The saturation field H5 decreases systematically as the Cr thickness increases.

83

 

   

 

 

 

50
‘ 40 ~ + 3111. Fe
' 0 5ML Fe
P D 7ML Fe
. o 15ML Fe
30 L 1‘ 25ML Fe
21? - e 301 Fe(OO 1) Baibich,
24, [ ~~~101n. Fe Perkin
5E.” 20 [-
10 l-
1.
f
L , ..
0 "' ': .111111.
0 5 10 15 20 25 30

Figure 4.9: The systematic change of saturation field H3 as a function of the Cr

thickness. Data for samples with different Fe thickness are plotted separately.

84

The antiferromagnetic coupling also has been observed in an evaporated 20.4 Fe/20A
Cr/20A Fe double layer by Carbone and Alvarado via in-situ spin-polarized LEED.[7]
[8] 30.4 (001)Fe/(001)Cr superlattices grown by the MBE method have been studied
by Baibich et al.[11] Their saturation fields also have a strong dependence on the
Cr layer thickness as depicted in fig.4.9 but the dependence upon the Fe thickness
for their and our samples differs. They ascribed the high saturation field of thin
Cr thickness sample as a signature of antiferromagnetic interlayer coupling when
the Cr layer thickness is below 30.4. Very recently Parkin et al. investigated (20.4
Fe/tc,)M superlattice samples fabricated in a dc magnetron sputtering system.[6]
They measured the saturation field and the magnetoresistance as functions of the
Cr layer thickness and observed high saturation fields for thin Cr thicknesses and
low saturation fields for thicker Cr layers. However, their saturation fields oscillate
as the Cr thickness changes rather than dropping monotonically as shown in fig.4.9.
They claimed this oscillatory behavior is evidence of oscillations in the exchange
interaction coupling the Fe layers across the Cr layers. *

In fig.4.9, the saturation fields of our Fe/Cr samples are plotted for each
Fe thickness as functions of the Cr interlayer thickness. The data points of’the
two other groups are reproduced for comparison. The saturation fields of our Fe/Cr
samples with Fe layer thicknesses below 15 ML are very high in the thin Cr thickness
region and drop rapidly and monotonically as the Cr layer become thicker. Any
oscillations like the data of Parkin’s group were not observable in our samples. The
behavior of thin Fe layer samples is qualitatively consistent with literature results
and suggests antiferromagnetic interlayer coupling in our Fe/Cr superlattices. The
strong dependence of H5 on the Cr interlayer thickness become weaker as the Fe layer
become thicker and for 25 ML Fe layers H5 is almost constant at about 4 KOe. This
value occurred for H5 in the Fe/Mo or Fe/ V systems where no interlayer interaction
occurred. The Fe layer thickness for the Baibich et al. was 15 ML but their samples
were prepared on GaAs(001) substrates and have a BCC(001) Fe/ Cr texture.Our
sputtered samples have a BCC(110)Fe/Cr texture. Whether the different behaviors
in H5 for these 15 ML Fe samples originates from the different texture or the quality

85

of the samples is not clear at this time. Although samples with 10 ML Fe layers
were not available in our study, the fine oscillations observed by Parkin’s group are
not seen in our data for thicker and thinner layers. While both studies used the
sputtering method there are two differences in the sample preparation conditions:
First, the deposition rate was 2.4/ sec in Parkin’s study and 721/ sec was used in our
sample preparations. Second, they used Si(111) substrates while sapphire(0001) was
used for our samples. How these conditions affect the sample quality is not clear.
As we pointed out, the difference between the perpendicular saturation mag-
netic field H .4 and the demagnetizing field 41rM5 is a measure of extra magnetic
anisotropy. The data for AH = H .4 — 41rM5 are plotted in fig.4.10 as functions of
the Cr thickness . The dependence of AH on the Cr layer thickness is quite similar
to that of H5 except a number of negative values occur for AH. This similarity
and difference raise the following two questions: i
(i) Does the extra anisotropy in our Fe/ Cr superlattices which is represented by AH,
originate solely from the antiferromagnetic interlayer coupling?

(ii)'If the answer for question (i) is ”yes” what does the negative value of AH mean?

In an effort to answer question (i), a plot of AH vs H5 is provided in fig.4.11.
Interestingly enough these two quantities are closely related over the positive range
of AH indicating the two quantities are closely related by a common physical origin,
the antiferromagnetic interlayer coupling. Another interesting fact to be noted is
that the negative values of AH are always occurred at the lowest values of H5
where antiferromagnetic interlayer coupling is weak or zero. Ferromagnetic interlayer

coupling may be associated with these negative values of AH.

 

30
20 - + 3ML Fe
- o 5ML Fe
' . X 7ML Fe
A * D 15ML Fe
m ' 0 25ML Fe
3 10 —
. :13
4

fl

 

 

 

—10h ...1....1....1...-c .......1
0 5 10 15 20 25 30

tCrlMIa)

Figure 4.10: Plot of AH = H A -— 41rM5 versus the Cr layer thickness.

87

 

 

 

 

30
_ +
20- ++
_ o
1? l X
2 10~
5’ ’ "
' '20 +3MLFe
’ o oSMLFe
Ong X7MLFe
bD< UlfiMLFe
' 025MLFe
"El
_IOJT..1....1....1...Li....

0 10 20 30 4O 5O
HS(KOe)

Figure 4.11: Plot of AH versus H5. The high degree of linear correlation between
the two parameters is clear for positive values. Note also that negative AH is always

associated with very low H5 values.

Bibliography

[1] M. Hansen, Constitution of Binary Alloys, 2nd edition Metallurgy and Metal- ,
lurgical Engineering Series (McGraw-Hill Book Company, 1958)

[2] R.M. Bozorth, Ferromagnetism, 2nd edition (D. Van Nostrand Company, 1953)

[3] T. Shinjo and T. Takada, Metallic superlattices (Elsevier Science Publishers
B.V., 1987)

[4] AH. Eschenfelder, Magnetic Bubble Technology (Springer-Verlag Berlin Hei-
. delberg New york, 1980)

[5] C.F. Majkrzak, J.W. Cable, J. Kwo, M. Hong, D.B. McWhan, Y. Yafet, J .V.
Waszczak, and C. Vettier, Phys. Rev. Lett., i9, 2700 (1986)

[6] S.S.P. Parkin, N. More and K.P. Roche, Phys. Rev. Lett., §_4_, 2304 (1990)
[7] C. Carbone and SF Alvarado, Phys. Rev. B., E, 2433 (1987)

[8] SF. Alvarado and C. Carbone, Physics B, L49 (1987) 43-48

[9] P. Grunberg, R. Schreiber and Y. Pang, Phys. Rev. Lett., 51, 2442 (1986)

[10] C. Kittel, Introduction to Solid State Physics, 6-th edition (John Wiley & Sons
Inc. NY, 1986)

[11] M.N. Baibich, J.M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Eitenne,
A. Friederich, and J. Chazelas, Phys. Rev. Lett., 6_1_, 2472 (1988)

88

Chapter 5

EXAFS studies

5.1 Introduction

The term extended X-ray absorption fine structure(EXAFS) refers to the oscilla-
tions of the X-ray absorption coefficient on the high-energy side of an absorption
edge. Such oscillations can extend up to 1000 eV above the edge and may have
a‘magnitude of 10 % or more. As an example, the EXAFS spectrum near the K
edge in a polycrystalline Fe foil sputtered onto a ultra high pure Al foil is shown
in fig.5.1 This EXAFS signal was taken by detecting the total electron yield which
is proportional to the X-ray absorption coeflicient. The total electron yield method
will be discussed in the next section. Core levels of atoms differ and thus the energy
of the absorption edge uniquely identifies the atomic constituent being studied; the
technique is element specific. The abrupt jump in the absorption coefficient is the
Fe K edge absorption (the binding energy of Fe K-shell is 7112 eV) and the height
of this jump is proportional to the amount of Fe in the sample. The oscillations at
energies greater than about 30 eV above the edge are EXAFS data and they can be
used to determine the local structure surrounding the absorbing atoms.

The oscillatory part of the absorption coefficient Au, normalized to the struc-
tureless(atomlike) background #0, is given by[1]

.411 _ Ni .
X(k)——!To- — -;Elf1(ka")l

89

.90

 

(1055

(1050

(1045

Ir/Io

(1040

 

llIllllllllllIrllIIlI

 

(1035

 

llllllllllllllllll

7000 7200 7400 7600 7800
photon energy(eV)

Figure 5.1: Total electron yield spectrum of a polycrystalline Fe foil. The sharp rise
in yield near 7112 eV is the Fe K edge and the modulation above the edge is the

EXAFS.

91
x sin[2kr,~ + ¢(k)]e"'jape"'5/Ai(") (5.1)

Eq.5.l describes the modification of the photoelectron wave function at the origin
due to scattering by N,- neighbors located at a radial distance r; away. This is
illustrated in fig.5.2 where (a) an X-ray photon is absorbed by an atom through
the excitation of an electron from a core state j to an unoccupied continuum state f
(i.e.,E, = Ej+hw Z Erma, (b) the photoexcited electron waves propagate outward
from the excited atom(nodes denoted by solid lines) and (c) a scattered wave from
a neighboring atom interferes with the outgoing wave at the excited atom(nodes
denoted by dashed lines), modulating the wave function at the core level and thus

the absorption cross section. The backscattering amplitude is given by

war) = |f(k,W)|¢‘“"’ (5-2)

1 2'. l
232,301+ l)(e " -— 1)(-1)

where 61(k) are the scattering phase shifts. The photoelectron wavevector k is defined

1: = [2.71.055 — 5.)]1/3/8 (53)

where w is the X-ray frequency and E0 is the threshold energy. It is clear that the
electron wave will be phase shifted by Zkrj by the time it makes the round trip to
the neighbor. To this we must add the total phase function 1950:) given by

116(k) = 451(k) + 2451(k) (5-4)

The first term 01,06) is the phase shift due to the backscattering from the j-th neigh-
boring atom as defined in eq.5.2, while the second term is twice the absorbing atom
phase shift 61(k) to account for the potential of the absorbing atom through which
the l = l photoelectron wave(excited from I = 0 state) has traversed.

The Debye-Waller-type term 63:14-20:19”) accounts for the thermal vibrations
of the atoms. Finally, electrons that have suffered inelastic losses will not have the
proper wave vector to contribute to the interference process. This is accounted for

by a mean free path, A300), in an exponential damping term ezp[—2r,-/A,-(k)]. This

92

 

 

 

 

 

 

 

 

 

Figure 5.2: The origin of the EXAFS. The outgoing photoelectron wave(solid lines)
and backscattered photoelectron wave(dashed lines) interfere at the center of the
absorbing atom and thereby modulates the absorption cross-section. After T.M.

Hayes and J .B. Boyce[2].

93

term has critical importance. The limited range for the photoelectrons in the energy
region of interest(30~1000eV) imposed by this damping term permits a short range
order description of EXAFS even in crystalline materials.

There are many parameters in eq.5.1 and this fact is often used in criticizing
EXAFS studies. B.N. Teo[3] reviews the progress made in EXAFS studies and gives
a more concise statement on the number of parameters: ”Each EXAFS spectrum
contains two sets of highly correlated variables; [ f(ls,1r),N, o, A] and [1/J(lc),Eo,r].”
Indeed by dividing eq.5.1 into the oscillatory part sin[2kr,- + 1bj((¢)] containing only .
distances r,- and phase shifts 415(k) and the amplitude function

40:) = - Z, $.07“,r)le""’""'e"”’*“"’ (5.5)
1

we can handle the two groups of parameters separately. The use of theoretical cal-
culations for f(lr, 17) and ¢(Ic), the use of model compounds of known structure and
the use of Fourier Transform (FT) techniques reduce the number of free parame-
ters to a manageable number. The resultant structural information is for the local

environment(generally about 6.4) around specific atoms.

5.2 Experimental techniques

Strictly speaking an EXAFS spectrum can be derived only from a measurement of
the photoabsorption cross section over an appropriate range of X-ray photon ener-
gies. The more direct approaches to this involve measuring the normal incidence
transmittance or grazing angle reflectance of the sample. In the transmission mode
the optimum signal-tocnoise ratio is obtained when the sample is about two absorp-
tion lengths thick.[2] Since this typically requires several microns of sample with
subsequent tests at slightly different thicknesses to verify the absence of thickness
effects, the transmission mode is- not suitable for ultrathin multilayers with their
attendant substrates.

The absorption cross section can also be inferred indirectly through mea-
surement of some particular response of the sample to the absorption events. Such

indirect schemes may involve detection of photoemitted electrons, of the fluorescent

94

X-rays or of Auger electrons emitted when the hole in the core of the excited atom
is ultimately filled.

Fluorescence or total electron yield spectroscopy were used in this thesis. The
core hole created by the photoabsorption process can decay by either a radiative or
a nonradiative transition. In radiative decay, a higher lying electron fills the core
hole with the emission of a photon of energy equal to the difference the two energy
levels. The intensity of the fluorescence is proportional to the probability that the
incident photon has created a core hole, that is, it is proportional to the absorption
coefficient. Thus the fluorescence exhibits EXAFS.

Total electron yield detection monitors all the photoemitted electrons includ-
ing Auger electrons and inelastically scattered secondary electrons as well as the
electrons that are elastically emitted from the sample.

The standard experimental geometry is shown in fig.5.3 A tunable X- ray
source is needed for EXAFS experiment and this is accomplished with a double single
crystal monochromator which is controlled by a computer. A focused monochromatic
X-ray beam is passed through a partially transparent ionization chamber to provide
incident beam normalization and then allowed to strike the sample mounted inside
the electron yield detector or fluorescence detector. EXAFS data in this thesis were
taken on beam lines X9A, X1 1A and X23B in the National Synchrotron Light Source
on the Brookhaven National Laboratories using experimental setups established by

the PRT groups.

5.3 EXAFS analysis

In this section we deal with the analysis of EXAFS data. Given a set of data and
the basic EXAFS equation eq.5.1, there are clearly a large number of approaches
for extracting distances and information about the phase shifts and the amplitudes.
In this thesis F T(Fourier Transform) and curve fitting with theoretically calculated
scattering amplitudes and phase shifts were used in an existing EXAFS analysis

software package.[4] It is clear that a knowledge of the phase Mk) = 261(k) + (Mk)

95

is essential for obtaining distances from EXAFS data. The theoretical values of
backscattering amplitude I f (It, ir)|, phase of the backscattering amplitude ¢(k) and
the central atom phase shift 261(k) calculated by Tee and Lee[5] were used for curve
fitting.

The EXAFS data shown in fig.5.1 for a pure Fe foil will be used to demonstrate
the EXAFS data analysis procedures.

5.3.1 Background removal

The structure of bulk Fe is well known and serves here only as a good test of our
analysis procedure. The modulation above the K edge near 7112 eV is due to the
EXAFS x(k) from several shells of neighboring atoms adding together. The first step
in the analysis is to isolate x(k) from the total absorption coefficient data. The pre-
edge background was removed by a linear spline fitting and the smooth background
above the edge was removed with polynomial splines using a least—square procedure.

Fig.5.4 shows the extracted pure EXAFS signal after removing the back-
grounds and converting from has to k. The curve has been multiplied by k3 and
this has the effect of weighting the EXAFS oscillations more uniformly. This step
is important in preventing the larger amplitude oscillations from dominating the
smaller ones in determining the interatomic distances, which depend upon only the

frequency and not the amplitude of the sin[2kr,- + 105(k)] function in eq.5.1.

5.3.2 Fourier transform filtering

The next step in the analysis is a FT. This isolates the contributions of the different
shells of neighbors and allows the use of filtering techniques both to remove much of
the noise and to study each shell separately.

Fig.5.5 shows the magnitude of the FT of the k3x(k) data in fig.5.4. The large
peak at ~ 2.2.31 is the contribution from the first shell of 8 atoms at the distance
24823.4 and the second shell of 6 atoms at the distance 2.8663A.[6] The resolution
into two peaks for the first two shells was not possible and the first peak in the

FT magnitude contains the contributions of both shells. The four arrows in fig.5.5

synchrotron

source
double crystal
monochromator

polychromsric

X-l'l 3
y monochromatic

x-rsys

96

Incident that l_ '— "‘ j
monitor I l

A. Transmitted flux
monitor

Sample (toil)

Fluorewenee
detect:

 

 

 

fluorescence

x-rsys

Figure 5.3: Standard experimental geometry for EXAF S experiment.

97

indicate the distances of the first four shells in BCC Fe. The FT peaks are located
at apparently lower distances due to the effect of the phase shift rig-(k).

The dashed line in fig.5.5 is a smooth filter window function for isolating the
first 2 shells EXAFS. After filtering, the inverse FT is performed to give the solid
curve in fig.5.6. Note that the absence of all higher frequency variations and noise.

5.3.3 . Curve fitting

A curve fitting has to be used to separate two or more radial distribution function
peaks which are not resolved by the FT technique.

Once the EXAFS data for particular shells has been extracted by the inverse
FT as shown by the solid line in fig.5.6, the data analysis turns to fitting the observed
EXAFS data with simulated data which is calculated assuming some hypothetical
structure and the EXAFS expression given by eq. 5.1. The curve fitting procedure
consists of a non-linear least square optimization process. The measure of goodness
of fit used by XFPAK is called the minimization function F, which is defined as

follows:

 

F = (mama) — x...(k))1= 15.6)

where x...(h) is the observed EXAFS data and xagflr) is the calculated data with
a model. The sum is over the entire data range. Thus I"2 is the sum of square of
errors between the observed and simulated data, weighted by 163.

Since the first peak in the FT magnitude in fig.5.5 contains the contributions
from the first 2 shells, we assumed 2 shells in our curve fitting. The known distances
and the number of atoms in the first 2 nearest shells (8 atoms at 2.4823171 and
6 atoms at 28663.4) were given as the initial parameters. These parameters and
the threshold energy E0 were allowed to vary during the optimization process. We
note that E0 is often shifted from its original value due to the change of chemical
environment[1] or systematic errors in data aquisition.

The best fitting was obtained with 8.8 atoms at 2.47:1:0.06A and 4.0 atoms at
2.84 :t 0.04.4 and the value of the minimization function was F = 0.346. The dotted

98

 

30

20

10

 

 

 

 

 

 

 

 

 

k‘xtk)
PTTIIIIgTTI‘IIIIITIIIT

 

TTTI

 

 

_30 lilLlLlllllllLllllLlJll
4

6 6 10 12
k(A'1)

Figure 5.4: k3x(k) derived from fig. 5.1 by removing smooth backgrounds using a
polynomial spline fit. The photon energy he: has been converted to the photoelectron

momentum k.

99

 

3

N
O
O Trrrllrlrlllrr'yllllrrrr

moms.)
' ..
0

he
0

 

 

 

 

 

 

 

O

 

r(A)

Figure 5.5: The magnitude of the Fourier transform of the curve in fig. 5.4. The
dashed line denotes a window function used to isolate the EXAFS signalof the first

peak. The 4 arrows indicate the actual positions of the first 4 nearest neighbors.

100

 

30

E
205-
105- ,) ii i)
g E
.3: 0

 

 

 

 

 

 

I
p—a
O
rrlrlrlr1erI
C
C

 

 

 

-30lllllellllllLlllLJll

6 s 10 12
1:01.“)

.5.

Figure 5.6: Inverse transform of Fourier transformed data in fig. 5.4 after multipli-
cation, by the window function shown in fig. 5.5. The dotted curve is the simulated

EXAFS using only the first 2 Fe neighboring shells.

101

line in fig.5.6 shows the simulated curve with this 2 shell model; the experimental

data and the simulated curve are nearly indistinguishable.

5.4 Structural changes observed by EXAFS in metallic

mult ilayers

In chapter 4, we discussed the loss of magnetism in metallic multilayers, especially
in the Fe/ Si and Fe/Mo systems.(see fig.4.2 and fig. 4.5) In this section EXAFS data
of these Fe multilayers will be described. To set a context for these EXAFS data we
give a brief review of findings for the Fe/ Si and Fe/ Mo systems.

The Fe layers in the Fe/ Si system lost their magnetism when the Fe layer
thickness was less than about 10.4. In chapter 4 the pattern of saturation magneti-
zation versus Fe layer thickness for Fe/ Si multilayers was explained excellently With
a model assuming magnetically dead Fe layers of 10.4 thickness in each Fe layer.
The Fe(110) X-ray Bragg line became weaker and broader as the Fe layer thickness
decreased and TED data also showed the systematic loss of the long range order in
Fe layers as we discussed in chapter 3. The magnetically dead layers are believed to
be amorphous.

The Fe/Mo samples with a constant 3ML Fe layer thickness and varying Mo
layer thicknesses showed a drastic change in the saturation magnetization. While
3ML Fe/3ML Mo samples are essentially non-magnetic, the saturation magnetization
reaches that of bulk value as the Mo thickness increases. It is strongly suspected
that structural changes in the Fe layers are responsible for this. magnetic behavior.
In contrast to systematic changes in XRD data for Fe/ Si samples, all 3ML Fe / t
ML Mo samples have rather sharp X-ray reflection lines as shown in fig. 3.20 and
fig.3.21. These sharp lines indicate well layered structure and no structural change
in the Fe layers, even in 3ML Fe/3ML Mo sample, was observable by XRD.

In the remaining part of this chapter, the structural changes in the Fe layers
in Fe/Si and 3ML Fe/t ML Mo samples determined from EXAFS analysis will he

discussed.

102

5.4.1 EXAFS data of Fe/ Si multilayers

EXAFS spectra of 2 Fe/ Si multilayers were taken using the fluorescence detection
method. The nominal sample parameters were 30.4 Fe/50A Si and 18A Fe/30A Si,
respectively. F ig.5.7 shows the spectra. One can notice the similarity between the
EXAFS spectrum of the 3014 Fe/ Si multilayer and the spectrum of a pure Fe foil in
fig.5.1 while the spectrum of the 18.4 Fe multilayer is qualitatively different.

The difference in the spectra is more clearly seen in the extracted pure EXAF S
spectra after removing the background and converting to k-space(Fig.5.8). The
EXAFS spectrum of the 30.4 Fe layer sample is quite similar to that of the Fe
foil in fig.5.5, showing multifrequency character , while the EXAFS spectrum of
the 18.4 Fe sample resembles a single frequency with weaker amplitude and shifted
peak positions. A single frequency in an EXAFS signal is a typical feature of an
amorphous structure implying the dominance of a single near-neighbor distance in
the EXAFS.[2]

The Fourier transform of an EXAFS spectra in k-space produces an approx-
imate radial distribution function in real space which is shown in fig.5.9. For the
3014 Fe layer sample, the FT magnitude of the EXAFS signal is essentially identical
to that of pure Fe with up to the third peak. But the FT magnitude of the 18:4
Fe sample shows only the first peak; no evidence of higher peaks is seen confirming
that the structure of the Fe layers in this sample is predominantly amorphous. The
peak in FT magnitude also suggests that the nearest neighbor distance in the 18.4 Fe
layers is substantially reduced. However the positions of each peak are not the actual
distances of each shell since the phase shifts of absorbing atoms and backscattering
atoms cause non- physical translations in the FT.

To calculate the nearest neighbor distances from the observed EXAFS data.
inverse FT and curve fitting were used. A smooth Gaussian window function with
the half width of 0.1.4 was used to isolate the first peak in each FT magnitude.
F ig.5.11(a) and (b) shows the observed EXAFS data of the first peaks (denoted by
solid lines) and the best curve fittings of them (denoted by dotted line). For the
30.4 Fe sample, the best fitting was obtained using a 2 shell model and for the 18A

103

 

0.45

0.40

 

0.35

Ir/lo

0.30

 

I‘IIIUWIWIII'IIIUUUII“!

 

0.25

 

 

7000 7200 7400 7000 7600 8000
Photon energy(eV)

Figure 5.7: X-ray absorption spectra of two Fe/ Si multilayers measured by the flu-

orescence detection method.

104

 

30

 

  

 

 

 

C """-.

 

UIIUI'IIUI'IIF

 

 

llllllllllllllllllllllll

2 4 o a 10 12
K0!)

 

Figure 5.8: Extracted EXAFS spectra k3x(k) for two Fe/ Si multilayers after remov-

ing backgrounds.

105

Fe sample a single shell model gave the best curve fitting. These results suggest
crystalline Fe is dominant in the 30.1.1 layers while amorphous Fe is predominant in
the 18}! Fe layers. The structural parameters for the best fit curves are as follows:
(i) 30A Ire/50A Si

2 Fe atomic shells: 4.7 atoms at 2365:0051 and 4.9 atoms at 2.80:!:0.02.:1

(ii) 18A Fe/3OA Si

1 Fe atomic shell: 10 atoms at 2.39:]:0.141°1

5.4.2 EXAFS data of 3ML Fe/t ML Mo systems

The Fe layers in 3ML Fe/t ML Mo multilayer samples(£rom now on we will de-
note such a multilayer just as 3/ t) show a drastic change in magnetism, being non-
magnetic with t = 3 and bulk Fe like ferromagnet with t 2 4. All 3/ t samples have
quite sharp average Bragg line( perpendicular structural coherence Q ~_ 200421).
There are satellites in the high angle XRD data and at least 2 harmonics in the low
angle XRD data indicating highly ordered samples composed of crystalline individ-
ual layers with good chemical modulation. Any evidence of structural change in the
non-magnetic 3/ 3 sample was not observable with XRD measurements.

Extracted EXAFS spectra k3x(lc) of 3/t samples(t =3,4,8 and 12) are de-
picted in fig.5.11. One immediately notices the uniqueness of the EXAFS data of
3 / 3 compared to the other spectra. The period of oscillation for 3/ 3 is clearly longer
than the periods of others and a longer period in k-space indicates a short distance
to the near neighbors. The envelope function expressed by eq.5.5 is a function of
the number of neighbors, the scattering amplitudes of neighbors, thermal vibrations
and the mean free path for photoelectrons. The envelope functions of the samples
with t =4, 8 and 12 appear to be very similar. These facts suggest that a structural
change occurred in the non-magnetic Fe layers of the 3 / 3 sample.

The FT magnitudes of the EXAFS spectra in fig.5.11 are shown in fig. 5.12.

As expected the position of first peak in the FT magnitude for 3/ 3 is shifted to a
shorter distance compared to other first peaks. The higher order peaks in the F T

106

 

n — 30Al'e
m: 10A to

 

10

 

 

ARE)

3..

on
IIIVIYYIIUTIIITVTTTYII]

 

 

 

*

 

o Lilllk'

0 2 4 5 5
r(A)

Figure 5.9: Fourier transform magnitudes of h3x(l¢) in fig.5.9. The FT magnitude of
301.1 Fe ilayers clearly shows higher order peaks indicating BCC crystalline structure.

107

 

,
5 .- IBA F0

 
   

 

 

 

 

 

 

0?
-5}
F..1 .l mirr.rl .1;
4 6 8 10 12
S? k(A"1)
.25?
H
30AFe
10
—5
-10
.rrrr...1....Lrnrninr..
4 6 8 10 12
k(A—1)

Figure 5.10: Observed(solid lines) and calculated(dotted lines) EXAFS data. The

fitting parameters for the simulated curves are given in the text.

108

 

15
— am --- 3/4

10 s/s -- s/a

 

Itllrtllitri

mi)
0

   

0|
IIIIIIIYII ,

-10

 

 

pill]

LlllllllllLlllLlllllLI

4 s a 10 12
MA“)

 

-15

Figure 5.11: Pure EXAFS spectra of 3/ t Fe/ Mo samples. Note the difference in the
period and envelope function of the EXAFS of the 3 / 3 system compared to the other

spectra.

109

 

 

T

" — 3/18
15 ~

:- ......... 3/5

’ "- 3/4
10 _ —— s/s

moan.)

 

 

 

 

 

 

 

r(A)

Figure 5.12: FT magnitudes of the EXAFS data of 3/t Fe/Mo samples in fig.5.ll.
The first peak in the FT magnitude of the 3/3 samples is shifted toward shorter

distances relative to the others.

110

magnitudes are rather weak; each sample with t 2 4 has a faint hint of a higher
peak at about 4.4A. Any trace of this higher peak in the 3/ 3 sample is lost in the
noisy background. In last section, it was noted that the absence of the high order
peaks in FT magnitudes is generally attributed to the highly disordered structure.
At the first sight the weakness of the higher order peaks in 3/ t Fe/Mo multilayers
is puzzling because the XRD data indicate good crystalline layer in these samples.

But our samples are layered with the Fe layer thickness being fixed at only V
3ML and the higher order peaks (i.e. more distant atomic shells) would have both
Fe and Mo atoms. In table 5.1, the number of Fe atoms and Mo atoms in the first
4 atomic shells of an Fe atom are counted for the case of 3 ML Fe layers having
Mo layers on each side with the (110) texture out of plane and atomically sharp
interfaces. In reality the number of Mo near neighbors would be even larger than
these values when we allow for the rough interfaces and possible interdiffusion. The
fact that the calculated back scattering amplitudes |f(l¢,1r)| and phase shifts ¢(le)
of Fe atoms and Mo atoms are much different from each other [5] and that the
structural information in EXAFS data has been spherically averaged could appear
as increased disorder around a central Fe atom. Increased disorder would damp the
higher order peaks in the FT magnitudes of our 3/t Fe/Mo multilayers even in the
case of crystalline individual layers. No attempt to calculate the EXAFS spectrum
with many number of shells with varying numbers of Fe atoms and Mo atoms was
done.

As noted earlier the first peak in the FT magnitude of BCC Fe contains the
contributions from the first 2 atomic shells. Furthermore noting in table 5.1 that the
average number of Mo atoms in the first 2 shells of an Fe atom in an ideal 3 ML Fe
layer is relatively small, curve fittings for the first peaks in the FT magnitudes were
done. Each fitting assumed only Fe atoms and trends rather than values are the goal.
Appropriate Gaussian filtering window functions were used each FT magnitude.

Fig.5.l3 depicts the observed and simulated EXAF S spectra of each 3 / t
sample. The curve fitting of 3/ 3 is very poor; the value of the minimization function

F = 0.923 and a negative number of atoms is required. The simulated EXAFS data

111

 

 

 

 

 

 

 

 

 

 

5 .-. (a)3/3
.s'“' '3'.
0 '~. . .-
-5
l a m L l . r l l .
b34
5 (H
o .
A -5
a r r J l l l r l . L
x ,
'3: 5 . (c)3/8
0
-5
L i . . L . . r L L. r Lml . . .
d3/12
5 ( )
o
-5
. . . . l . . . . l . m. . l a . . .
4 ‘ » 6 8 10 12
k(A'1)

Figure 5.13: Observed(solid line) and calculated EXAFS spectra for 3/t Fe/ Mo
systems. (a)3/3 (b)3/4 (c)3/8 (d)3/ 12. The 3/3 system is not fitted very well by
the 2 Fe shell model.

112

of samples with t = 4,8 and 12 shows much better curve fittings with smaller values
of F. The variables in these curve fittings were the near neighbor distance r and
the half width of its fluctuation a, the number of neighbors n and the threshold
energy A30. The structural parameters obtained from the best curve fittings in
fig. 5.13 are given in table5.2. In general the number of Fe atoms in the first 2
shells obtained by simulation is rather far from the values of the ideal model system
for 3/t samples. This is in contrast to the 12/ 12 sample for which the obtained
structural parameters are quite close to the bulk crystalline values. The crudity of
the 2 shell model involving Fe atoms only forces poor results. Never-the—less, the
relative constant value of n in the first shell and the lack of unrealistic n values in
the second shell for 3/4, 3/ 8 and 3/ 12 are encouraging. Such features may indicate
better BCC like crystalline Fe layers in these samples than in the 3/ 3 samples.

113

 

 

 

 

Total Atom at center layer Atom at interface Average
j No. of N.N Fe Mo Fe Mo Fe Mo
1 8 8 0 6 2 6.67 1.33
2 6. 6 0 4 2 4.67 1.33
3 12 10 2 7 5 8 4
4 8 4 4 6 2 5.33 2.67

 

 

 

 

 

 

 

 

 

 

 

 

Table 5.1: The number of Fe atoms and Mo atoms in the first 4 nearest neighbor
shells of the Fe atoms in an ideal 3 ML Fe(110) layer with thick Mo layers on both

sides.

First shell Second shell

r(A) n a AEo r(A) n o AEo F

3/3 2.61 7.3 0.1 29.3 2.94 -l4.3 0.17 45 0.923
3/4 2.50 5.5 0.08 -5.2 2.90 0.32 0 -l3.2 0.152
3/8 2.50 5.5 0.08 -6.5 2.78 2.0 0.08 -5.2 0.111
3/12 2.48 5.82 0.07 -6.8 2.90 0.7 0.06 -23.6 0.118
12/12 2.43 7.5 0.06 -4.13 2.79 5.3 0.04 6.0 0.129

 

 

 

 

 

 

 

 

Table 5.2: The optimum fitting parameters of the EXAFS data for the Fe/ Mo sys-

tems considering only the first 2 Fe atomic shells.

Bibliography

[1] P.A. Lee, P.H. Citrin, P. Eisenberger, and B.M. Kincaid Rev. of Mod. Phys.,
§§,769,(1981)

[2] T.M. Hayes and J .B. Boyce Solid State Physics 31, 173, (1982)

[3] Boon K. Teo EXAFS: Basic Principles and Data Analysis (Springer-Verlag,
1986)

[4] EXAFS Analysis Software Package School of Chemical Science, University of

Illinois Urbana
[5] B.K. Teo and P.A. Lee Jour. of Am. Chem. Soc. 111, 2815 (1979)

[6] CRC Hand book of Chemistry and Physics, 66th edition 1985

114

 

 

Chapter 6

Summary and recommendations

6.1 Structure and magnetism

Metallic multilayers, Fe/ Si, Fe/Mo, Fe/ V and Fe/ Cr, were prepared using a sputter-
ing system. The individual layer thicknesses were between 3 ML and 40 ML.

In the XRD(X-ray diffraction) data of the Fe/ Si multilayers, at least 3 har-
monics were observed at small angles indicating a compositionally modulated struc-
ture. No high angle satellite was seen; only a broad Fe(110) bragg line was observed.
Si layers were amorphous and the ultrathin Fe layers were structurally isolated in
our Fe / Si multilayers. The saturation magnetization decreased with decreasing Fe
layer thickness and vanished near 5 ML. A simple magnetic model assuming mag-
netically dead Fe layer of 5ML explained the reduction of magnetism in Fe/ Si as
the Fe layer thickness decreased. Both XRD data and TED(Transmission Electron
Diffraction) data were consistent with a crystalline to amorphous transition as the
Fe layer thickness decreased. EXAFS data confirmed this transition. We conclude
that about 10.4 of amorphous Fe were grown on the amorphous Si layers before
crystalline Fe layers were resumed and the amorphous Fe layers were non-magnetic.

For Fe/X(X=Mo, V and Cr) systems, successful crystalline layered structures
were confirmed by XRD data and calculation. In most of our samples, values of the
modulation period determined from XRD data agreed to the nominal values within

5% or less. All the transition metal layers had BCC(110) texture in the film normal.

115

116

The typical value of the perpendicular structural coherence length(PSCL) from the
FWHM of the average lines was ~ 200A without device broadening correction.

Fe/V was crystalline at all layer thickness but strains in the layers were
observed when the layers were thinner than 16 ML. Both XRD data and TED
data are consistent with the onset of a SLS(strained layered superlattice) in Fe/ V.
Comparison between XRD data and model calculations suggested that strains reside
in Fe/ V up to individual layer thickness 16 ML and that the strain is uniaxial. TED '
data provided the direct evidence of a SLS. Fe/V samples with layer thicknesses
greater than 16 ML have a double BCC lattice in the sample plane while samples
with thinner layers have a single BCC lattice.

XRD data and TED data for Fe/Mo systems also exhibited a double BCC
to single BCC transition. However this transition differed significantly from that of
Fe / V. First, the transition occurred abruptly without the gradual modification of
individual layer structures that occurred in Fe/V. Second, the transition occurred
at a smaller layer thickness, between 6 ML and 10 ML rather than 16 ML.

A reduction of magnetism started at layer thicknesses around these struc-
tural transitions in both the Fe/V and Fe/Mo systems. Fe/Mo lost its magnetism
abruptly at thicknesses below 6 ML and was non-magnetic at 3 ML. The reduction
of magnetism in Fe/ V was gradual and 3 ML Fe layers still retained about 50% of
the magnetization of bulk Fe. Fe layers in Fe/ Cr had bulk Fe magnetizations at all
layer thicknesses.

3 ML Fe/ X systems showed an interesting interplay between structure and
magnetism. The 3 ML Fe layers in 3ML Fe/Mo samples had a transition from non-
magnetic to ferromagnetic(like bulk Fe) as the Mo layer thickness increased from 3
ML to 5 ML. While XRD data indicated crystalline structure in all Fe/Mo systems,
at least in the film normal, preliminary EXAF S data analysis suggested better BCC?
like Fe layers in the samples with more than 4 ML Mo layers. The 3ML F e/ V samples
had considerably reduced magnetization(below 70% of bulk value) at all V layer
thicknesses but no drastic change in magnetism was seen. Fe and V are mutually

soluble and the intermixing at interfaces could cause the reduction of magnetism

117

with relatively small structural change. The 3ML Fe/ Cr sample retained the bulk
magnetism at all layer thicknesses , neither structural change nor intermixing is

indicated in this system.

6.2 Magnetic interlayer interaction in Fe / Cr

In parallel field magnetic measurements, saturation fields(H5) of 4K0e are typical
for all Fe/Mo and Fe/ V samples independent of the layer thicknesses. In Fe/ Cr,
however, anomalously large saturation fields up to 46K0e have been observed when
both the Fe layers and the Cr layers are thinner than 10ML. These saturation fields
decrease rapidly and monotonically to ~4K0e as the Cr interlayer thickness is in-
creased to about 20ML. These anomalously large Hs’s are believed to be from the
antiferromagnetic coupling between the magnetic Fe layers across the Cr interlayers.
H3 is also strongly dependent on the Fe layer thickness. In the samples with an
Fe layer thickness of 25ML, H5 is ~4KOe, the typical value for Fe/Mo and Fe/V,
andno dependence on the Cr thickness is observed. This behavior suggests the
disappearance of antiferromagnetic coupling for these thicker Fe layers.
Perpendicular field magnetic measurements provide a measure of magnetic
anisotropies. The perpendicular saturation fields(HA) of Fe/ Mo and Fe/V satisfy
H A = 47M; within the experimental error indicating no anisotropy other than the
shape anisotropy. Again, however, H A’s for Fe/ Cr showed large deviations from this
relation. The value of the deviation, AH = H A — 41rM5, ranged from —9K0e to
24K0e depending on the Fe layer thickness and the Cr layer thickness. The positive
values of AH are closely related to the values of H5 giving essentially a linear
function. It is believed that the large anisotropy is due to the magnetic interlayer
coupling . The idea that the positive AH’s are from antiferromagnetic coupling and

the negative AH’s are from ferromagnetic coupling is suggested.

\

1 18
6.3 Recommendations

(1) While XRD data indicate a crystalline structure for 3ML Fe/3ML Mo samples, at
least in the film normal, EXAFS data suggest some kind of structural change in the
non-magnetic 3ML Fe layers. Since TED data are not available in this thesis, TED
measurements on this sample should be done to determine the in-plane structure.
(2) From the results of magnetic measurements it is believed that the Fe/ Cr system
has strong magnetic interlayer interactions while no, or very weak, magnetic inter-
actions are present in the Fe/Mo or Fe/ V systems. The conduction electrons in Cr
layers are believed to be responsible for this interlayer coupling between Fe layers.
The quality of the interfaces is generally believed to be important for this coupling.
The nearest of Fe and Cr in the periodic table and the small lattice mismatch be-
tween them make structural studies by XRD or TED very difficult. A systematic
perpendicular transport study of Fe/X(X=Mo, V, and Cr) is suggested as means of
studying Fe/ Cr interfaces relative to Fe/Mo and Fe/V interfaces.