Microscopic origin of magnetism in the hematite-ilmenite system [Elektronische Ressource] / by Seyed Hasan Sadat Nabi

S. Hasan Sadat Nabi

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2010
• Nombre de lectures: 14
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

MICROSCOPIC ORIGIN OF
MAGNETISM IN THE
HEMATITE-ILMENITE SYSTEM
by
Seyed Hasan Sadat Nabi
PhD thesis
Submitted in Partial Fulflllment of the
Requirements for the Degree of
Dr. rer. nat.
at the
Faculty of Geosciences
Ludwig-Maximilians University
Munich, Germany
February 2010Supervisor:
PD Dr. Rossitza Pentcheva
Supervisor:
Prof. Dr. Wolfgang Moritz
Date of Oral Examination: 27.05.2010i
Ehrenw˜ortliche Versicherung
Ich versichere hiermit ehrenw˜ortlich, dass die Dissertation von mir selbst˜andig und
ohne Beihilfe angefertigt worden ist.
Seyed Hasan Sadat Nabi
Munc˜ hen, February 2010
Erkl˜arung
Hiermiterkl˜areich,dassdieDissertationnochnichtineinemanderenPrufungsv˜ erfahren
vorgelegt und bewertet wurde.
Hiermiterkl˜areich,dassichmichnichtanderweitigeinerDoktorprufung˜ ohneErfolg
unterzogen habe.
Seyed Hasan Sadat Nabi
Munc˜ hen, February 2010Contents
Introduction 1
1 Introduction to Ab-initio Calculations 5
1.1 Many-body quantum mechanics . . . . . . . . . . . . . . . . . . . . . 5
1.1.1 Principle of quantum mechanics . . . . . . . . . . . . . . . . . 5
1.1.2 Expectation values . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.3 The Born-Oppenheimer approximation . . . . . . . . . . . . . 8
1.2 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 The Kohn-Sham method . . . . . . . . . . . . . . . . . . . . . 12
1.2.2 The LDA and GGA potentials . . . . . . . . . . . . . . . . . . 15
1.2.3 Beyond LDA/GGA: The LDA+U method . . . . . . . . . . . 17
1.2.4 Solving the Kohn-Sham equation . . . . . . . . . . . . . . . . 22
1.3 The WIEN2K code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Properties of Bulk fi-Fe O and FeTiO 292 3 3
2.1 Calculational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Bulk properties of FeTiO . . . . . . . . . . . . . . . . . . . . . . . . 313
2.2.1 Structural properties . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.2 Equation of state . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.3 Electronic and magnetic properties: GGA vs. GGA+U . . . . 33
2.3 Bulk properties of fi-Fe O . . . . . . . . . . . . . . . . . . . . . . . . 352 3
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Origin of Magnetism in Hematite-Ilmenite Heterostructures 39
3.1 Fe O -FeTiO phase diagram . . . . . . . . . . . . . . . . . . . . . . 392 3 3
3.2 Fe O -FeTiO interface . . . . . . . . . . . . . . . . . . . . . . . . . . 402 3 3
3.2.1 Structural relaxation . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2 Compensation mechanism and energetic trends . . . . . . . . 44
3.2.3 Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 Strain efiect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Magnetic exchange interaction parameters . . . . . . . . . . . . . . . 53
3.4.1 Calculation of magnetic interaction parameters . . . . . . . . 53
3.4.2 Magnetic exchange interaction of the end members . . . . . . 55
3.4.3 interactions at the Fe O /FeTiO interface . . . . . 572 3 3
3.4.4 Efiect of strain on the magnetic interactions . . . . . . . . . . 60
3.4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
iiiiv CONTENTS
4 Bulk Properties of EuTiO 633
4.1 Equilibrium lattice constant andbulk modulus . . . . . . . . . . . . . 64
4.2 Electronic and magnetic structures of EuTiO . . . . . . . . . . . . . 653
4.3 Calculation of exchange integrals . . . . . . . . . . . . . . . . . . . . 66
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5 Comparative Study on EuLiH and EuTiO 693 3
5.1 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6 Conclusions and Perspectives 75
A Functional Derivatives 79
B The Table of Magnetic Conflgurations 81
C The Interaction Type Matrix 85
D The Connectivity Matrix 87
Manuscript M1 89
Manuscript M2 95
Manuscript M3 101
Manuscript M4 109
Manuscript M5 121
Bibliography 133
Acknowledgements 135
Publications 137
Curriculum Vitae 139List of Figures
1.1 WIEN2K owchart . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1 Crystal structure of Fe O . . . . . . . . . . . . . . . . . . . . . . . . 302 3
2.2 Ilmenite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 Magnetic moment and total energy of ilmenite . . . . . . . . . . . . . 32
2.4 DOS of ilmenite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 Magnetic moment and total energy of hematite . . . . . . . . . . . . 36
2.6 DOS of hematite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1 Fe O -FeTiO phase diagram . . . . . . . . . . . . . . . . . . . . . . 402 3 3
3.2 Structures modelled in a 30-atom unit cell . . . . . . . . . . . . . . . 41
3.3 mo in a 60-atom unit cell 33% Ti-doped Fe O . . . 422 3
3.4 Structures modelled for 17%, 50%, 66% and 83%ed Fe O . . 432 3
3.5 DOS of 33% Ti-doped in Fe O . . . . . . . . . . . . . . . . . . . . . 462 3
3.6 DOS of Fe Ti O with x= 17%, 50%, 66% and 83% . . . . . . . . 472¡x x 3
3.7 Formation energy versus ilmenite concentration . . . . . . . . . . . . 48
3.8 TEM image of hematite exsolution lamellae . . . . . . . . . . . . . . 49
3.9 The c=a-ratio, volume and formation energy vs. ilmenite concentration 51
3.10 Density of states of Fe Ti O . . . . . . . . . . . . . . . . . . . . 521:67 0:33 3
3.11 Deflnition of the pair magnetic exchange parameters . . . . . . . . . . 54
3.12 The magnetic pair interaction parameters. . . . . . . . . . . . . . . . 56
3.13 Structures used for magnetic interaction parameters at interface . . . 58
3.14 Comparison of magnetic interaction at interface . . . . . . 59
3.15 The magnetic pair interaction parameters on an Al O substrate . . . 612 3
4.1 Crystal structure of cubic EuTiO . . . . . . . . . . . . . . . . . . . . 643
4.2 Total energy versus volume of cubic EuTiO . . . . . . . . . . . . . . 653
4.3 Total and partial DOS of EuTiO . . . . . . . . . . . . . . . . . . . . 663
5.1 Variation in J and J vs. U in EuLiH . . . . . . . . . . . . . . . . . 701 2 3
5.2 V in J and J vs. lattice parameter of EuLiH . . . . . . . . 711 2 3
5.3 Variation in the relative energy vs. volume of . . . . . . . . . 723
5.4 DOS of ferromagnetic EuLiH . . . . . . . . . . . . . . . . . . . . . . 733
5.5 Variation in the band gap of EuLiH and EuTiO . . . . . . . . . . . 733 3
vList of Tables
2.1 Lattice parameters and bulk modulus of ilmenite . . . . . . . . . . . 33
2.2 Band gap of ilmenite within HF, B3LYP, GGA, GGA+U and Exp. . 35
2.3 Magnetic moments and energy difierences of ilmenite . . . . . . . . . 35
2.4 Lattice parameters and bulk modulus of hematite . . . . . . . . . . . 37
3.1 The cation-anion distances in the system . . . . . . . . . . . . . . . . 44
3.2 The experimental lattice constants of Fe O , FeTiO and Al O . . . 492 3 3 2 3
3.3 N¶eel temperature for hematite and ilmenite . . . . . . . . . . . . . . 57
q3.4 The J for Fe O , FeTiO and interface . . . . . . . . . . . . . . . . 592 3 3m
q3.5 The J for Fe O , FeTiO and in on an Al O substrate . . . . 602 3 3 2 3m
4.1 Values of J and J of EuTiO . . . . . . . . . . . . . . . . . . . . . . 671 2 3
5.1 Relative energies of various magnetic structures of EuLiH . . . . . . 703
B.1 E and spin arrangements in Fe O . . . . . . . . . . . . . . . . . . 82rel 2 3
B.2 E and spints in FeTiO . . . . . . . . . . . . . . . . . . 83rel 3
B.3 E and spints in interface-a . . . . . . . . . . . . . . . . 83rel
B.4 E and spin arrangements in interface-b . . . . . . . . . . . . . . . . 84rel
vii