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Local Atomic Structure and the Metal —

Insulator Tran51t10n of Lal-X CaX MnO3

presented by

REM) GIOVANNI DIFRANCESCO

has been accepted towards fulfillment
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Ph . D. degree in PHYSICS

 

    

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1110:) mm.“

 

LOCAL ATOMIC STRUCTURE AND THE METAL-INSULATOR TRANSITION
OF La1_,,.Ca,MnO3

By

Remo Giovanni DiFrancesco

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

2000

ABSTRACT

LOCAL ATOMIC STRUCTURE AND THE METAL-INSULATOR TRANSITION
OF La1_3CaanO3

By

Remo Giovanni DiFrancesco

La1_zCazMnO3 is one of a class of materials which were recently found to display
Colossal Magnetoresistance. This has generated a great deal of interest in attempting
to explain this phenomenon. Recent work has suggested that the lattice plays an
important role in the electronic behavior of these compounds by way of the Jahn—
Teller effect, leading to polarons. We have probed the lattice using atomic pair
distribution functions, a local structural technique, to determine if changes in the

lattice are present and how they correlate with the various electronic phases.

The structure is found to respond strongly to the metal-insulator transition with
a distortion of the six oxygen atoms surrounding each Manganese site. We interpret
this as the formation of polarons which are first seen in the ferromagnetic metallic
(FM) phase and increase in density as the paramagnetic insulating phase is entered.
The FM state is seen to contain two regions: a low temperature state in which all
carriers are delocalized and the structure is undistorted, and a higher temperature

area in which the delocalized charges coexist with polarons.

The PM state in the x = 0.5 material is found to contain a similar mixture of
phases for a narrow range of temperatures. A charge ordering transition eventually
suppresses the delocalized state which ultimately destroys the ferromagnetism. The
PDF reveals that at high temperatures the carriers remain localized but their ordering

is lost through an order-disorder transition.

Multas per gentes et multa per aequora uectus
aduenio has miseras, frater, ad inferias,
ut te postremo donarem munere mortis
et mutam nequiquam alloquerer cinerem.

~Catullus

iii

ACKNOWLEDGMENTS

Of course the first person I need to thank is Simon Billinge. I’m deeply indebted
not only for everything he has taught me but also for his patience and tolerance.
Thanks also Julius Kovacs, S. D. Mahanti, Wayne Repko, and Stuart Tessmer for

their time and effort in serving on my committee.

So many people have passed through the Billinge group during my stay that I
can’t list them all, but each of them helped me in this work in some way. I hope
my colleagues have enjoyed working with me as much as I have enjoyed the time I’ve

spent with them.

Numerous other members of the department have made my time here something
I’ll remember: Kelly Page, Michael Narlock, Freddie Landry, Michael Hamlin, Charles

Moreau, Declan Mulhall, and Jerry Pollack to name a few.

Finally, thanks to my parents for their support and their trust.

iv

TABLE OF CONTENTS

LIST OF TABLES vii
LIST OF FIGURES viii
1 Introduction to Colossal Magnetoresistant Manganites 1
1.1 Introduction ................................ 1
1.1.1 Early work ............................. 2

1.1.2 Colossal magnetoresistance .................... 4

1.1.3 Experimental evidence for a strong electron lattice interaction 8

1.2 Measuring local structure ......................... 8
1.2.1 Average and local structure ................... 8

1.2.2 PDF technique .......................... 9

1.2.3 XAFS ............................... 9

1.3 Polarons and the Jahn-Teller effect ................... 10
1.3.1 Jahn-Teller effect ......................... 10

1.3.2 Polarons .............................. 10

1.4 La1_xCaanOs .............................. 12
1.4.1 Phase diagram .......................... 12

1.4.2 Average structure ......................... 13

1.4.3 Properties ............................. 13

1.5 Summary ................................. 14

2 The Pair Distribution Function Technique 15
2.1 Introduction ................................ 15
2.2 Data collection .............................. 18
2.2.1 Neutrons .............................. 18

2.2.2 X-Rays ............................... 21

V

2.3 Analysis ..................................
2.3.1 Neutrons ..............................
2.3.2 X—Rays ...............................
2.3.3 Obtaining the PDF ........................

2.4 Modeling ..................................

2.5 PDF peak height and width .......................

Metal-Insulator Transition at Tc and xc

3.1 Introduction ................................
3.2 Structural Response to Temperature ..................
3.2.1 Atomic disorder from PDF peak-heights ............
3.3 Doping across the phase transition ...................
3.3.1 Within the metallic region ....................
3.4 Polarons and modeling ..........................
3.4.1 Fitting the Jahn-Teller distortion ................

Metal Insulator Transition at x=0.5

4.1 Introduction ................................
4.2 Experiments and results .........................
4.3 Summary .................................

Discussion and Conclusions

5.1 Summary .................................
5.1.1 Results ...............................

5.2 Future work ................................

APPENDIX

Bibliography

vi

23
23
24
26
27
28

29
29
30
32
35
39
41
41

44
44
45
49

51
51
51
53

55

56

List of Tables

3.1 First seventeen atomic correlations and amplitudes for La1_zCa,Mn03
based on the crystal structure model. Note the strong Mn-O peak at
1.96A and the strong O-O peak at 2.74A ................. 33

vii

1.1

1.2

1.3

1.4

1.5

2.1

2.2
2.3

3.1

3.2

3.3

LIST OF FIGURES

Basic structure of the perovskite cell. In Lal_,Ca,MnO3 the A and B
sites are a random mixture of Lanthanum and Calcium. The oxygen
sites form an octahedron about each Manganese .............

Resistivity vs. temperature curves for La1_,SrzMnOg at various com-
positions. Note the large changes in slope near T6 for the intermediate-
doped compounds [1] ............................

Phase diagram of temperature versus average A-site size. Open sym-
bols show Tc measured by magnetization and closed symbols are Tc de-
termined by resistivity. Tolerance factor is a measure of the deviation
away from perfect cubic structure [2] ...................

Phase diagram of average A-site radius vs. dOpant concentration. Ef-
fects of Sr and Ca substitution are shown by the dashed lines. Values
of T6 are shown in the FMM region[3]. .................

Electronic and magnetic phases of La1-zCa,MnOa [4] ..........

X—ray parafocusing geometry. The detector and the source are kept
equidistant from the sample ........................

Structure function of 1431-303.an03 up to 22A“. ..........
Typical neutron PDF of La1_xCa,MnO3 . ...............

PDFs of Lao,83Cao,12MnO3 measured at 150K and 188K, difference
plotted below. Dashed lines indicate two-sigma level of uncertainty.
Note that the difference curve remains largely within the dashed lines,
showing that the structure remains largely unchanged. ........

PDFs of Lao,33Cao,12MnOg measured at 160K and 192K, difference
plotted below. Note the large amplitude of the difference curve rel-
ative to the uncertainty. Between these temperatures the sample has
passed through the MI transition and the structure has changed no-
ticeably. ..................................

Peak heights vs. temperature for three compositions: x = 0.25 (top) ,
a: = 0.21 (middle), and a: = 0.12 (bottom). The upper two panels show
a large drop in height well below Tc , marked with arrow. Bottom panel
shows a composition with no MI transition. The peak heights follow
the expected Debye behavior. Insets show resistivity vs. temperature.

viii

7
12

21
25
26

32

34

3.4

3.5

3.6

3.7

3.8

4.1

4.2

5.1

PDFs of Lao,79Cao,21MnO3 and Lao.38Cao_12MnO3 . (A) Both measured
at 220K, both in the insulating phase. The structures are remarkably
similar although the compositions are different.(B) Both measured at
10K, the a: = 0.21 sample is now in the FM phase and is sharper
relative to the a: = 0.12 sample. .....................

Comparison of PDF difference curves between Lao,79Cao,21Mn03 and
Lao,38Cao,12MnO3 at 220K (solid line) and 10K (triangles). At low tem-
perature, when the two samples are in different phases, the structures
show larger differences than at higher temperatures at which they are

both PI. ..................................

36

37

Difference curves: Triangles are again the difference between Lao,79Cao_21MnO3

and Lao.33Cao,12MnO3 PDFs at 10K. Solid line is the difference between
Lao,79Cao,21MnO3 at 225K and 140K. The changes in the structure
caused by entering the FM phase through a decrease in temperature
or an increase in doping are large and correlate well ...........

Height of the Mn-O peak at 10K vs. Calcium concentration. Dashed
line shows the boundary composition between insulating and metallic
regions at this temperature. The peak sharpens smoothly through
:rM, and continues sharpening well into the FM phase. This suggests
that local distortions exist close to the phase boundary even at low
temperatures. ...............................

Undistorted crystal model fit to Lao,75Cao,25MnO3 in the FM phase at
20K (left) and in the PI phase at 260K (right). Darker lines are data.
Note that the quality of the fit is considerably poorer at the higher
temperature .................................

PDFs of Lao,5oCao,5oMn03 measured at 112K. The solid line is the
PDF measure while warming and the circles while cooling. Difference
is plotted underneath. Dashed lines indicate two sigmas of statistical
uncertainty. Note the close agreement between PDFs ..........

Top: Heights of PDF peak at 16.2A as a function of temperature.
Squares indicate data collected while warming, circles while cooling.
Peak height rises dramatically with temperature between T N and T00-
This is due to the loss of charge ordering which leads to a higher symme-
try state. Bottom: Heights of PDF peak at 2.75A. Peak heights tend to
follow Debye curve (solid line) except on cooling between T6 and T N .
Those peak heights (filled circles) increase due to charge delocalization
which is suppressed by charge-ordering ..................

PDFs of Lao.75Cao,25MnOa measured at room temperature using x-rays
and neutrons. ...............................

ix

38

40

42

46

47

Chapter 1

Introduction to Colossal
Magnetoresistant Manganites

1.1 Introduction

This thesis deals with the local atomic structure of 1481-303an03 and how this
affects its physical properties. First, early work on these materials from the 1950’s is
described. Interest in these materials was recently reawakened with the discovery of
an extremely large magnetoresistance in thin films as we discuss in Section 1.1.2. The
importance of the lattice, and in particular the local structure, to this phenomenon
was predicted theoretically and verified experimentally as we describe in Section 1.1.3.
In Section 1.2 we introduce different methods for measuring local structure including
the atomic pair distribution function (PDF) technique, which is the approach we
have used. The origin of the strong electron-lattice coupling is the Jahn-Teller effect
which is introduced in Section 1.3.1. This results in lattice polaron formation which
is briefly described in Section 1.3.2. Finally, we describe the structure and properties

of the La1_zCa3MnO3 system which is the system studied in this work.

A number of recent reviews [3, 5] and collections [6, 7, 8] are available.

 

 

 

 

 

 

 

 

 

 

0’ Q X.
,0 . A&B
G {9' 0 0 Mn
0’ 0 Oxygen
J. 6’ a}

Figure 1.1: Basic structure of the perovskite cell. In La1_zCa,Mn03 the A and B
sites are a random mixture of Lanthanum and Calcium. The oxygen sites form an
octahedron about each Manganese.

1.1.1 Early work

In 1950 Jonker and van Santen [9] synthesized a series of manganese oxides of the
general formula A1_$BanO3, where A is a trivalent and B a divalent ion. These
compounds form in the perovskite structure shown in Figure 1.1 in which the A, B,
and Mn ions form interpenetrating simple cubic sublattices with O at the cubic faces

and edges.

At finite d0ping values Mn takes on a mixed valence in order to preserve charge
balance. A fraction of the ions, 2:, takes on a Mn4+ (d3) state while the remainder
are left in the Mn3+ (d4) state. The doping level was found to influence the magnetic
and electrical properties of these materials. For values of a: close to 0 and 1 the
ground state is antiferromagnetic while for intermediate (0 < a: < 0.5) dOping levels
a ferromagnetic ground state was observed with a Curie temperature reaching its

maximum at a: z 0.3.

Subsequently, van Santen and Jonker [10] found that above Tc the resistivity

was semiconductor-like, dp/dT < 0, while below Tc there is a transition to metallic

2

 

103‘
102
10‘
10°

10'1

 

 

Resistivity (Qcm)

 

X=0.17

10'2

X=O v /

-3
1° iIIIIII'D" xstts
. .x:o«i

1 04 . . l 1 l . I n l La
0 100 200 300 400 500
Temperature (K)

 

Figure 1.2: Resistivity vs. temperature curves for La1_,,erMn03 at various com-
positions. Note the large changes in slope near T6 for the intermediate-doped com-
pounds [1].

behavior, dp/dT > 0, as well as a sharp reduction in resistivity as shown in Figure 1.2.

A mechanism called double exchange (DE) was proposed by Zener [11] to explain
the coincidental appearance of metallicity and ferromagnetism. The essential ingre-
dients of DE are that Mn is in a mixed valence state so that Mn3+ and Mn4+ are
both present in the structure, that there is localized spin (in this case 3/ 2 spin) in the
localized tgg orbitals on each Mn ion, and that the tgg holes are Hunds-rule coupled to
the electron in a delocalized eg orbital on the Mn3+ ions. Charge transport happens
through the hopping of an eg electron to an empty eg orbital on a neighboring Mn4+

ion. The probability of hopping will depend on the relative alignment of the spins

of neighboring Mn sites. Specifically, the hopping probability varies like cos %, where
0 is the angle between core-spins on neighboring Mn sites [12]. Therefore when the

spins align ferromagnetically there is an enhancement in electron hopping.

The lattice does not play an important part in DE and the crystal structure re-
ceived little attention until recently. Elemans et al. [13] published structural param-
eters from neutron diffraction for the series La1-zBa,Mn1_yTiyOg. The endmember
LaMn03 was found to be highly distorted, with rotations and elongations of its oxygen
octahedra. Although perovskites often show such rotations, the observed octahedral
elongations were thought to be caused by the Jahn-Teller effect [14] which we will
discuss in Section 1.3.1. With doping, these elongations seemed to vanish based on
diffraction studies and the rotations decreased in magnitude. Overall, these materials
remained of purely academic interest until the discovery of their magnetoresistance

(MR).
1.1.2 Colossal magnetoresistance

Interest was reawakened with a series of experiments [15, 16] that studied the MR
of these compounds associated with the transition from paramagnetic insulator (P1)
to ferromagnetic metal (FM). They found large decreases in resistance when a field
sufficient to drive the system into the FM region was applied. A much larger MR
was found in thin films of several manganese oxides [17, 18, 19] which led to the term
colossal magnetoresistance (CMR) to distinguish it from the previously discovered gi-
ant magnetoresistance (GMR). GMR is found in metallic multilayers with alternating
layers of a ferromagnetic metal like Fe or C0, and normal metals like Cu with each
layer being the thickness of the oscillation period of the RKKY interaction. GMR
is created by reversing ferromagnetic domains defined by the layer thicknesses. The

field strength needed to saturate the magnetoresistance is usually several tenths of a

4

Tesla, while a similar effect in CMR materials requires a field of over 5T.

It was found that the size of the MR effect is inversely related to Tc [20]. This
can be understood quite easily. The large MR occurs because the sample is driven
through an insulator-metal transition by the application of a strong external field.
In the insulating (high-temperature) state the resistivity increases exponentially on
cooling. At Tc the sample changes to a metal and the resistivity dr0ps dramatically.
If Tc is lower, the dr0p in the resistivity is larger simply because the resistivity of the
insulating state is so high. The same argument can be applied to the case where the

sample is driven metallic by an external magnetic field.

The Tc can be changed by varying the Mn“ density, which changes the hole
concentration and bandfilling. But we can also affect Tc by varying the bandwidth.
This is done by changing the average size of the A ion in the ABO3 formula which
changes the lattice constant. In Lao,7yPryCao_3MnO3 and Lao,7yYyCao,3MnO3 Hwang
et al. [2] studied the evolution of Tc with the Ca-concentration, hence hole density,
fixed. They found that as the average size of A, < ra >, decreases, Tc also decreases

(Figure 1.3).

Instead of creating internal pressure by changing < ra >, external hydrostatic
pressure can be applied to alter the lattice parameters. A number of such exper-
iments [21, 22] have found that Tc increases as external pressure is applied, with
ch/dP increasing as a: is decreased, showing increased sensitivity of T6 to 1:. Sim-
ilar experiments [2] on Pro_7Cao,3MnO3 and Lao,7Cao,3MnOa directly correlate with
results from internal pressure studies. This sensitive dependence of Tc on pressure is
one indicator that the structure has a role [23, 24] in the properties of these materials

and that DE is not an adequate theory.

Internal pressure studies show that a decrease in the Mn-O—Mn bond angle arises

 

     
 

 

 

1.15 1.20 1.25 1.30
400 r 1 I
A0 ‘7" osMnOa
300 -
A PHI
5; 200 -
E" warming
open-1'."
10° cloud-1' ' d
to“ 0037C.“
on. Ca. Sr
: 143.; Sr :Ba):
4 I

 

o J l
0.89 0.90 0.91 0.92 0.93 0.94 0.95
Tolerance factor

Figure 1.3: Phase diagram of temperature versus average A-site size. Open sym-
bols show Tc measured by magnetization and closed symbols are Tc determined by
resistivity. Tolerance factor is a measure of the deviation away from perfect cubic
structure [2].

from decreasing < ra >. The increase in orbital overlap created by pressure allows
electrons to delocalize, and the kinetic energy gained by the carriers would seem to
be the driving force behind the relationship between < ra > and Tc . In addition,
it was found that DE alone cannot give the magnitude of the change in resistivity
at T6 [23]. A theory was put forth by Millis [25] which argues that the important
parameter governing Tc is the e-ph coupling constant A. Millis’ theory is discussed
further in Section 1.1.3. The idea that there is a universal relationship between MR
and Tc can be seen if we plot To for the various phases as a function of a: and < re >

as in Figure 1.4. The PM ground state is bound by the size of the La3+ ion above

and by CO, AF, and spin glass states below which are strongly coupled to lattice

         

W//
é Lanthanide

1.8 6 ._
5 Contraction ~50

 

<rm>(A)

 

1.7

.....
..

 
 

L...

1.6 . - a 7. .
0.0 0.1 0.2 0.3 0.4 0.5
X

 

Figure 1.4: Phase diagram of average A-site radius vs. dopant concentration. Effects
of Sr and Ca substitution are shown by the dashed lines. Values of T6 are shown in
the FMM region[3].

distortions as we might expect since A is increasingly important in that region.

While the pressure studies attempted to vary only bandwidth or bandfilling, these
parameters are too connected to be varied alone. In the < ra > experiments, although
a: is constant the effective filling likely changes as the e-ph coupling is changed. In
the external pressure studies, varying the La concentration changes < ra >. The e-ph
coupling, A, would seem to be the parameter which is actually responsible for the re
sults of these experiments. In Millis’ theory [25] an effective A depends on bandwidth,
which in turn depends on the spin alignment through the usual DE expression, and

this would seem to fit well with the observed phenomenology.

1.1.3 Experimental evidence for a strong electron lattice in-
teraction

Other experiments have strongly suggested an important interaction between the elec-
tron and the lattice. One of these was a study of the isotope effect in Lao,3Cao_2MnOa [26].
After a 95 per cent exchange of 180 for 160, a reduction of To from 210K to 190K was
observed. No change was seen in SI‘RUOa, an itinerant ferromagnet, which had 80

per cent exchange.

A number of other experiments including XAFS [27 , 28] and diffraction studies [29]
have found large thermal factors on oxygen sites in the PI phase which dr0p rapidly
near Tc . All of these experiments demonstrate that the transition from P1 to FM is
not solely electronic in origin and that e—ph coupling must play an important part.
The theory of Millis [25] attempts to explain the electron-lattice interaction in terms
of polarons (see Section 1.3.2). Localized carriers in the PI state are believed to distort
their immediate environment, and it is this distortion which XAFS and diffraction
experiments may be sensing as exaggerated thermal factors. Other, more specialized

types of experiments may be better able to detect and characterize these distortions.

1.2 Measuring local structure

1.2.1 Average and local structure

A typical diffraction experiment analyzes the position and intensity of scattered parti-
cles in the form of Bragg peaks. These peaks form when the change in the wavevector,
Q, of the scattered particle is a vector of the reciprocal lattice, K, of the scattering
structure. However, this assumes an infinite, perfectly periodic array of atoms. In
the case where imperfections exist, we still recover Bragg peaks but their analysis

cannot give us the true picture of the structure in question. Since Bragg scattering

8

arisies from perfect periodic arrangements of atoms, it only carries information about
the average structure. Average in this sense does not carry its usual meaning, but is

often used in place of long—range structure.

Any arrangement of atoms which is ordered over long ranges will be discernible
through the analysis of Bragg peaks. Short-range structures which are not spatially
ordered do not give rise to Bragg peaks but instead produce diffuse scattering. The
analysis of diffuse scattering from single crystals to determine local structure has
been done for some time but is hampered by the low collection rate and difficulties

of sample preparation.

1.2.2 PDF technique

As we discuss in Chapter 2, the atomic pair distribution function (PDF) technique
uses powder diffraction data by Fourier transforming the entire pattern: Bragg peaks
and diffuse scattering. The result is a real-space radial projection of the atomic pair
correlations. Because the entire diffraction pattern is accepted, this function contains
information on both the local and average structure. This technique has been applied
for some time to the study of liquids and glasses but with modern synchrotrons and

neutron sources it has now been extended to crystalline materials [30].

1.2.3 XAFS

Another experimental approach that gives local structural information is XAFS (X-
ray Absorption Fine Structure). XAF S works by examining changes in the absorption
spectrum near the resonant x-ray energy of a particular ion. At the resonance energy
an atom of the resonant species absorbs a photon and photoemits an electron. The
outgoing electron wave is backseattered by neighboring atoms and interferes with
itself. This gives rise to a measurable modulation of the absorption probability at

9

energies above the absorption edge; the so-called extended x-ray absorption fine struc-
ture or XAFS. These fluctuations in the absorption cross-section depend sensitively
on details of the local atomic structure and it is possible to infer the local struc-
ture from them [31, 32]. This has the advantage of chemical-specificity if one desires
to know the structure in the region about one particular type of atom. However,
the response of the absorption spectra to structure is highly r-dependent, making
information beyond the nearest neighbor somewhat problematic. The PDF has the

advantage that it can be applied on all length scales.

1.3 Polarons and the J ahn—Teller effect

1.3.1 J ahn-Teller effect

One type of local distortion that is present in these manganites is caused by the
Jahn-Teller effect. This is an atomic distortion which certain ions create in order
to break the degeneracy of their electron levels [33, 34]. In our case Mn“, which
has 3 d-electrons in the tgg state and one in an eg state, is a Jahn-Teller ion. In the
octahedral coordination of Mn3+ , the two eg levels are degenerate if all six oxygen
atoms are equidistant from the manganese. By distorting the octahedra, the two e9
states lose their degeneracy and the electron can occupy the lower of them. In Jahn-
Teller ions the energy thus gained is greater than the elastic penalty of stretching
bonds. In Mn3+ ions this leads to an elongation of the octahedron with the d,2_,2

orbital occupied.

1.3.2 Polarons

The term polaron is used to refer to a large class of quasiparticles in which a localized

charge polarizes the background medium where it resides. In Millis’ theory of electron-

10

phonon coupling the type of polarons created specifically are small lattice polarons.
These form when carriers become self-trapped [35]. The condensed charge cloud exerts
a force on the previously charge-balanced environment: attracting and repelling the
variously charged ions in its vicinity. This “polarizes” the lattice, hence the name.
As the local ions adjust to the new situation, the carrier in turn responds to the new
potential created by the shifting ions. It is forced to spatially condense further until
it is finally contained on a single atomic site. We might expect to see polarons on Mn

sites in the PI phase as a distortion in the position of neighboring oxygen sites.

In the case of La1_,CaanO3 , the existence of polarons and the Jahn—Teller
effect depends on the behavior of the carriers. The carriers may be fully localized
onto discrete manganese sites, or they may be itinerant, with each site sharing them
evenly. The ability of manganese to adopt a mixed valence state means that at
finite doping levels, when the carriers are localized a fraction of the Mn ions, 1 — x,
can still be in the 3+ state and so will still display a Jahn-Teller distortion. This
means the remaining Mn ions carry a 4+ charge which would attract the surrounding
oxygen ions, contracting those MnOe octahdera and creating a polaron. The two
distinct charge states create two distinct local structures which we hope to detect.
On the other hand, if the carriers are delocalized, all the manganese ions will carry
the equivalent charge of 3 + 2:. In that case all the octahedra will be identical, with
neither Jahn-Teller nor polaronic distortions. Thus the presence of these two effects

are not only intimately linked to each other, but also tied to the electronic state.

11

 

- T. H, mm,“ ' [mic-Moo.

 

      
   
 

  

Temperature (K)
N
8

 

 

 

180- ~
’s
100 , §
140 F" N Am
insulator met-l § Insulator
120. §
§ \
1m IL L 1 § 1 r n
0 10 20 30 40 50 60 70 80 90 100
9603

Figure 1.5: Electronic and magnetic phases of La1_zCa;Mn03 [4].

1.4.1 Phase diagram

The phase diagram of La1_,CazMn03 has been studied by a number of groups [4, 36]
and is reproduced in Figure 1.5. At a: = 0, the ground state is an antiferromagnetic
insulator (AFI) and a ferromagnetic insulator when 0 < :L‘ < 0.2. For 0.2 < :1: < 0.5
the ground state is FM with a Tc which can be driven upwards by the application
of a magnetic field, hence the CMR effect. For a: > 0.5 the ground state is again
AFI although there is a well-defined line in the T6 -x plane in this region which
defines a charge-ordering (CO) transition seen from TEM [37]. For a: z 0.5 there are
three distinct states: COI, FM, and PI. We will discuss this special case further in

Chapter 4.

12

1.4.2 Average structure

The structure of La1_xCa,MnOg was first studied by several groups [38] in the 1950’s.
They found for the undoped material orthorhombic, rhombohedral, and monoclinic
symmetries could all be found depending on the method of preparation. Later, El-
emans et at. [13] found the compound to be orthorhombic, space group Puma. The
average structure shows a large, ordered, Jahn-Teller distortion which disappears with

the presence of the dopant.

1.4.3 Properties

At temperatures above Tc , transport is characterized by an activated resistivity,
p(T) or exp(Ap/T) [9] where Ap z 2500 - 1000K for La1-,Ca¢MnO3 , 0.1 < :1: < 0.6
[39]. Thermopower measurements also show semiconductor-like behavior: 3 (T) or
AS/ T, where AS z 120K. In simple semiconductor models with a single carrier type
Ap = AS, while the experiments show an order of magnitude difference strongly
suggesting an additional excitation. A number of papers [40, 41] have demonstrated

that these results are consistent with transport via small polarons.

Hall efl'ect measurements done above and below Tc on films of La1_zCa1MnOg
with a Tc around 260K show a carrier density n z 1 hole/ Mn site in the FM region,
or about three times the Ca concentration [42]. They also find that the mobility is
independent of field near Tc for strengths up to several Tesla. This suggests that
CMR is due to a field-induced increase in the density of delocalized carriers, and not

to a change in the hopping rate as DE holds.

Optical conductivity measurements of a Lao,825Cao,1-,5Mn03 single crystal [43]
found a broad peak centered at about 1.4eV. A similar structure was found in thin

film Ndo,7Sro,3MnOa [44]. The authors argue that this peak is the result of a charge-

13

transfer transition from a Mn3+ eg level split by the Jahn— Teller effect to an unoccu-
pied adjacent Mn4+ eg level. One group [45] studied the optical reflectivity of RMO3
(R = La, Y; M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu) and found a charge gap for
most of these compounds but not in LaMnOg, which has no Mn“. The presence of
the 1eV feature in the doped versions of this compound supports the polaron theory

of transport.

1.5 Summary

The phenomenon of colossal magnetoresistance is of great technological and scientific
interest. A qualitative understanding of the phenomenology was made possible by
the insights of Zener and his Double exchange model which coupled magnetism and
charge transport. Two things have happened recently to renew interest in these
materials and this phenomenon. First, an extremely large magnetoresistance (so-
called colossal magnetoresistance) has been observed in thin-film samples exciting
interest in these materials in possible magnetic field sensing applications. Second,
it has been shown that DE alone does not explain the magnitudes of the resistivity
changes that are observed. As a result, the importance of the electron-lattice coupling
through the Jahn-Teller effect has been proposed by Millis, Roder, and others. These
theories suggest that the strong e-ph coupling leads to polaronic effects. It is clearly
important to verify these proposals to understand better the CMR phenomenon. The
local structure is a useful probe to do this because when lattice polarons form they
distort the lattice in their vicinity. This has a small effect on the average crystal
structure, but is evident in the local structure. A number of techniques can be used
to study local structure but in this thesis we have used exclusively the atomic pair
distribution function technique. This is described in detail in Chapter 2 and the

results are described and summarized in Chapters 3-5.

14

Chapter 2

The Pair Distribution Function
Technique

2.1 Introduction

All information contained in the PDF comes from the scattering of x-rays and neu-
trons. Each scattering event involves the interaction of a particle with an atomic
potential, causing a change in the particle’s momentum and, in general, its energy.
By measuring the final states of scattered particles one can determine the nature of

the potentials they interact with if the incident state is well known.

In our case [46, 47], to measure atomic structure we are interested in elastic
scattering, in which the energy of the scattered particle is unchanged. As soon as we
have more than one atom acting as a scattering center we create interference among
our scattered particles. When we introduce an infinite periodic array of atoms, we
arrive at the well known von Laue condition, yielding Bragg peaks wherever the
change in wave vector Q of the scattered particle is a vector of the reciprocal lattice,
K. The analysis of Bragg peaks has been a tool for determining crystal structure since
1913, but is limited only to information on the average structure. In the case of a
perfect crystal this is no drawback since the average and actual structures are identical

on all length scales, but in most materials there are important local deviations away

15

from the average. Because Bragg scattering arises only from long-range periodicity,

it cannot tell us anything about such structures.

Fortunately, disorder within a crystal gives rise to diffuse scattering. As the name
implies, this scattering has a broad, oscillatory appearance with very low intensity
relative to Bragg peaks. In principle, diffuse scattering can be analysed analogous to
Bragg peaks to determine the exact nature of the disordered structures. In practice
this is extremely difficult, especially in powder diffraction experiments due to intensity
problems and unwanted contributions from Bragg peaks. We need not bother with

such issues if we accept both diffuse and Bragg scattering.

The total elastic scattering amplitude for a crystal is given by

fk(9,¢) : le—ik-x U(x) eikf-xdax (2.1)

where k is the wave vector of the incident plane wave, k' of the scattered wave, and
U (x) is the scattering potential from the array of atoms. We can write this potential

as the sum of individual atomic potentials located at each point in the array

U(x) = 2 mm.) (2.2)

where R.- = x — xi. Thus

MM) = Z<e““""""‘ / e"""""""U.-(R.-) d3R,) . (2.3)
Squaring this amplitude gives the scattering intensity

1(0) = 02m) ZJB‘Q'RW (2.4)

16

where Q = k’ — k and R“: is the vector separating the 2th and i’th atoms. U (Q)
is the Fourier transform of the atomic potential, called the atomic form factor. We
have separated U (Q), which depends only on the atomic potentials, from the rest of

the expression. The structure function, S (Q), is then
S Q) = Ze’Q'Ris" , (2.5)

which depends solely on the atomic arrangement. An accurate measurement of S (Q)

therefore gives important information about the atomic structure.

If we rewrite e‘Q'x" as 1/27r f e‘Q'x 6(x — x,)d:r , we can express S (Q) as a Fourier

transform

S(Q)=-2—1—7r/e‘Q"Z6(—(x,—xl)dx (2.6)

Notice the double summation, indicating it is not the absolute but rather the
relative positions of the atoms which determine S (Q) If the structure is isotropic, we

can reduce S (Q) to a one-dimensional integral over the radial coordinate r = I a: — x' |,

=1 + 4_7r/0(( —po) r sin Qr dr. (2.7)

Inverting the Fourier transform yields p(r), the spherically averaged microscopic

atomic density:

 

p = P0 + 273,, /0°° Q(S(Q) — 1) sin or do . (2.8)

The function p(T)-p0 is called the pair-distribution-function (PDF) or pair-correlation
function denoting its dependance on the relative positions of atomic pairs. Because we

have accepted all elastic scattering within the structure function, the PDF contains in-

17

formation on the average structure as well as local distortions. The PDF label is com-
monly applied to a number of other correlation functions including G (r) = 41rr[p— p0].
This function has among its advantages a statistical uncertainty that is constant in 1‘.

Unless otherwise mentioned I will restrict myself to using PDF to mean G (r)

2.2 Data collection

2.2.1 Neutrons

In contrast to x-rays, which scatter from an atom’s electron cloud, neutrons interact
directly with the nucleus. The elementary theory of neutron scattering [48, 49] is
based on the Born approximation and uses the Fermi pseudopotential to represent
the effective interaction between neutrons and nuclei. Because the range of the strong
force is much less than the wavelength of thermal neutrons, neutron-nucleus scattering
is isotropic, i.e. it contains only s-wave components. It can therefore be characterized

by a single parameter, b, the scattering length.

Within the Born approximation, the only potential which gives purely s-wave
scattering is a delta function [50]. Using perturbation theory in this case is strictly
incorrect because the interaction is very strong, although it is short-ranged. The
Fermi psuedopotential merely gives the answer we know to be correct for s-wave

scattering. For an array of nuclei this gives a potential with the form

__ 27th2
— m

 

v0) 2 b,- 6(r — R.) . (2.9)

Substituting this potential into Equation 2.1 we obtain

fk(0, <13) = Eb,- [e‘ik’f 6(r — R1) 6“” dr . (2.10)

18

As in Equation 2.4, we can separate U(Q), the Fourier transform of the potential, from
the rest of the expression for the scattered intensity. Because the atomic potential is
a delta function, its Fourier transform is merely the scalar constant b. This is much
simpler than the atomic form factor for x-rays, removing one level of difficulty in

obtaining S(Q) from the measured intensity.

All the neutron diffraction measurements described herein were performed at the
Special Environment Powder Diffractometer (SEPD) at the Intense Pulsed Neutron
Source (IPNS) and the High Intensity Powder Diffractometer (HIPD) at the Manuel
Lujan Jr. Neutron Science Center (MLNSC) at Los Alamos National Laboratory. In
both cases, pulses of neutrons are produced by accelerating bundles of protons into a
heavy metal target. For example, at IPNS the protons achieve 450MeV and strike the
target at a frequency of 30Hz. The resulting spallation produces a pulse of neutrons
which enter a moderator of liquid methane kept at 100K. The moderator produces
a spectrum of neutrons with wavelengths from z 0.25A to 8A, suitable for elastic
scattering. At the SEPD, the pulse travels down an evacuated flight path of 14 meters
before striking the sample, which is a fine powder sealed in a hollow vanadium tube
about 2 inches tall and 1/4 inch in diameter. Since the MLNSC operates on similar
principles, I will only refer to it where there are significant differences. The vanadium
can is mounted onto a displex, helium refrigerator. The sample temperature can be
controlled to within z 2/ 10 of a degree from 8K to 300K. A Helium atmosphere
is maintained within the vanadium can to act as an exchange gas and ensure good

thermal contact between the cold stage and the sample.

After being scattered by the sample, the neutrons travel to a surrounding array
of detectors 1.5 meters away. The time of arrival as well as the location of incoming
neutrons is recorded in order to determine the momentum transfer, Q. In the case
of elastic scattering, Q = 47r sin(0/A) where /\ is the wavelength of the neutron and

19

0 is half the scattering angle. Knowing the time of a neutron’s arrival allows us to
determine the wavelength from the total time of flight since all the particles emerge
from the target together in a pulse. The total time of flight t = L/v where L is
the total flight length and v is the speed. Knowing v we have the magnitude of the
momentum, and the deBroglie relation gives us the wavelength, A = h/ p. Since each
detector is at a fixed position, we also know the scattering angle for each detected

particle.

There are 130 total detectors, located in ten individual banks. These banks are
time focused onto nominal 26 angles of :l: 15, 30, 60, 90 and 150°. Time focusing is
a process whereby arrival times at a detector located at 20+60 are modified to give
them the times they would have had at 20. This maps data from multiple detectors
onto a single effective detector without significant loss of resolution. The data at
positive and negative angles are summed together, leaving only five separate banks.
Because of the finite neutron spectrum and the different locations of the detectors,
each bank covers a different range of Q and has a different resolution. We will see in
the next section that Q resolution is rarely an issue in obtaining accurate PDFs, so
all the banks are summed together to cover the greatest range of Q possible with the
best statistics. For manganites, four to six hours usually provides adequate counts to

obtain highly reproducible PDFs.

In order to remove scattering which does not come from the sample, additional
data must be taken to characterize the experimental conditions. A background run
is taken, which includes scattering from the displex and heat shields. Also, a run
is taken to measure the scattering from the empty sample container. And finally,
a vanadium rod is used as a reference sample to characterize the detector efficiency
and source spectrum. The procedure for applying these data to correct S(Q) will be
discussed in the Analysis section.

20

 

Detector

Figure 2.1: X-ray parafocusing geometry. The detector and the source are kept
equidistant from the sample.

2.2.2 X-Rays

Although the underlying scattering mechanism is different, elastic x-ray scattering
can also be used to obtain a structure function and a PDF. Unfortunately, we can-
not blast a sample with a broad spectrum of x-rays and obtain useful information
because we cannot recover Q through time of flight measurements as with neutrons.
Energy-dispersive x-ray measurements are possible with a polychromatic source and
an energy-sensitive detector. However it is much simpler to use the angle-dispersive
method, in which a single wavelength is chosen and the scattering angle is systemat-

ically rotated.

Our x-ray experiments are performed on a Huber four-circle diffractometer. X-
rays are produced from a sealed tube with a silver cathode kept at 45kV. A graphite
monochromator is used to select the Km emission, with a wavelength of 0.559A. Two
sets of slits define the beam on the sample, a fine powder mounted onto a flat plate.
The plate is centered on a circle which rotates, defining 0. A scintillation-counter is
mounted on a circle which rotates at twice the rate of the sample to maintain the
detector at 20. With the source-to—sample distance equal to the sample-to-detector

distance, this arrangement generates ‘parafocusing’, shown in Fig. 2.1 This allows us

21

to use a divergent beam, thus better counting statistics, and still maintain reasonable

resoultion.

Data are collected incrementally, one Q-value at a time, with 0 and 20 systemat-
ically rotated over the entire accessible range. With Ag Kal radiation we can reach
a maximum Q of z 21A’1. Low count rates, particularly at high 26, can stretch
collection times to several days. This can vary greatly depending on the scattering
power of the sample. Each element has a well-defined scattering length b,-, which is
used to define its scattering cross section a,- = 47rbf. X—ray scattering lengths are
proportional to the number of electrons an atom contains. Thus, a sample made from
heavy elements will scatter strongly. Unfortunately, the oxygen in La1_¢Ca,MnOg

makes it only a weak xray scatterer.

The sample environment is again a helium displex, used to maintain a steady
temperature down to leK. X-rays penetrate through a Berrylium window in the
vacuum shroud. Low-Z elements such as Berrylium are virtually transparent to x-
rays, and the window does not contribute to the scattering in any noticeable way.
The geometry of the displex makes it impossible to measure the background directly,
so the beam is carefully focused to avoid scattering off the sample holder. In addition,
the sample can be held in place by mixing it with a polymer that produces very little

signal.

Because of the intrinsically low intensity of the x-ray source it is of paramount
importance to ensure proper alignment of the diffractometer. This begins with setting
the monochromator correctly to select the desired wavelength. The sample must be
in the physical center of the theta circle so that it does not translate when rotated.
The beam must strike the sample squarely and all slits must be in a position to allow

a minimum of background scattering while preserving maximum scattered intensity.

22

2.3 Analysis

In an ideal case, a PDF would be calculated from a structure function which depends
only on the structure of the sample. Experimentally, we can never eliminate contri-
butions from extraneous sources which contaminate the measured S(Q). A series of

corrections are necessary to recover only the scattering which arises from the sample.

2.3.1 Neutrons

The characterization scans described in the last section are designed to allow the
structure function to be recovered from real data as accurately as possible. First,
the instrument background intensity is removed. A constant background of delayed
neutrons must also be subtracted. These neutrons emerge from the source with the
same energy spectrum as the pulse but at a different time, making time-of-flight
calculations impossible. Since they account for a background of approximately 3-5

per cent of the scattered flux they can easily be accounted for.

Next we must account for neutrons which are inelastically scattered. Since the
detectors only measure the time of flight, and not the actual energy of a neutron,
the Q—bin which an inelastically scattered neutron is placed in will be incorrect. The

shift in Q is due to the neutron being slowed or accelerated in the scattering process.

The amount of inelastic scattering at low Q is a tiny fraction of the elastic scat-
tering, but as Q rises it quickly becomes significant. When Q> 300w the inelastic
scattering dominates the difl'raction pattern, where How is the Debye-Waller temper-
ature factor. This is the width of the Gaussian envelope which damps the intensity
of Bragg peaks as a function of Q due to the uncorrelated motion of the atoms. The
error in Q-binning still should not produce a large effect because features in inelastic

scattering such as phonon dispersions tend to be broad and vary slowly with Q. In

23

addition, assuming we understand the sources of the inelastic scattering, we can re-
bin a predicted quantity of neutrons into their correct Q-values. This is known as a

Placzek correction and is discussed by a number of authors [51, 52].

Corrections for absorption and multiple scattering are calculated for cylindrical
samples following the procedure of Price [53] and Blech and Averbach [54]. This
takes into account the absorption and multiple scattering from the sample as well as
the container, and corrects these effects before the container scattering is subtracted
from the total. Finally, the source spectrum and detector efficiency are accounted
for. This is done by taking the ratio of structure factors from the sample to structure
factors from a reference vanadium rod. Vanadium is an almost perfectly incoherent
scatterer of neutrons and so the scattering intensity measured from a vanadium rod

reflects the incident spectrum modified by the detector efficiency.

Before calculating the PDF, we convert S(Q) into the single-particle structure
function by dividing by the total number of scatterers. This should yield a normalized
function which goes to 1 as Q approaches infinity. In practice, the density of the
sample during the experiment and the volume irradiated by the beam are not precisely
known so the effective density is varied as a parameter until the proper normalization

condition is met.

2.3.2 X-Rays

Extracting a PDF from x-ray data uses the same fundamental mathematics, but some
different corrections must be made. In our case, no sample holder or shielding is in
the path of the beam so no characterization runs are needed as with neutron data.
Because x-rays are scattered off electrons, the finite size of the atom must be taken
into account. This is done by dividing the scattered intensity by the average form

factor, which contains the Q—dependence of the scattering due to the atom’s physical

24

15

 

cu _ _
v-t
)-
a b _
6"
°¢
V
a:
c)- _

 

 

 

 

 

 

j. l A LILLAJJAALJ L...‘ 1111

0 5 10 15 20
0(3)“)

 

Figure 2.2: Structure function of La1_zCa,MnO3 up to 22A‘1.

extent. As neutrons scatter off of the atomic nucleus, we can ignore the neutron form

factor.

Compton scattering is another challenge posed by x—rays. While Compton-scattered
photons should always have a lower energy than elastic scattering, it is difficult to
discriminate between them, especially at low angles. Therefore, both Compton and
elastic scattering is accepted. The contribution due to Compton is calculated from
theory and subtracted from the data. Absorption and multiple scattering are removed
similarly as in the case of neutrons. After these corrections are applied, the resulting
structure function can be processed to obtain a PDF without regard to the method
of data collection. Figure 2.2 shows a typical structure function from

La1_xCazMnOg .

25

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.1ffifir.1.r...r,rs..
c” -1
i
m...

,A i [ [l H

at:

5° ”H H H H
w ~
L
o_ d
I iamLirnrlrkalmnnk

5 10 15 20

r(A)

Figure 2.3: Typical neutron PDF of La1_xCa,MnO3 .

2.3.3 Obtaining the PDF

After S(Q) is known, the PDF is calculated through direct Fourier transform, accord-
ing to Equation 2.8. Figure 2.3 shows a PDF calculated from the structure function
in Figure 2.2. Care must be used in determining the range of Q to keep when carrying
out the integral. Going to higher Q improves the resolution of the PDF, but the count
rate tends to fall quickly with rising Q. Thus, we Fourier transform a higher fraction
of noise as we increase QM and the benefit of improved resolution is washed out by

increasing statistical fluctuations.

Fourier transforming the structure function with its finite Q—range will introduce
high-frequency termination ripples into the PDF, which will be discussed in the next

section. These arise from the convolution of S (Q) with a step function. Applying a

26

damping function to high-Q data so that S (Q) smoothly approaches 1 at high Q is
a common practice but its benefits are mainly cosmetic. It does reduce termination
ripples but at the cost of broadening PDF peaks due to the loss of high-Q information.
The same can be achieved by simply choosing a lower Qm. Since the termination
ripples produced by the convolution can be mimicked in the modeling stage, we have

not used any damping.

2.4 Modeling

Although modeling is an important element in determining local structural infor-
mation from PDFs, most of this work will not refer to results obtained from any
modeling. Therefore, I will only briefly discuss the features of the procedure. In
general, the average structure of a material is known from a Rietveld refinement of
powder diffraction data or some other means. These parameters, including atomic
positions, thermal factors, and occupancies, can be taken as a starting point to cal-
culate a model-PDF. Parameters may be refined using a least-squares fitting routine
while preserving the long-range order of the system. The agreement of this model-
PDF with data tells us how well the long-range ordered structure does at fitting the

local structure.

Once the best fit has been achieved using the constraints of the average structure,
local distortions and / or occupancy inhomogeneities may be introduced into the local
structure. Once again these variables may be refined to look for a local structure
which is superior to the average. Clearly the parameter space can be enormous so
unless there is some indication of the type of distortion necessary to fit the data it

can be very difficult to identify through modeling.

27

2.5 PDF peak height and width

A simple yet important way to learn about disorder from a PDF without resorting to
modeling is to examine the height and width of PDF peaks. Each peak in the PDF
arises from a pair of atoms separated by a particular distance. A perfect experiment
on a fully—ordered crystal with static atoms would yield a series of delta functions,
located at every r-value which separates an atomic pair. Actual peaks have a finite
width because of the intrinsic thermal and static disorder within a solid, as well as
convolution effects. However, the integrated area of a given peak must be conserved
since that depends on the total number of contributing atoms. Therefore, any change
in the height, and therefore width, of a peak means a change in the disorder associated
with that particular correlation since we always convolute our structure functions
identically. If we have a number of PDFs, measured at closely spaced values of
temperature or composition, we can compare heights of various peaks to spot when
local disorder increases or decreases and which atoms are affected. While this alone
cannot tell us the shape of distortions, it does tell us when external parameters are

having an impact on local structure.

28

Chapter 3

Metal-Insulator Transition at
Tc and xc

3.1 Introduction

In this research we use the local atomic structure as a probe of the electronic state
of the CMR materials from the system La1_zCaanO3 . In particular we are inter-
ested in determining whether local Jahn-Teller distorted octahedra can be detected,
whether polaronic distortions can be detected and characterized, and whether these
features have a temperature or composition dependence. As we will see, these features
can be seen and have a particularly large response to the metal-insulator transition.
In this chapter we describe the nature of the JT and polaronic distortions and how
they change on crossing the metal-insulator transition as a function of temperature.
We will also describe preliminary results of what happens as the MI transition at
~ .1: = 0.18 is crossed at low-temperature as a function of doping. In the next chap-
ter we will look at the temperature dependence of a sample with :r = 0.5 which lies

exactly on another low-T MI-transition. Finally, in Chapter 5, we sum up.

29

3.2 Structural Response to Temperature

To look for the signs of lattice polarons at Tc we performed neutron diffraction on
La1_$CazMnO3 samples with a: = 0.12, 0.21, and 0.25 at temperatures ranging from
10-300K looking for changes in the PDF corresponding with the MI transition. Sam-
ples were made by Dr. J. J. Neumeier at Los Alamos National Lab (LAN L) by a solid
state reaction of 1432003, CaC03 and M1102 with repeated grindings and firings at
temperatures up to 1400°C, with a final slow cool at 1°C per minute. The nominal
Mn valences were determined by idometric titration and were 3.25, 3.24, and 3.29
for the a: = 0.12, 0.21, and 0.25, respectively. The DC magnetization was measured
at LANL using a commercial SQUID magnetometer and the temperature dependent
resistivity was measured using the standard 4-probe dc technique. Neutron data were
collected at the Special Environment Powder Diffractometer (SEPD) instrument at
the Intense Pulsed Neutron Source (IPNS) and at the Manuel Lujan Jr. Neutron
Scattering Center (MLN SC) at Los Alamos National Laboratory. Collection and

Analysis procedures are described in Chapter 2.

Figure 3.1 shows PDFs obtained from Lao_33Cao_12MnOa at 150K and 180K.
This sample has no MI transition, hence we only expect the structure to change
slightly due to thermal effects. The difi'erence in PDFs is plotted below the data and
shows reproducibility within statistical uncertainty. Compare this with Figure 3.2,
which shows PDFs of Lao,79Cao,21MnO3 at 160K and 192K. This sample has a MI
transition, at approximately 182K. We see that the PDFs match up substantially less

well, particularly in the region of the first two peaks at the low-r end of the PDF.

Table 3.1 shows all the atomic pair correlations below 2.75A, and their respec-
tive amplitudes based on the crystal structure. Note that the first PDF peak in

La1_zCa¢MnOa arises from correlations between Mn and neighboring oxygen atoms.

30

 

 

 

 

 

 

 

 

 

0 5 10 15 20
r(A)

Figure 3.1: PDFs of Lao,33Cao,12Mn03 measured at 150K and 188K, difference plotted
below. Dashed lines indicate two-sigma level of uncertainty. Note that the difference
curve remains largely within the dashed lines, showing that the structure remains
largely unchanged.

Any changes in the size or shape of the MnOs octahedra will be reflected in changes of
this peak. The second peak at r = 2.75A is largely due to neighboring oxygen-oxygen
correlations, although there are also contributions from La/Ca-oxygen and La/Ca-
La/ Ca pairs. These two peaks, and no others, are directly dependent on the structure
of the Mn06 octahedra. The appearance of changes in the PDF at these peaks is
suggestive of polaron formation, which would distort the local arrangement of oxygen
atoms. In order to confirm this, we fit models containing polaronic distortions to the
data and compared the results to fits containing no distortions. Unfortunately, the

structural differences proved too small for our fitting program to distinguish between.

We therefore resorted to examining peak-heights.

31

 

 

 

car”)
0

 

 

-3
«:1
l

 

0 5 10 15 20
1‘01)

Figure 3.2: PDFs of Lao,88Cao,12MnO3 measured at 160K and 192K, diflerence plotted
below. Note the large amplitude of the difference curve relative to the uncertainty.
Between these temperatures the sample has passed through the MI transition and
the structure has changed noticeably.

3.2.1 Atomic disorder from PDF peak-heights

In Chapter 2 we mentioned that the sharpness of an individual PDF peak is deter-
mined by (among other things) the degree of static and/ or dynamic disorder present
in the contributing correlations. In the case of a temperature-dependent study, as
T increases peaks should become broader due to increased thermal vibration. Since
the integrated intensity under each peak must remain constant, the height of that
peak must decrease. The same holds true in the case of static disorder: an increase
will cause associated peaks to broaden and lose height. In La1_xCa,Mn03 we are
interested in polaronic and Jahn-Teller distortions which should impact short-range

Mn-oxygen and oxygen-oxygen correlations. Since individual PDFs show changes in

32

Table 3.1: First seventeen atomic correlations and amplitudes for La1_xCazMnO3
based on the crystal structure model. Note the strong Mn-O peak at 1.96A and the

strong O-O peak at 2.74A.

 

 

Atom 1 Atom 2 r (Angst) amplitude
Mn 01 1.9600 0.8000
Mn 02 1.9600 0.4000
Ca O2 2.4200 0.0250
La 02 2.4200 0.0750
Ca 02 2.4300 0.0250
La 02 2.4300 0.0750
Ca 01 2.4700 0.1000
La 01 2.4700 0.3000
Ca. 02 2.6000 0.0250
La 02 2.6000 0.0750
Ca 01 2.6400 0.1000
La 01 2.6400 0.3000
Ca O2 2.6900 0.0250
La 02 2.6900 0.0750
01 O2 2.7300 0.2000
01 01 2.7400 0.8000
01 02 2.7400 0.2000

 

 

 

 

the corresponding low-r peaks, we plot the height of these peaks as a function of

temperature.

Figure 3.3 shows the height of the r = 2.75A peak as a function of temperature
for three difl'erent samples. Both this and the 1.9A peak show the same qualitative
behavior. We concentrate on the r = 2.75A, however, because the statistical and
systematic errors on this peak are smaller. The reason for the former is that the peak
is much stronger (there are 12 O-O bonds contributing to this peak instead of just
6 M-0 bonds for the 1.9A peak) and for the latter we note that systematic errors
tend to die out with increasing-r in the PDF since they tend to originate from long-
wavelength artifacts in S (Q) coming from inadequate data corrections. Beginning

with the bottom panel, peak-heights for the a: = 0.12 sample drop smoothly with

33

 

' I V Y Y j I Y Y I V I

 

 

1
F
L

 

140

Peak Height (1")
120 130

 

 

140

 

130

 

 

120

 

 

 

 

 

Temperature (K)

Figure 3.3: Peak heights vs. temperature for three compositions: :0 = 0.25 (top) ,
:r = 0.21 (middle), and a: = 0.12 (bottom). The upper two panels show a large drop
in height well below Tc , marked with arrow. Bottom panel shows a composition with
no MI transition. The peak heights follow the expected Debye behavior. Insets show
resistivity vs. temperature.

increased temperature. The solid line is a prediction of expected thermal broadening,
calculated using the Debye model [47, 55]. Again, this sample has no MI transition

and we see that the drop in peak-height is well fit by thermal motion.

The middle panel shows the data from the a: = 0.21 sample. The same Debye
curve is plotted, and the data in this and the bottom panel have been re-scaled so that

the low—temperature points lie near the curve. As Tc is approached there is a very

34

large drop in peak-height which begins at least forty degrees below Tc and continues
right up to and perhaps a bit beyond the transition temperature. A similar large
effect is seen in the a: = 0.25 sample in the top panel. This sudden drop in height is
not explained by thermal effects and must be due to a sudden increase in structural
disorder of the MnOs octahedra. Such a change, taking place at the temperatures
where the sample is leaving the metallic phase, is just what one might expect if the
mechanism becomes polaronic at high-T. In Section 3.4 we will discuss our efiorts to

characterize the size and shape of these polarons.

3.3 Doping across the phase transition

We can only conclude from the previous section that the local structure becomes
more disordered above Tc and that it is relatively more ordered below. We have not
shown that the metallic phase is free from polaronic or Jahn-Teller effects, merely
that such distortions seem to increase upon approach of the insulating state. In order
to determine this, and to help establish that the PI state is indeed polaronic, we

examine local structural changes as a function of composition.

Once again we carried out neutron diffraction over a range of temperatures on
samples with doping values of a: = 0.21 and :1: = 0.12. Figure 3.4 shows PDFs
for each sample measured at 10K in the lower panel. Clearly, there are significant
differences between the two structures. This in itself is not surprising as the two are
chemically distinct materials as well as being in different phases: the lower-doped
sample has no metallic state and is a ferromagnetic insulator at low temperatures.
The upper panel shows PDFs for the same two samples measured at 220K. Here the
a: = 0.21 sample has passed through Tc and is fully in the insulating phase. Now the

two structures are virtually indistinguishable. The compositional differences therefore

35

 

200 400
I ' r
A
D
v
1 J

 

e (um 4)

-400-200 0
. , .

" l
l
d b .

 

‘-

200400
. .,
A
U
v
1

G (nm '8)

-400 -200 0
, . , .
l

 

 

 

 

Figure 3.4: PDFs of Lao.79Cao_21Mn03 and Lao.3gcao.12MnO3 . (A) Both measured at
220K, both in the insulating phase. The structures are remarkably similar although
the compositions are different.(B) Both measured at 10K, the a: = 0.21 sample is now
in the FM phase and is sharper relative to the a: = 0.12 sample.

do not appear to impact the PDFs significantly, while crossing the MI transition line
seems to make both samples structurally identical. This can be explained if small
polarons, present in the respective insulating phases, disappear when entering the
metallic regime regardless of whether they do so because of a decrease in temperature

or an increase in doping.

We can test whether this is so by examining changes in the PDFs as a function
of temperature and composition. Figure 3.5 shows a pair of PDF difierence curves.

The solid line is the difference between a: = 0.12 and a: = 0.21 samples at 220K

36

 

 

 

 

 

 

3 t i 1
c. 2‘ z
_ ‘- :2; 31$ 2:: f
5 g“ .‘ .2 .2 3e [
r ”*1 = : . I :: l l
c e g .
5 r l ‘. : 1 ‘ i
v .: h. .. y '.
o t e “‘5‘: 4. 9. ..::
‘ '2‘ 1‘5 '2 . :2 ,‘ i.
.. ‘. 3:2 3 2. ‘4
2‘1 ‘. a :z: 7: t .e
1 “' o.
S l- .e ‘ .5. .. Ci
I . 3 e.
‘ 2‘
a f
5
: d
l 1 L 1 l 1 l
0.2 0.4 0.5 0.8

:- (run)

Figure 3.5: Comparison of PDF difference curves between Lao,79Cao,21Mn03 and
Lao,33Cao,12MnOg at 220K (solid line) and 10K (triangles). At low temperature,
when the two samples are in different phases, the structures show larger differences
than at higher temperatures at which they are both PI.

and the triangles are the differences between the PDFs at 10K from Figure 3.4. We
see again that the changes at low temperature are much greater, and there appears
to be no significant correlation between the two curves. Thus we can reasonably
rule out chemical differences as a major source of structural changes between these
two samples. However, if we again plot the difference curve at 10K in Figure 3.6,
together with the difference between a: = 0.21 sample at 225K and 140K, we see
a remarkable coincidence. Once again, the solid line in Figure 3.6 is the difference
caused by a decrease in temperature through the insulator-metal transition of the

higher-doped sample while the triangles show the difference when doping is increased

through the insulator-metal transition at low temperature. There is no reason for these

37

 

I»

A
D

V

 

 

1..

 

 

 

A A

 

A

 

 

 

 

v» I
’0'.

M’.’

 

 

 

 

Figure 3.6: Difference curves: Triangles are again the difference between
Lao,79Cao,21MnO3 and Lao,38Cao,12MnOa PDFs at 10K. Solid line is the difference
between LangCaomMnOg at 225K and 140K. The changes in the structure caused
by entering the FM phase through a decrease in temperature or an increase in doping
are large and correlate well.

two changes to have similar effects on a structure, yet we see that both curves are
large and strongly correlated over a wide range of r. The only thing these difference
curves have in common is they were both produced by crossing from the insulating

to the metallic phase, albeit via different paths.

These results point out that in this compositional region, the division of the phase
diagram between metallic and insulating phases also separates two distinct local struc-
tures. The insulating phase is identified by local distortions caused by polarons which

are not seen in the metallic phase.

38

3.3.1 Within the metallic region

In the previous discussion we considered only compositions which lie well inside their
respective phases. This does not address how the system evolves from one state
to another: whether it changes suddenly or continuously passes through a series
of intermediate structures from disordered to fully ordered. Distinguishing between
these two modes of behavior is important because this will tell a great deal about the

electronic state of both the metallic and insulating regions.

If the structure gradually becomes more ordered as we increase doping at low
temperature across the phase boundary into the metallic region, then the two phases
are qualitatively similar on a microscopic scale. They both contain a mixture of
distorted and undistorted MnOa octahedra with a ratio set by the doping level. The
structure becomes more ordered with increased doping because the number of Jahn-
Teller distorted sites drops proportionally. In this case the metallic state is not
created by any change in the behavior of carriers but merely by changing the relative
number of holes and electrons. This would support a percolative model [56, 57] for
the phase transition whereby transport is enhanced once a contiguous path of Mn4+
is established. In this case polarons would still exist in at least some of the metallic

phase, albeit in smaller numbers.

On the other hand, if the structure remains relatively unchanged below the critical
doping value and then suddenly becomes ordered upon crossing the phase boundary,
this would indicate a qualitative difference in the nature of the carriers in the two
phases. The discontinuous increase in structural order could be explained by a de-
localization of carriers, creating a uniform distribution of non-Jahn-Teller distorted
octahedra. Therefore, determining the structure will tell us a great deal about the

mechanism responsible for the change in electromagnetic properties.

39

 

4.5

 

 

 

I
.
r l [-
I l I I I i
*T I II 1
3? I I f
:5 . I
'33.” l 1
s f .
a ’ i I
at“ If ' j
I l .
I l l
3: | 1
'i1 1 l [[444 l LLLLLI
0 01 0.2 03 04
x(Ce)

Figure 3.7: Height of the Mn-O peak at 10K vs. Calcium concentration. Dashed
line shows the boundary composition between insulating and metallic regions at this
temperature. The peak sharpens smoothly through 3M1 and continues sharpening
well into the FM phase. This suggests that local distortions exist close to the phase
boundary even at low temperatures.

Figure 3.7 shows the height of the Mn—O peak taken from PDFs of 14 samples
at 10K with compositions ranging from a: = 0 to :1: = 0.4, concentrated about the
critical doping value of 0.19. With the exception of the :r = 0 sample, all the data were
collected on the same device during one continuous run under identical conditions to
maximize reproducibility. Clearly the structure is undergoing a transition over a wide
span of composition from most disordered at a: = 0 until saturation at about a: = 0.22.
This would strongly support the percolation argument for metallicity as we see no
discontinuity at the phase transformation as well as some persistent disorder in the
metallic regime. Unfortunately, susceptibility measurements showed high degrees of
inhomogeneity in the higher-doped samples which would smear out the MI transition’s
position even if it were occuring at a single value. The samples with lower doping

levels were closer to an ideal homogeneous state, and the linear behavior of their

peak-heights makes it tempting to say we are seeing a linear evolution toward the

40

ordered state but until adequate samples can be re-tested the result is inconclusive.

This requires considerable beam-time and has not been carried out to date.

3.4 Polarons and modeling

3.4.1 Fitting the J ahn-Teller distortion

Beyond simply measuring changes in peak-height to look for local distortions, we can
learn something about the nature of the Mn06 octahedra through modeling. Looking
at Figure 3.2 we immediately notice a difference between PDFs of manganites in the
metallic and insulating phases. The first peak in the metallic phase, besides being
sharper as we discussed previously, has a noticeable secondary peak appearing as a
shoulder near 2.2A which is conspicuously absent when the same material is in the
insulating phase. This qualitative difference is repeated over the entire doping range

0<:1:<0.5.

At first glance, this secondary peak would seem to present a contradiction. If
we presume that the metallic state is more ordered, with polaronic and Jahn-Teller
distortions appearing as the insulating state is approached, we might hope to see
secondary Mn-O peaks in that region arising from the inhomogeneous distribution of
Mn—O bond-lengths. Instead, the reverse is true. One could argue that this secondary
peak is evidence of a local, full magnitude Jahn-Teller distortion within the metallic
region at all temperatures. While we would agree there are residual distortions in the
metallic region near the phase boundary, we shall see that this secondary peak is an

experimental artifact.

In Chapter 2 we discussed the effects of convolution in the Fourier integral due
to finite data in Q-space. As we know, convolution with a step function will cause

sharp peaks in the PDF to broaden, as well as introducing ripples according to the

41

 

 

 

 

 

 

 

rm 1'01)

Figure 3.8: Undistorted crystal model fit to Lao.75Cao.25MnOg in the FM phase at
20K (left) and in the PI phase at 260K (right). Darker lines are data. Note that the
quality of the fit is considerably poorer at the higher temperature.

equation [58]

 

 

(3.1)

0.20") _ 71/000 C(T,)[sinq,,m(r — r’) _ sin qmax(r + T’)]dr’

_ T—W r+fl
where G (r) is the theoretically calculated function and Ge(r) is that function mea-
sured experimentally. Of course, we can convolute any model we wish to calculate in
the same manner. A model based on an undistorted crystal structure, i.e. a single
Mn—O bond-length, is plotted in the left panel of Figure 3.8 together with a PDF

from La0,75Ca0.25MnO3 measured at 20K.

The data had a Q—max of 22A“1 so the model was convoluted with the correspond-
ing step function to reproduce the broadening and ripple pattern. Notice that both
the 1.9A peak as well as the secondary peak at 2.3A are reproduced by the model.
This model has no correlations at 2.3A , the existence of a peak in the model PDF
is due to the sharpness of the 1.9A peak in the metallic phase. Since the structure is

well-ordered in this region, and the motion of neighboring atoms is highly correlated,

42

this peak should have the smallest natural width in the entire PDF, hence it will show
the greatest effects of the convolution. In contrast, the right panel in Figure 3.8 shows
a PDF from Lao_75Cao,25Mn03 at 250K together with a fit from the same undistorted
model. Notice that the model once again has a peak at 2.3A which fails to fit the data
at all. Because the 1.9A peak is so broadened by distortions in the PI phase, clearly
visible in its decreased height, the effects of convolution on its appearance are greatly
diminished. The model, which assumes no distortions, still preserves the secondary
feature. However, the data shows a great deal of intensity in the region between the
two peaks which the model completely misses. This feature is in the wrong position
and has the wrong shape to be a termination ripple, it can only be intensity which
has escaped from the first peak. It is this feature, and not the 2.3A peak, which is
the signature of a long Mn-O bond caused by Jahn-Teller distortions. The extremely
good fit of the undistorted model to the data in the metallic phase convinces us that
at very low temperatures well inside the FM state, the structure is free from local
distortions. However, as we have seen the height of the low-r peaks begin to fall
well below Tc and this model gradually fails to capture the correct low-r features as
temperature increases within the FM region. This indicates that there are distortions
present within much of the FM phase arising from a coexistence of delocalized carriers

and polarons. In Chapter Four we will see this situation arise again.

43

Chapter 4

Metal Insulator Transition at
x=0.5

4.1 Introduction

In La1_zCazMnO3 there is a MI transition at low temperature on increasing Ca con-
tent through :1: = 0.5 [4, 59]. The M1 boundary is almost vertical on the 1: vs. T
phase diagram. The composition LalszCazMnO3 with :1: = 0.5 is clearly a very spe-
cial material which has marginal properties and which can hardly decide between
having a ferromagnetic metallic groundstate (characteristic of a: < 0.5) or an an-
tiferromagnetic, charge-ordered, insulating ground-state (characteristic of :1: > 0.5).
In fact, on cooling the sample goes from a paramagnetic insulator at high tempera-
ture first to a ferromagnet with improved metallic properties. On further cooling it
charge-orders with an incommensurate ordering vector. Finally, at low temperature,
the spins order antiferromagnetically. The sample has the charge-ordered insulating

ground-state, but only marginally.

The interesting possibility exists that on cooling the charges delocalize, the small
polarons evident at high-temperature are destroyed, but on further cooling they re-
form in an ordered array at low-temperature. An alternative possibility is that the
polarons exist at all temperatures and on charge-melting they undergo an order-

44

disorder transition. In this picture, it is not clear what gives rise to the ferromagnetic
phase at intermediate temperature. Clearly, the PDF is a useful tool for diagnosing

the local state of the carriers in the intermediate phases.

The evolution of the phases in the x = 0.5 sample is as follows. The ground state is
antiferromagnetic and charge ordered in striped arrays [60] until z 155K where there
is a transition to a ferromagnetic metallic (FM) state. This region is considered more
metallic only in the sense that the reisitivity curve bends downwards. Initially, charge
ordering survives in the FM state but it gradually becomes more incommensurate with
temperature [61]. At z 225 K a second transition results in a paramagnetic insulating
(PI) phase with activated polaronic transport [4]. The existence of all three distinct
phases, specific to this particular composition, allows one to study two separate MI
transitions within the same sample. Thus we can determine if the polaronic distortions
seen in the low-temperature insulating phase reappear after crossing the intermediate

metallic state.

4.2 Experiments and results

Measurements were made during both cooling and warming cycles, ranging between
15K and 325K using a closed cycle helium refrigerator. Examples of G (r) are shown

in Figure 4.1.

Two sets of data are plotted together to demonstrate the level of reproducibility.
They were both measured at 112K, well into the charge ordered phase, first upon
cooling and then while warming. The difference curve, plotted below the data, is
seen to fall largely within the dashed lines, which show uncertainties due to statistical
fluctuations at the level of two standard deviations. Thus we conclude that PDFs

obtained as a function of temperature are reproducible within the limits of statistical

45

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r(fi)

Figure 4.1: PDFs of Lao,5oCao,5oMnOg measured at 112K. The solid line is the PDF
measure while warming and the circles while cooling. Difference is plotted underneath.
Dashed lines indicate two sigmas of statistical uncertainty. Note the close agreement
between PDFs.

noise.

We begin looking for structural changes by examining PDF peak-heights as a
function of temperature. As discussed, peak-height is a strong indicator of changes
in the degree of structural disorder within a given correlation. If there were a sudden
increase in the disorder of the arrangement of atoms which contribute to a given
correlation, that peak would broaden and its height would show a correspondingly
sudden decrease. This would be directly analogous to a sharp increase in refined

thermal parameters.

The top panel of Figure 4.2 shows the height of a peak at 16.2A as a function
of temperature. The peak’s height clearly drops once the sample enters the charge

ordered region. This behavior is reproduced in a number of other peaks located at

46

 

  
 

4
l

35
fi ' I
m .
0100400?

 

  

Peek height. (1")
s .

 

Peek height. (1")
e

 

 

 

Figure 4.2: Top: Heights of PDF peak at 16.2A as a function of temperature. Squares
indicate data collected while warming, circles while cooling. Peak height rises dra-
matically with temperature between TN and T00- This is due to the loss of charge
ordering which leads to a higher symmetry state. Bottom: Heights of PDF peak at
2.75A. Peak heights tend to follow Debye curve (solid line) except on cooling between
Tc and TN . Those peak heights (filled circles) increase due to charge delocalization
which is suppressed by charge-ordering.
higher (>10A) values of r. This indicates some change of the average structure into a
higher symmetry state because peak-heights are increasing as the temperature rises.
This is more remarkable considering that thermal effects are simultaneously broad-
ening these peaks. However, on shorter length scales the structure evolves differently
over the same temperature range.

The strong positive peak in the PDF at r z 2.75A arises primarily from oxygen-

oxygen correlations and so is a good indicator of changes in the shape of the oxygen

octahedra which surround the manganese ions. The bottom panel in Figure 4.2 shows

47

the height of this peak: the large changes seen on intermediate length scales are gone.
The first PDF peak, at 1.9A , shows the same qualitative behavior. This peak arises
solely from Mn-O correlations and so is also sensitive to local distortions of the octa-
hedra. As the carriers clearly are localized in the charge ordered state, this suggests
that they remain so throughout this entire temperature range, because we can observe
a large effect that delocalization has on this peak [47]. Therefore, while charge or-
dering gradually disappears in the FM state, localized charges persist but the charge
ordering melts away through an order-disorder transition.

If we again examine the bottom panel of Figure 4.2 we notice interesting behavior
in the FM state. The solid line shows shows the change in peak-height expected due
to thermal motion predicted by the Debye law. Most of the points lie on or near this
line, and the cooling and warming cycles show good agreement except in the hys-
teretic region. This indicates that there is some response of the Mn-Os octahedron
to the electronic and magnetic transitions, but certainly a subtler one than that seen
on longer length scales. In particular, the cooling cycle points between T ,m (shown
by the dashed line) and Ta, are shifted up away from the Debye curve even though
the 16.2A peak shows no change at this point and there are no charge ordering su-
perlattice peaks. The octahedra are responding to the increase in metallicity. We do
not see a similar effect on the warming cycle because there is no temperature range
in that case where the sample is ferromagnetic without being charge ordered also.

We can compare the sharpening of this peak to that observed in lower doped
samples. In this material the sharpening is much less than that seen in the a: = 0.25
sample. We see this in the inset to Figure 4.2(b) which shows the same data from the
main panel with the z = 0.25 data superimposed as solid circles, with 0.25A'2 added
to make them line up with the other points in the polaronic region. The dashed line

drawn through the a: = 0.25 points shows power-law behavior suggesting a second-

48

order transition added to the transition from the Debye curve. The peak-heights
from the a: = 0.25 data fit this curve well over the entire range. The same function is
plotted in Figure 4.2(b) as a curved dashed line and the cooling cycle points, shown
as filled circles, between Tim and Ta, begin following the curve as well. The first two
points below T I", lie on this line, while the third point, which has just entered the
charge ordered phase, is between the line and the Debye curve.

We explain the electronic behavior of the ferromagnetic phase through a coex-
istence of localized and delocalized charges. As we cool through T ,m the polaronic
charges begin to delocalize and we see the local structure begin to sharpen accordingly.
However, the remaining localized carriers begin ordering around 180K which stabi-
lizes the the polaronic state. This suppresses further delocalization, and the number
of delocalized carriers begins to fall until they are all back to a polaronic state. This
explains why the charge ordering is originally incommensurate, since the number of
carriers available for ordering is originally less than the % per Mn site required to be
commensurate with the lattice. However, charge ordering increases the number of lo-
calized carriers and polaron density gradually approaches 50%. Eventually, when the
density of delocalized carriers becomes too small, superexchange coupling becomes
favored over double exchange and ferromagnetism is lost. This point, where virtually
all carriers are relocalized as polarons, as determined from the PDF coincides with

the point where charge ordering becomes commensurate.

4.3 Summary

These PDF measurements allow us to understand in some detail the nature of the
different phases of the [18.1-303an03 a: = 0.5 compound. At high temperatures
the carriers are all localized but there is no charge ordering. The FM state contains

a mixture of polarons and delocalized charges. It attempts to behave as the lower-

49

doped compounds do in this phase, by delocalizing more and more carriers as the
temperature falls until it reaches a ground state where there are no polarons and
the structure is undistorted. But long before it can reach this point the appearance
of charge ordering stops further delocalization by creating a lower energy state for
localized carriers. When all the charges relocalize the charge ordering can be fully
commensurate and we arrive in the insulating ground state. The behavior of the FM
state at a: = 0.5 agrees with our view of the CMR region. In both cases charges
delocalize in the FM phase but not instantaneously. Not until we are deep in this
region do all traces of polarons disappear, but the 2: = 0.5 compound simply never
gets that far. The low-temperature, z-dependent measurements shown in Figure 3.7
support the picture that much of the FM phase close to the MI transition boundary

actually contains a large fraction of residual polarons.

50

 

 

 

Chapter 5

Discussion and Conclusions

5.1 Summary

We set out to understand the phase diagram of La1_,,CazMnO3 using local structure
as our guide. In particular, we wanted to understand the mechanism behind the
interesting CMR behavior these materials display. The motivation for our approach
was the suggestion [23, 24] that electron-lattice effects played an important part in
the properties of this class of compounds through the Jahn-Teller efiect which leads
to polarons in some regions of the phase diagram. Since a local structural probe is
capable of detecting the distortions caused by polarons we attempted to test this idea

using the atomic pair distribution function method.

5.1.1 Results

Our findings confirm that polaronic effects are important in this CMR material. In
Chapter Three we showed that large changes in PDF peak heights are closely corre-
lated with crossing the Tc /Tm,- boundary. These changes indicate a large increase
in disorder of the Mn-Oe octahedra as the PI phase is approached and then entered.
This is just the sort of distortion which would be caused by small polarons. In addi-

tion, there are large qualitative changes in the PDF upon crossing the MI transition

51

line as a function of temperature or composition. Similar changes in T and a: which
do not cause a phase change create a much smaller change in the PDF. Clearly there
is a connection between the structure and the electronic state, which we explain with

the appearance of polarons.

At low temperatures, the FM state contains carriers which have essentially all
delocalized. The structure contains no disorder and no Jahn-Teller efl'ect is present.
Models based on the average structure, containing no JT distortions, fit data in the
FM state at low temperature very well but performed much worse in other parts
of the phase diagram. This agreement between local and average structure means
there is very little disorder in this region, hence few if any polarons. Also, at low
tempearatures the peak heights in Figure 3.3 reached a saturation point. After they
had risen steeply around Tc they displayed canonical behavior according to the Debye
curve. This indicates that the delocalization process has stopped, presumably because
there are no more carriers left as polarons. At intermediate temperatures the FM state
is microscopically inhomogeneous or phase-separated. It consists of both localized and
delocalized carriers. This is seen through the drop in peak height which begins much
below Tc , and also through the growth of the secondary peak near 2.3A before Tc has

been achieved.

The transition from metal to insulator as a function of composition is qualitatively
difl'erent from the temperature-dependent transition. We see the smooth evolution
of peak heights through 3M; in Figure 3.7 in contrast to the dramatic effects around
Tc . This suggests that am) is defined by the appearance of a percolative path
of undistorted Mn ions which would allow metallic transport. Unfortunately, the
poor quality of the samples involved in this experiment makes this a somewhat more
tentative result at the moment. However, increase in peak height which continues
until a: = 0.25 does support the earlier result that much of the FM phase contains

52

polarons as well as delocalized carriers.

We can now understand the strange phenomenology of the a: = 0.5 sample. The
FM transition is identical to those with a: < 0.5 : charges begin to delocalize but are
still significantly polaronic. At Too the remaining polarons order, which lowers the
energy of the localized phase. This causes the delocalized fraction to progressively re-
enter the polaron state until they are used up. This is the point when superexchange
becomes preferred over DE and we enter the AFI state. This result supports our
previous conclusions because without the ability of both types of carriers to coexist
there is no way to explain ferromagnetism in the a: = 0.5 compound without the

carriers changing from completely localized to completely delocalized.

5.2 Future work

One of the main questions which we were unable to resolve is the exact shape of the
Jahn-Teller distortion. A primary difficulty had to do with the scattering lengths
of our constituent atoms. While oxygen is a fairly strong neutron scatterer which
made oxygen correlations show up well, manganese has a negative neutron scattering
length. Because of this, all Mn—to—other correlations have a negative sign and there
is considerable cancellation of signal in the final PDF. This was one reason why we
considered turning to x-rays. Obviously, a problem would then be that oxygen corre-
lations would be overwhelmed by those of the larger atoms. However, a combination

of both techniques could be succesful in solving many of these difficulties.

Figure 5.1 shows PDFs measured on Lao,75Cao,25MnOg using neutrons and x-
rays. Some of the most prominent features in each PDF are barely present in their
counterpart. This is not an experimental artifact but the result of very different

scattering properties when x-rays are substituted for neutrons. Since Lanthanum

53

Neutrons

 

 

 

 

 

 

wax-rays
r I ‘ I
10 ~ 73 -
.‘I l]
t :1 I ’
5 if??? ft If if j
+6 .‘7 I] ff it . f
e; 0. .0 'i I. I .'+
. ‘I :t 9* :1 I +
3 [I , fit f #0 , l’ . f:
0 o 2.4.7 ‘t + ‘. :'
r e . I ‘1 l 1 s".
.‘ 1 1 . ' 4 i
:l K‘ I:
-5 _ g *I .
’10 2:5 5:0 7:5 10.0
WWW)

Figure 5.1: PDFs of Lao,75Cao,25MnOg measured at room temperature using x—rays
and neutrons.

correlations dominate the x-ray PDF, these data could be used to pin down the
structure of the La/Ca sublattice. Once these positions are known, they could be
used when modeling a neutron PDF. This should produce a better model and reduce
the number of variables to be refined. We then would stand a better chance at being

able to fit the shape of the Jahn-Teller distortion.

Another experiment that should be performed is to re-measure PDFs at base tem-
perature for compounds with sic-values closely spaced from 0 to 0.33. While difficulties
persist in obtaining homogeneous samples in sufl'icent quantities for neutron diffrac-
tion, this remains an important piece of work. If we can confirm our results from
our first attempt it would not only support the percolative model of conduction, but
boost all of our previous results. If the peak heights show a large response at a: M),

this would force us to reexamine many of our ideas.

54

APPENDIX

Publications:

S. J. L. Billinge, R. G. DiFrancesco, M. F. Hundley, J. D. Thompson, and G.
H. Kwei, Competition between charge localization and delocalization in
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