transition metal oxide perovskites: band structure, electrical and magnetic properties

Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry

Transition Metal Oxide Transition Metal Oxide Perovskites:Perovskites:

Band Structure, Band Structure, Electrical and Magnetic Electrical and Magnetic

PropertiesPropertiesChemistry 754Chemistry 754

Solid State Chemistry Solid State Chemistry Lecture #24Lecture #24

May 27, 2003May 27, 2003


Transition Metal OxidesTransition Metal Oxides

To illustrate the relationship between To illustrate the relationship between crystal crystal structurestructure, , bondingbonding, , band structureband structure, , electricalelectrical andand magnetic propertiesmagnetic properties we are we are going to consider transition metal oxides of three going to consider transition metal oxides of three structure types.structure types.

– Perovskite (AMOPerovskite (AMO33)/ReO)/ReO33

– Rock Salt (MO)Rock Salt (MO)

– Rutile (MORutile (MO22))

For all three structures M-O interactions will For all three structures M-O interactions will dictate the properties. In the latter two structure dictate the properties. In the latter two structure types we also need to consider M-M bonding.types we also need to consider M-M bonding.


Perovskites and Band Perovskites and Band StructureStructure

• Octahedral Molecular Orbital DiagramOctahedral Molecular Orbital Diagram

• *(t*(t2g2g) and ) and *(e*(egg) Bands) Bands

• Orbital Overlap and Bandwidth (ReOOrbital Overlap and Bandwidth (ReO33 vs. vs. MnOMnO33

2-2-))

• Structural Distortions (Octahedral Tilting)Structural Distortions (Octahedral Tilting)• Exchange Splitting (Spin Pairing Energy)Exchange Splitting (Spin Pairing Energy)

• The d-electron count (SrTiOThe d-electron count (SrTiO33 to SrFeO to SrFeO33))

• Instabilities and the dInstabilities and the d44 electron count electron count

– SrFeOSrFeO33

– LaMnOLaMnO33

– CaFeOCaFeO33


Perovskite Crystal StructurePerovskite Crystal Structure

OO

AA

MM


Generic Octahedral MO Generic Octahedral MO DiagramDiagram

a1g ()

t1u ()

eg ()t2g ()

t1g & t2u

a1g ()

t1u ()

t2g ()

eg ()

nd eg (dx2-y2, dz2)

(n+1)d t2g (dxy, dxz, dyz)

(n+1)s

(n+1)p

O 2p (6) - t2g, t1u

O 2p NB(6)-t1g, t2u

O 2p (6)a1g, t1u, eg

TransitioTransition Metaln Metal

OxygenOxygen


Simplified Band StructureSimplified Band Structure

nd eg (dx2-y2, dz2)

(n+1)d t2g (dxy, dxz, dyz)

(n+1)s

(n+1)p

O 2p

O 2p (6)a1g, t1u, egTransitioTransitio

n Metaln Metal

OxygenOxygen

M-O

M-O

O 2p NB

M-O [3]

M-O [2]

[4] Bands of Bands of interestinterest


Orbital Overlap Orbital Overlap * and * and * * BandsBands

* Overlap (M d t2g – O 2p )

Band Runs Uphill

* Overlap (M d eg – O 2p )

Band Runs Uphill

point(kx=ky=0)

non-bonding

point(kx=ky=/

a)antibondi

ng

Greater Spatial Overlap

W(*) > W(*)


Overlap in 3DOverlap in 3DSo far we have been working So far we have been working mostly in 1D and 2D. In 3D mostly in 1D and 2D. In 3D keep the following overlap keep the following overlap considerations in mind:considerations in mind:

X Point (kX Point (kxx==/a, k/a, kyy=k=kzz=0)=0)ddxyxy, d, dxzxz 1/2 antibonding 1/2 antibondingddyzyz nonbonding nonbonding2 degenerate bands2 degenerate bands

M Point (kM Point (kxx=k=kyy==/a, k/a, kzz=0)=0)ddxyxy, , antibonding antibondingddyzyz, d, dxzxz 1/2 antibonding 1/2 antibonding2 degenerate bands2 degenerate bands

R Point (kR Point (kxx=k=kyy=k=kzz= = /a)/a)ddxyxy, d, dyzyz, d, dxzxz antibonding antibonding3 degenerate bands3 degenerate bands

x

y

X point


Band Structure ReOBand Structure ReO33 and and MnOMnO33

2-2-

*(e*(egg) ) W~7 eVW~7 eV

*(t*(t2g2g) ) W~5 eVW~5 eV

*(t*(t2g2g) ) W~2 eVW~2 eV


ReOReO33 MnO MnO332-2-


Structural Distortions: Structural Distortions: CaMnOCaMnO33

MnMn OO MnMn MnMnOO

MnMn

Cubic (Pm3m)Cubic (Pm3m)Linear Mn-O-Linear Mn-O-

MnMn

Orthorhombic Orthorhombic (Pnma)(Pnma)

Bent Mn-O-MnBent Mn-O-Mn


Octahedral Tilting & Band Octahedral Tilting & Band StructureStructureCubic (Pm3m)Cubic (Pm3m)

Linear Mn-O-MnLinear Mn-O-MnOrthorhombic Orthorhombic

(Pnma)(Pnma)Bent Mn-O-MnBent Mn-O-Mn

*(t*(t2g2g) ) W~2 eVW~2 eV


*(t*(t2g2g) ) W~1.5 W~1.5

eVeV

*(e*(egg) ) W~2.5 eVW~2.5 eV


eg(*)

EF

DOS

t2g(*)

eg(*)

t2g(*)

Spin Polarized Band Spin Polarized Band StructureStructure

CaMnO3 is a Mott-Hubbard Insulator, rather than a metal!


3d TM Oxide Perovskites3d TM Oxide Perovskites

Compound ElectronConfig.

ElectricalProperties

MagneticProperties

SrTiO3 (d0) *0*0 Semiconductor Diamagnetic

SrVO3 (d1) *1*0 Metallic Pauli Paramagnetic

SrCrO3 (d2) *2*0 Metallic Pauli Paramagnetic

CaMnO3 (d3) t2g

3*0 Semiconductor AntiferromagneticTN = 110 K

SrFeO3 (d4) t2g

3*1 Metallic Spiral AFMTN ~ 130 K

*, * implies delocalized electronst2g, eg implies localized electrons


SrFeOSrFeO33-The Edge of -The Edge of InstabilityInstability

eg

t2g

eg

t2g

Fe4

+

Fe4

+

Cubic StructureCubic StructureNo Jahn-Teller DistortionNo Jahn-Teller DistortionAll Fe atoms equivalentAll Fe atoms equivalentLocalized tLocalized t2g2g electrons electrons

Delocalized eDelocalized egg electrons electronsMetallic to at least 4 KMetallic to at least 4 K

t2g(*)

eg(*)

t2g(*)

eg(*)

EF

DOS


Cubic Band Structure Cubic Band Structure CalculationsCalculations


LaMnOLaMnO33-Cooperative Jahn Teller -Cooperative Jahn Teller Dist.Dist.

Fe(Mn)-O DistancesFe(Mn)-O Distances

LaMnOLaMnO33

2 1.907(1) Å

2 2.178(1) Å

2 1.968(1) Å

SrFeO3 6 1.92 Å

Fe(Mn)-O-Fe(Mn) Fe(Mn)-O-Fe(Mn) AnglesAngles

CaFeOCaFeO33

155.48(5)

155.11(5)

SrFeO3 180

Octahedral tilting and decreased Octahedral tilting and decreased covalency both narrow the covalency both narrow the * (e* (egg) )

band. band. This leads to electron This leads to electron localization and a cooperative Jahn-localization and a cooperative Jahn-

Teller DistortionTeller Distortion


Orthorhombic StructureOrthorhombic StructurePronounced Jahn-Teller Pronounced Jahn-Teller

DistortionDistortionAll Mn atoms equivalentAll Mn atoms equivalent

Localized tLocalized t2g2g & e & egg electronselectrons

SemiconductorSemiconductor

LaMnOLaMnO33-Cooperative Jahn Teller -Cooperative Jahn Teller Dist.Dist.

eg

t2g

dz2

t2g

Mn3

+

Mn3

+

dx2-y2

Symmetric Symmetric MnOMnO66

Jahn-Teller Jahn-Teller DistortionDistortion

t2g(*) dz2(*)

t2g(*)

EF

DOS

dx2-y2 (*)

dz2(*)

dx2-y2 (*)


CaFeOCaFeO33-Charge -Charge DisproportionationDisproportionation

Ca

Fe-O DistancesFe-O Distances

CaFeOCaFeO33

2 1.919(2) Å

2 1.927(2) Å

2 1.919(1) Å

SrFeO3 6 1.92 Å

Fe-O-Fe AnglesFe-O-Fe Angles

CaFeOCaFeO33

158.1(1)

158.4(2)

SrFeO3 180Octahedral tilting narrows Octahedral tilting narrows * * (e(egg) band, leads to electron ) band, leads to electron

localization!localization!


Soft Mode Condensation Soft Mode Condensation (290 K)(290 K)

eg

t2g

eg

t2g

eg

t2g

eg

t2g

Fe3

+

Fe5

+Oxygen shift alters crystal field Oxygen shift alters crystal field

splittingsplittingLocalizes the eLocalizes the egg electrons electrons

Drives Metal to Semiconductor Drives Metal to Semiconductor TransitionTransition

transition metal oxide perovskites: band structure, electrical and magnetic properties

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