Transition metal oxide perovskites band structure electrical and magnetic properties
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Transition Metal Oxide Perovskites: Band Structure, Electrical and Magnetic Properties. Chemistry 754 Solid State Chemistry Lecture #24 May 27, 2003. Transition Metal Oxides.

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Transition metal oxide perovskites band structure electrical and magnetic properties

Transition Metal Oxide Perovskites:Band Structure, Electrical and Magnetic Properties

Chemistry 754

Solid State Chemistry

Lecture #24

May 27, 2003


Transition metal oxides

Transition Metal Oxides

  • To illustrate the relationship between crystal structure, bonding, band structure, electricalandmagnetic properties we are going to consider transition metal oxides of three structure types.

    • Perovskite (AMO3)/ReO3

    • Rock Salt (MO)

    • Rutile (MO2)

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


Perovskites and band structure

Perovskites and Band Structure

  • Octahedral Molecular Orbital Diagram

  • p*(t2g) and s*(eg) Bands

  • Orbital Overlap and Bandwidth (ReO3 vs. MnO32-)

  • Structural Distortions (Octahedral Tilting)

  • Exchange Splitting (Spin Pairing Energy)

  • The d-electron count (SrTiO3 to SrFeO3)

  • Instabilities and the d4 electron count

    • SrFeO3

    • LaMnO3

    • CaFeO3


Perovskite crystal structure

Perovskite Crystal Structure

M

O

A


Generic octahedral mo diagram

Generic Octahedral MO Diagram

t1u (s* + p*)

(n+1)p

a1g (s*)

Oxygen

(n+1)s

eg (s*)

nd eg (dx2-y2, dz2)

t2g (p*)

O 2p p (6) - t2g, t1u

O 2p NB(6)-t1g, t2u

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

t1g & t2u

O 2p s (6)

a1g, t1u, eg

Transition Metal

t2g (p)

eg (s)

t1u (s + p)

a1g (s)


Simplified band structure

Simplified Band Structure

Bands of interest

s* [4]

(n+1)p

Oxygen

(n+1)s

M-O s* [2]

nd eg (dx2-y2, dz2)

M-O p* [3]

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

O 2p p (12)

O 2p NB

O 2p s (6)

a1g, t1u, eg

M-O p

Transition Metal

M-O s


Orbital overlap s and p bands

Orbital Overlap s* and p* Bands

p*Overlap (M d t2g – O 2pp)

G M Band Runs Uphill

Greater Spatial Overlap

W(s*) > W(p*)

M point

(kx=ky=p/a)

antibonding

G point

(kx=ky=0)

non-bonding

s*Overlap (M d eg – O 2ps)

G M Band Runs Uphill


Overlap in 3d

y

x

X point

Overlap in 3D

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

X Point (kx=p/a, ky=kz=0)

dxy, dxz 1/2 antibonding

dyz  nonbonding

2 degenerate bands

M Point (kx=ky=p/a, kz=0)

dxy,  antibonding

dyz, dxz  1/2 antibonding

2 degenerate bands

R Point (kx=ky=kz=p/a)

dxy, dyz, dxz antibonding

3 degenerate bands


Band structure reo 3 and mno 3 2

s*(eg)

W~7 eV

s*(eg)

W~4 eV

p*(t2g)

W~5 eV

p*(t2g)

W~2 eV

Band Structure ReO3 and MnO32-

ReO3 MnO32-


Structural distortions camno 3

Mn

Mn

O

Mn

Mn

O

Structural Distortions: CaMnO3

Cubic (Pm3m)

Linear Mn-O-Mn

Orthorhombic (Pnma)

Bent Mn-O-Mn


Octahedral tilting band structure

Octahedral Tilting & Band Structure

Cubic (Pm3m)

Linear Mn-O-Mn

Orthorhombic (Pnma)

Bent Mn-O-Mn

s*(eg)

W~4 eV

s*(eg)

W~2.5 eV

p*(t2g)

W~2 eV

p*(t2g)

W~1.5 eV


Spin polarized band structure

eg(s*) 

EF

DOS

Spin Polarized Band Structure

t2g(p*) 

eg(s*) 

t2g(p*) 

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


3d tm oxide perovskites

3d TM Oxide Perovskites

p*, s* implies delocalized electrons

t2g, eg implies localized electrons


Srfeo 3 the edge of instability

eg(s*) 

t2g(p*) 

eg

eg

eg(s*) 

EF

t2g(p*) 

t2g

t2g

Fe4+

Fe4+

DOS

SrFeO3-The Edge of Instability

Cubic Structure

No Jahn-Teller Distortion

All Fe atoms equivalent

Localized t2g electrons

Delocalized eg electrons

Metallic to at least 4 K


Cubic band structure calculations

Cubic Band Structure Calculations


Lamno 3 cooperative jahn teller dist

LaMnO3-Cooperative Jahn Teller Dist.

Fe(Mn)-O Distances

LaMnO3

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) Angles

CaFeO3

155.48(5)

155.11(5)

SrFeO3  180

Octahedral tilting and decreased covalency both narrow the s* (eg) band. This leads to electron localization and a cooperative Jahn-Teller Distortion


Lamno 3 cooperative jahn teller dist1

dx2-y2

dx2-y2 (s*) 

eg

dz2(s*) 

dz2

t2g(p*) 

dx2-y2 (s*) 

t2g

EF

t2g

dz2(s*) 

Mn3+

Mn3+

t2g(p*) 

DOS

LaMnO3-Cooperative Jahn Teller Dist.

Symmetric MnO6

Jahn-Teller Distortion

Orthorhombic Structure

Pronounced Jahn-Teller Distortion

All Mn atoms equivalent

Localized t2g & eg electrons

Semiconductor


Cafeo 3 charge disproportionation

Ca

CaFeO3-Charge Disproportionation

Fe-O Distances

CaFeO3

2  1.919(2) Å

2  1.927(2) Å

2  1.919(1) Å

SrFeO3  6  1.92 Å

Fe-O-Fe Angles

CaFeO3

158.1(1)

158.4(2)

SrFeO3  180

Octahedral tilting narrows s* (eg) band, leads to electron localization!


Soft mode condensation 290 k

eg

eg

eg

eg

t2g

t2g

t2g

Fe5+

Fe3+

t2g

Soft Mode Condensation (290 K)

Oxygen shift alters crystal field splitting

Localizes the eg electrons

Drives Metal to Semiconductor Transition


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