ELECTRONIC PROPERTIES OF TRANSITION METAL OXIDES

A THESIS SUBMITTED TOTHE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OFTHE MIDDLE EAST TECHNICAL UNIVERSITY

BY

ERSEN METE

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

IN

THE DEPARTMENT OF PHYSICS

December 2003

Approval of the Graduate School of Natural and Applied Sciences.

Prof. Dr. Canan OzgenDirector

I certify that this thesis satisfies all the requirements as a thesis for the degreeof Doctor of Philosophy.

Prof. Dr. Sinan BilikmenHead of Department

This is to certify that we have read this thesis and that in our opinion it isfully adequate, in scope and quality, as a thesis for the degree of Doctor ofPhilosophy.

Prof. Dr. Sinasi EllialtogluSupervisor

Examining Committee Members

Prof. Dr. Sinasi Ellialtoglu

Prof. Dr. Atilla Ercelebi

Prof. Dr. Metin Durgut

Assoc. Prof. Dr. Hatice Kokten

Dr. Sadi Turgut

ABSTRACT

ELECTRONIC PROPERTIES OF TRANSITION METAL OXIDES

Mete, Ersen

Ph. D., Department of Physics

Supervisor: Prof. Dr. Sinasi Ellialtoglu

December 2003, 80 pages

Transition metal oxides constitute a large class of materials with variety of

very interesting properties and important technological utility. A subset with

perovskite structure has been the subject matter of the current theoretical

investigation with an emphasis on their electronic and structural behavior. An

analytical and a computational method are used to calculate physical entities

like lattice parameters, bulk moduli, band structures, density of electronic

states and charge density distributions for various topologies. Results are

discussed and compared with the available experimental findings.

Keywords: perovskite, tight binding, ab initio, pseudopotential

iii

OZ

GECIS METAL OKSITLERIN ELEKTRONIK OZELLIKLERI

Mete, Ersen

Doktora, Fizik Bolumu

Tez Yoneticisi: Prof. Dr. Sinasi Ellialtoglu

Aralk 2003, 80 sayfa

Gecis metal oksitleri cesitli ve cok ilginc ozellikleri ile onemli teknolojik uygu-

lamalar olan genis bir malzeme snfn olusturmaktadrlar. Perovskit yapsna

sahip bir alt kumenin elektronik ve yapsal ozellikleri bu kuramsal arastrmann

konusu olmaktadr. Degisik topolojiler icin orgu sabiti, hacim modulu, bant

yaps, durum yogunlugu ve yerel yuk daglm gibi fiziksel nicelikler, biri anal-

itik ve digeri numerik olmak uzere iki ayr yontemle hesaplanms ve deneysel

verilerle karslastrlarak yorumlanmstr.

Anahtar Kelimeler: perovskit, sk bag, ilk-prensipler, potansiyelimsi

iv

To my wife, Pnar

v

ACKNOWLEDGMENTS

I would like to thank Prof. Dr. Sinasi Ellialtoglu for the discussions and his

support. I would also like to thank to my family. They supported me like

nobody else can do.

This work was supported by TUBITAK, The Scientific and Technical Re-

search Council of Turkey, Grants No. TBAG-2036 (101T058) and by the

Institute of Natural and Applied Sciences of METU, Grants No. BAP-2001-

07-02-00-97.

vi

TABLE OF CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

OZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

DEDICATON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . vi

TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

CHAPTER

I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1

II TIGHT-BINDING APPROXIMATION . . . . . . . . . . . . . . 4

II.1 Energy Bands . . . . . . . . . . . . . . . . . . . . . . . 4

II.2 Density of States . . . . . . . . . . . . . . . . . . . . . . 11

III AB INITIO PSEUDOPOTENTIAL METHOD . . . . . . . . . 16

III.1 Density Functional Theory . . . . . . . . . . . . . . . . 17

III.1.1 Hohenberg-Kohn Theorems : Proof of Exis-tence and Variational Principle . . . . . . . . . 18

III.1.2 Many Body System : The Kohn-Sham Equation 24

III.1.3 Exchange and Correlation . . . . . . . . . . . . 26

III.1.3.1 Local Density Approximation . . . 27

III.2 Pseudopotential Approximation . . . . . . . . . . . . . . 29

III.2.1 Norm-Conserving Pseudopotentials . . . . . . 30

vii

III.2.2 A Pseudopotential Generation Example : Ti . 36

III.3 Total Energy Computation . . . . . . . . . . . . . . . . 41

III.3.1 Supercells and Plane Wave Representation . . 41

III.3.2 The Conjugate-Gradients Minimization Tech-nique . . . . . . . . . . . . . . . . . . . . . . . 44

III.3.3 ABINIT Code . . . . . . . . . . . . . . . . . . 45

III.3.3.1 Ground State Calculations . . . . . 46

III.3.3.2 Structural Calculations . . . . . . . 47

III.3.3.3 Memory and Speed . . . . . . . . . 47

III.3.3.4 Parallelism . . . . . . . . . . . . . . 48

IV ELECTRONIC AND STRUCTURAL PROPERTIES OF 4d-PEROVSKITES . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

IV.1 Insulating Case . . . . . . . . . . . . . . . . . . . . . . . 50

IV.1.1 Introduction . . . . . . . . . . . . . . . . . . . 50

IV.1.2 Calculation Method . . . . . . . . . . . . . . . 53

IV.1.3 Results and Discussion . . . . . . . . . . . . . 54

IV.2 Metallic Case . . . . . . . . . . . . . . . . . . . . . . . . 60

IV.2.1 Introduction . . . . . . . . . . . . . . . . . . . 60

IV.2.2 Parameters for Computational Method . . . . 61

IV.2.3 Results and Discussion . . . . . . . . . . . . . 62

V TIGHT BINDING PARAMETRIZATION USING AB-INITIORESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

VI CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

viii

LIST OF TABLES

III.1 Input parameters of Titanium for the package fhi98PP. . . . . . 37

IV.1 Calculated and experimental values for lattice parameter andbulk modulus of SrTiO3 and SrZrO3 . . . . . . . . . . . . . . . 55

IV.2 Calculated and experimental values for lattice parameter andbulk modulus of SrMO3 . . . . . . . . . . . . . . . . . . . . . . 62

V.1 Tight-binding parameters (in eV) fitted to ab initio results. . . 67

ix

LIST OF FIGURES

II.1 ABO3 cubic perovskite lattice structure. . . . . . . . . . . . . . 5II.2 Cubic perovskite single unit cell. . . . . . . . . . . . . . . . . . . 5II.3 ABO3 energy levels. . . . . . . . . . . . . . . . . . . . . . . . . . 6II.4 nn interactions for t2g-symmetry orbitals. . . . . . . . . . . . . . 7II.5 nn interactions for eg-symmetry (dx2y2) orbitals. . . . . . . . . 7II.6 nn interactions for eg-symmetry (d3r2z2) orbitals. . . . . . . . . 8II.7 1st Brillouin Zone for cubic unit cell and special k-points. (a,

b, c are the reciprocal primitive vectors.) . . . . . . . . . . . . 9II.8 Bulk energy bands along symmetry lines in the 1st Brillouin Zone. 10II.9 Typical DOS structure for a perovskite. . . . . . . . . . . . . . . 15

III.1 Pseudopotential and pseudowavefunction vs all-electron coun-terparts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

III.2 (a) True radial wavefunctions and (b) pseudo versus all-electronwavefunctions for Titanium. . . . . . . . . . . . . . . . . . . . . 38

III.3 (a) Screened and (b) ionic pseudopotentials for Ti. . . . . . . . . 39III.4 Logarithmic derivatives of radial wavefunctions for Titanium. . . 40

IV.1 Ab initio band structure for SrTiO3 . . . . . . . . . . . . . . . . 55IV.2 Ab initio band structure for SrZrO3 . . . . . . . . . . . . . . . . 56IV.3 Charge density contour plots for bands for (a) SrTiO3 and

(b) SrZrO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59IV.4 Ab initio band structures for SrMoO3 . . . . . . . . . . . . . . . 63IV.5 Ab initio partial density of states for SrMoO3 . . . . . . . . . . 64IV.6 Ab initio band structures and DOS for SrRuO3 . . . . . . . . . 65IV.7 Ab initio band structures and DOS for SrRhO3 . . . . . . . . . 66

V.1 Comparisons of band structures and DOS functions of TB (thinlines) and ab initio (thick lines) results for SrTiO3. . . . . . . . 68

V.2 Comparisons of band structures and DOS functions of TB (thinlines) and ab initio (thick lines) results for SrZrO3. . . . . . . . 69

x

LIST OF SYMBOLS

BZ Brillouin Zone

CPU Central Processing Unit

DFT Density Functional Theory

DOS Density of States

DRAM Dynamic Random AccessMemory

FFT Fast Fourier Transform

GS Ground State

KB Kleinmann-Bylander

LCAO Linear Combination of AtomicOrbitals

LDA Local Density Approxima-tion

LDOS Local Density of States

MPI The Message Passing Inter-face

nn Nearest Neighbor

OpenMP A GNU project for Shared-Memory Systems

PP Pseudo Potential

PS Pseudo

PW92 Perdew Wang 92

SCR Screened

SMP Synthetic Multi-Processing

SOV Surface Oxygen Vacancy

TB Tight Binding

TMO Transition Metal Oxide

XC Exchange Correlation

xi

CHAPTER I

INTRODUCTION

The main difference of transition metals (TM)