Understanding Complex Ordering In Transition Metal Oxides

141 Pages·2013·2.43 MB·English

Understanding Complex Ordering
In
Transition Metal Oxides

Thesis submitted to
WEST BENGAL UNIVERSITY OF TECHNOLOGY
in partial fulfillment of the Degree of
DOCTORATE OF PHILOSOPHY
2013

Abhinav Kumar
School of Management and Sciences,
West Bengal University of Technology
Salt Lake, Kolkata-700098
West Bengal, India
Thesis Certificate

This is to certify that the thesis entitled ‡Understanding Complex Ordering in
Transition Metal Oxides·(cid:15)(cid:3)VXEPLWWHG(cid:3)E\(cid:3)Abhinav Kumar to the West Bengal
University of Technology for the award of the degree of Philosophy, is a bona
fide record of the research work done by him under my supervision in the
duration of five and half years from August 2007 to January 2013. He has
completed the work truthfully and successfully to the best of my knowledge.
The contents of this thesis, in full or in part have not been submitted to any
other Institute or University for the award of any degree or diploma.

Priya Mahadevan(Supervisor)
Associate Professor
Department of Condensed Matter Physics and Material Sciences
S.N. Bose National Centre for Basic Sciences
JD block, Sector-3, Salt Lake
Kolkata-700098
Dedicated to
My parents
whocreatedme
iii
Acknowledgments
I would like to take this opportunity to express my heart-felt gratitude to those people who have
guided me, motivated me and have been with me all through these five years of my academic journey
thathasculminatedintothisthesiswork.
The first person I would like to express my gratitude to is my supervisor Prof. Priya Mahadevan
withoutwhomthisthesiswouldnothavebeencompleted. Itismoreimportanttobeagoodpersonthan
a good scientist. And ma’am you are combination of the two. I am really thankful for these five and
halfyearsispenthere. Duringmythesisworkyourvastscientificknowledgeandinsightintovarious
problemshasimpressedmemanytimes. Workingwithyouwaslikeworkingwithinafamily.
I would also like to take this opportunity to thank Prof. Binayak Dutta-Roy, whom I have found
to be the best teacher till now. He inspired me to approach any problem in a simple way. Numerous
scientific discussions with him have greatly matured my thinking process. I would like to thank my
M.Sc. friendsManish,Vikash,Rashid,Anirban,Ramuandallothers.
I thank PMG (Priya Mahadevan Group) members starting with my best friend in Kolkata Hirak
Kr. Chandra who understands me better than any one on earth. Multi talented Saikat, Ruma madam
(G-99),Dr. Basu,ShishiRO(KU),SrimanataDa,Ashisda,BipulDa,Azahar,Sagar,my’Uttradhikari’
Dilip,KapilandmyseniorRobyda.
Now I come to the members of S.N. Bose center where I have spent more than seven years of my
life. In the course of this time I have made a huge number of friends and each of them together has
affected me in some way or the other. Starting with Mitali Di whom I call ’DA’, Srimoyee Ganguly
andSoaurabhDawithwhomIreallyenjoyedthisplace. TheymademefeelasifIampartofafamily.
Nearest to my heart is Rajiv Kr. Chouhan who has shared each and every thing with me in these past
years,SandeepAgarwalandSinghwhogavemerespectlikeanelderbrotherandRumaMondalwhois
likeasistertome. Wasimbhai,Rajashree,JenaJi,Prashnat-Soma,Saumojit,Abhijit,Sujoy,Swastika,
Saimanti, Sushmita, the coolest person Sudip Garain (Babu) and Arka(KK) whom I consider as my
verygoodfriends. IwouldliketothankmyseniorsAbhishekBhiaya,MrinalDa,DebuDa,VenkatDa
andallotherswhohelpedmeintheirownwaystogetmeaccustomedtothisplace.
The rest will also hold a special place in my heart as long as it beats. I would like to mention
Tukun-DebolinawhomalthoughImetintheseventhyearofmystayinthisinstitute,havebecomethe
closestpeopletomyheart. TheymademefeelwhyIdidnotinteractwiththemoneyearearlierwhen
theyhadnewlyjoinedtheinstitute. Whenonetalkswiththeduo,onelosescountofthehoursthatone
hasspentwiththem.
Last but never the least I would like to thank my family who has always been a pillar of strength
andsupportformeinmylife.
AbhinavKumar
S.N.BoseNationalCenterforBasicSciences,
Kolkata,India.
ListofPublications
1. Chargeorderinginducedferromagneticinsulator: K Cr O
2 8 16
P.Mahadevan,AbhinavKumar,D.ChoudhuryandD.D.Sarma
Phys. Rev. Lett. 104,256401(2010).
2. Strongcorrelationsandaweak-couplinggapacrossferromagnetic-metaltoferromagnetic-insulator
transitioninK Cr O
2 8 16
P.A.Bhobe,A.Chainani,R.Eguchi,M.Matsunami,AbhinavKumar,P.Mahadevan,D.D.Sarma
et. al.
(Underpreparation).
3. MicroscopicmodelforchargeorderinginK Cr O
2 8 16
AbhinavKumar,A.K.NandyandP.Mahadevan.
(Underpreparation).
4. MagnetisminK Cr O
2 8 16
A.K.Nandy,AbhinavKumarandP.MahadevanandD.D.Sarma
(Underpreparation).
5. OriginofferromagneticinsulatingstateinCrdopedVO
2
AbhinavKumarandP.Mahadevan
(Underpreparation).
6. IsBi NiMnO amultiferroic?
2 6
AbhinavKumarandP.Mahadevan
(Underpreparation).
7. AmodelforferroelectricityinBaTiO
3
AbhinavKumar,H.K.ChandraandP.Mahadevan
(Underpreparation).
8. Effectofquantumconfinmentontheconductionbandminimumofsemiconductors
: CherianRoby,AbhinavKumarandP.Mahadevan
JournalofNanoscienceandNanotechnologyVol-9,5673-5675(2009)
Contents
TableofContents v
ListofFigures vii
ListofTables xii
1 Introduction 1
1.1 ElectronicstructureofTransitionMetalOxides . . . . . . . . . . . . . . . . . . . . . 1
1.2 StructuralaspectsofTransitionMetalOxides . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Perovskitestructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 GdFeO distortioninperovskites . . . . . . . . . . . . . . . . . . . . . . . . 5
3
1.4 Crystalfieldtheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Jahn-TellerDistortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Magnetism: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 MagneticMomentsinAtoms/Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.7 MagnetisminSolid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.7.1 CorrelationEffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.7.2 TheMott-HubbardModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.8 DirectExchange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.9 Superexchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.10 Magnetisminmetal: DoubleExchangeModel . . . . . . . . . . . . . . . . . . . . . . 21
1.11 ModelforFerromagneticInsulators . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.11.1 Goodenough-Kanamori-Andersonrule . . . . . . . . . . . . . . . . . . . . . 22
1.11.2 Kugel-KhomskiiModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.12 MotivationoftheThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Theoryofelectronicstructurecalculations 33
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Single-particleapproximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.1 Wavefunctionbasedapproaches . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.2 DensityFunctionalTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.2.1 BasictheoremsofDFTandKohn-Shamequation . . . . . . . . . . 36
2.2.3 Exchange-correlationfunctional . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.3.1 Localdensityapproximation(LDA) . . . . . . . . . . . . . . . . . 41
v
vi CONTENTS
2.2.3.2 Generalizedgradientapproximation(GGA) . . . . . . . . . . . . . 41
2.3 Thebasicmethodstocalculateelectronicstructure. . . . . . . . . . . . . . . . . . . . 42
2.3.1 PseudopotentialMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.2 TheProjector-Augmented-WaveFormalism . . . . . . . . . . . . . . . . . . . 45
2.3.3 Thetight-bindingmethod(LCAOmethod) . . . . . . . . . . . . . . . . . . . 46
3 K Cr O : electronicstructure 51
2 8 16
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 AmicroscopicmodelforK Cr O 67
2 8 16
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3 ResultandDiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4 ComparisonwithRb Cr O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
2 8 16
5 CrdopinginVO : Ferromagnetismininsulator. 89
2
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6 FerromagneticinsulatorBi NiMnO : 99
2 6
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7 AmodelforferroelectricityinBaTiO 111
3
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.3 Resultanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
List of Figures
1.1 Zaanen-Sawatzky-Allenplotforclassifying3dtransitionmetalcompounds. Thestraight
line U/∆ separates the Mott-Hubbard regime(A) and charge-transfer regime(B). Fig
Ref: Zaanen,Sawatzky,AllenPhys. Rev. Lett. 55,418(1985). . . . . . . . . . . . . . . 3
1.2 TwodifferenttypesunitcellstounderstandPerovskitestructure. . . . . . . . . . . . . 5
1.3 BO octahedra in a) ideal cubic unit cell and b) in distorted unit cell with tilts and
6
rotationoftheoctahedra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Schematicrepresentationofthesplittingpatternofdorbitalsundervariouscrystal-field
symmetriestetrahedral,forfreeion,foroctahedralrespectively.. . . . . . . . . . . . . 7
1.5 (a) and (b), schematically represent the vibrational modes, Q and Q , respectively
2 3
for an example of perovskite, LaMnO , while (c) describes the resultant Jahn-Teller
3
splittinginthet ande manifolds. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2g g
1.6 Theschematicmetal-insulatorphasediagramwithintheHubbardmodelintheelectron
correlationstrength(U/Wor∆/W)andbandfilling(n)plane. Therearetworoutesfor
themetal-insulatortransition(MIT),whichareshownasthebandwidth-controlledMIT
andthefilling-controlledMIT.ThisfigureisredrawnfromRef.[50] . . . . . . . . . . 16
vii
viii LISTOFFIGURES
1.7 A simple picture of direct exchange, (a), favors the antiparallel alignment of the spins
(lower) as it allows the electrons to hop to the neighboring site and costs an energy of
U . While,intheparallelalignmentofthespins(upper)hoppingissuppressedbythe
dd
Pauliexclusionprinciple. TheBethe-Slatercurvein(b)yieldsthatelementsabovethe
horizontalaxisareferromagnetic,belowthataxisareantiferromagnetic. . . . . . . . . 17
1.8 A simple picture of super-exchange where the orbital on the central site is different
fromtheorbitalsonthesides. Typically,twodorbitalsarecoupledviaanintermediate
oxygen p orbital as in 4(a). For antiparallel alignment of the spins on two d orbitals,
(b)describethewaysthattwoconsecutivehoppingprocessesarepossible,whilein(c)
forferromagneticcase,thePauliprincipleforbidsthesecondhoppingprocess. . . . . . 19
1.9 Ina90 arrangementofd-p-dgroupasin(a),onefindsthatthedorbitalsarecoupled
◦
to the orthogonal p orbitals, the ferromagnetic super-exchange in (b) is mediated via
theCoulombexchangeontheconnectingoxygen. . . . . . . . . . . . . . . . . . . . . 20
1.10 The double-exchange mechanism in hole doped manganite perovskite. coupling be-
tween the localized spins on Mn3+ and Mn4+ ions and the itinerant electrons in a)
ferromagneticalignment(b)antiferromagneticalignmentoflocalizedspin. Theferro-
magneticalignmentofthelocalizedspinsstabilizedthroughHund’sexchangecoupling. 21
1.11 TheGoodenough-Kanamori-Andersonrules: Ina180 geometryofd-p-dgroup,(a)
◦
and (b) yield the antiferromagnetic alignment of spins on d orbitals, while in (c) and
(d)thefavoredalignmentsareferromagnetic. . . . . . . . . . . . . . . . . . . . . . . 23
1.12 Super-exchange in the case of two-fold degenerate orbitals, two colors blue and red
represent two different orbitals. (a) shows ferromagnetic and anti-ferromagnetic spin
alignmentandcorrespondingenergiesinferro-orbitalstackingand(b)showsferromag-
netic and anti-ferromagnetic spin alignment and corresponding energies in antiferro-
orbitalstacking.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
LISTOFFIGURES ix
3.1 The network of Cr atoms (a) in the z=0 plane z=0.5 in the xy plane unit cell has been
shown within solid lines. (b) Connection of two nearest Cr ions along Z direction has
beenshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 Thecalculatedatomandspinprojectedpartialdensityofstatesfor(a)O1 p,(b)O2 p,
(c)Crd and(d)KsforU=0. ZeroofenergycorrespondstotheFermienergy. . . . . . 55
3.3 The calculated Cr3+ d spin projected partial density of states for (a)U=2 eV, (b)U=3
eV, and (c) U=4 eV with the optimized crystal structure of the U=4 eV calculation
assumed. Zero of energy corresponds to the Fermi energy. The near fermi energy
region of the up spin Cr3+ and Cr4+ partial density of states is shown in the inset of
panel(c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4 Thespinarrangementsinoneunitcellfor(a)AFM1and(b)AFM2. . . . . . . . . . . 57
3.5 Thecalculatedchargedensityofthefeaturebetween-0.5eVandthefermienergyhas
beenplotted. TheCr3+ andCr4+ ionshavebeenindicated. . . . . . . . . . . . . . . . 58
3.6 The network of Cr3+ and Cr4+ atoms in the z=0 and 0.5 planes for (a) farthest Cr3+
atomsand(b)observedarrangementofCr3+ atomsintheunitcell. . . . . . . . . . . . 59
3.7 Aschematicleveldiagramofthesplittingofthepartiallyoccupiedt orbitalsonCr3+
2g
andCr4+ hasbeenshown. Variationofδwithintractionstrengthhasalsobeenshown. 60
3.8 The energy level diagram for the levels formed by the interaction of Cr3+ and Cr4+
atomsin(a)FMand(b)AFMarrangements. . . . . . . . . . . . . . . . . . . . . . . . 60
3.9 ComparisonofsimulatedXRDpatternforbothexperimental(tetragonal)andrelaxed(monoclinic)
structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.1 ThedifferentCrsiteswithingsmallunitcell. Thefourcolorsrepresentsfourinequiva-
lentCrsites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2 Banddispersioncomparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3 Interactionstrengthasafunctionofbondlength. . . . . . . . . . . . . . . . . . . . . 74