1. Transition Metal Oxide Perovskites: Band Structure, Electrical and Magnetic Properties
Chemistry 754
Solid State Chemistry
Lecture 22
May 20, 2002

2. Transition Metal Oxides
To illustrate the relationship between crystal structure, bonding, band structure, electrical and magnetic 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.

3. 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

4. Perovskite Crystal StructureM O A

5. 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)

6. 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
Transition Metal
M-O p
M-O s

7. Orbital Overlap s* and p* Bands
p* Overlap (M d t2g – O 2p p)
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 2p s)
G  M Band Runs Uphill

8. 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
R Point (kx=ky=kz= p/a)
dxy, dyz, dxz  antibonding
3 degenerate bands x y
X point

9. Band Structure ReO3 and MnO32-
s*(eg)
W~7 eV
p*(t2g)
W~5 eV
W~2 eV
W~4 eV
ReO MnO32-

10. Structural Distortions: CaMnO3
Cubic (Pm3m)
Linear Mn-O-Mn
Orthorhombic (Pnma)
Bent Mn-O-Mn Mn O Mn O

11. 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

12. Spin Polarized Band Structure
eg(s*)  EF
DOS
t2g(p*) 
eg(s*) 
t2g(p*) 
CaMnO3 is a Mott-Hubbard Insulator, rather than a metal!

13. 3d TM Oxide Perovskites p*, s* implies delocalized electrons
t2g, eg implies localized electrons

14. SrFeO3-The Edge of Instability
t2g(p*) 
eg(s*) 
t2g(p*) 
eg(s*)  EF
DOS eg
t2g
Fe4+
Cubic Structure
No Jahn-Teller Distortion
All Fe atoms equivalent
Localized t2g electrons
Delocalized eg electrons
Metallic to at least 4 K

15. Cubic Band Structure Calculations

16. 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

17. LaMnO3-Cooperative Jahn Teller Dist.
t2g(p*) 
dz2(s*) 
t2g(p*)  EF
DOS
dx2-y2 (s*) 
dz2(s*) 
dx2-y2 (s*)  eg
t2g
dz2
Mn3+
dx2-y2
Symmetric MnO6
Jahn-Teller Distortion
Orthorhombic Structure
Pronounced Jahn-Teller Distortion
All Mn atoms equivalent
Localized t2g & eg electrons
Semiconductor

18. 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
158.1(1)
158.4(2)
SrFeO3  180 Ca
Octahedral tilting narrows s* (eg) band, leads to electron localization!

19. Soft Mode Condensation (290 K)eg
t2g
Fe3+
Fe5+
Oxygen shift alters crystal field splitting
Localizes the eg electrons
Drives Metal to Semiconductor Transition