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Transition Metal Oxide
Perovskites:
Band Structure, Electrical
and Magnetic Properties
Chemistry 754
Solid State Chemistry
Lecture 22
May 20, 2002
Chemistry 754 - Solid State Chemistry
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.
Chemistry 754 - Solid State Chemistry
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
Chemistry 754 - Solid State Chemistry
Perovskite Crystal Structure
M
O
A
Chemistry 754 - Solid State Chemistry
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
Transition
Metal
t2g (p)
eg (s)
O 2p s (6)
a1g, t1u, eg
t1u (s + p)
a1g (s)
Chemistry 754 - Solid State Chemistry
Simplified Band Structure
(n+1)p
(n+1)s
nd eg (dx2-y2, dz2)
s* [4]
M-O s* [2]
Bands of interest
Oxygen
M-O p* [3]
(n+1)d t2g (dxy, dxz, dyz)
O 2p p (12)
O 2p NB
Transition
Metal
M-O p
O 2p s (6)
a1g, t1u, eg
M-O s
Chemistry 754 - Solid State Chemistry
Orbital Overlap s* and p* Bands
p* Overlap (M d t2g – O 2p p)
G  M Band Runs Uphill
G point
(kx=ky=0)
non-bonding
M point
(kx=ky=p/a)
antibonding
Greater Spatial Overlap
W(s*) > W(p*)
s* Overlap (M d eg – O 2p s)
G  M Band Runs Uphill
Chemistry 754 - Solid State Chemistry
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
y
x
X point
Chemistry 754 - Solid State Chemistry
Band Structure ReO3 and MnO3230
30
s*(eg)
W~7 eV
Energy (vs. O 2s)
25
20
M eg
p*(t2g)
W~5 eV
25
EF
20
s*(eg)
W~4 eV
15
15
10
10
X
R
G
M
k
ReO3
R0
3
DOS
O 2p
M t2g
p*(t2g)
W~2 eV
X
R
G
M
k
MnO
R0
6
DOS
2-
Chemistry 754 - Solid State
3 Chemistry
Structural Distortions: CaMnO3
Cubic (Pm3m)
Linear Mn-O-Mn
Mn
O
Mn
Orthorhombic (Pnma)
Bent Mn-O-Mn
Mn
O
Mn
Chemistry 754 - Solid State Chemistry
Octahedral Tilting & Band Structure
Cubic (Pm3m)
Linear Mn-O-Mn
s*(eg)
W~4 eV
Energy (vs. O 2s)
20
p*(t2g)
W~2 eV
Orthorhombic (Pnma)
Bent Mn-O-Mn
s*(eg)
W~2.5 eV
20
p*(t2g)
W~1.5 eV
15
15
10
10
X
R
G
M
k
G
T
Y

X
U
R
Chemistry
754Z - Solid
State
Chemistry
k
R
Spin Polarized Band Structure
spin polarized
low spin
Energy (vs. O 2s)
eg(s*) 
20
20
t2g(p*) 
EF
eg(s*) 
t2g(p*) 
15
15
DOS
10
10
X
R
G
M
k
R
O 2p
Mn 3d t2g
Mn 3d eg
X
R
G
M
R
k
s = +1/2
s = 1/2
CaMnO3 is a Mott-Hubbard Insulator, rather than a metal!
Chemistry 754 - Solid State Chemistry
3d TM Oxide Perovskites
Compound
Electron
Config.
Electrical
Properties
SrTiO3 (d0)
p*0s*0
SrVO3 (d1)
Semiconductor
Magnetic
Properties
Diamagnetic
p*1s*0
Pauli Paramagnetic
SrCrO3 (d2)
Metallic
p*2s*0
Pauli Paramagnetic
CaMnO3 (d3)
Metallic
t2g3s*0
SrFeO3 (d4)
t2g3s*1
Semiconductor Antiferromagnetic
TN = 110 K
Spiral AFM
Metallic
TN ~ 130 K
p*, s* implies delocalized electrons
t2g, eg implies localized electrons
Chemistry 754 - Solid State Chemistry
SrFeO3-The Edge of Instability
Fe4+
eg
eg
t2g
t2g
Fe4+
eg(s*) 
t2g(p*) 
EF
eg(s*) 
t2g(p*) 
DOS
Cubic Structure
No Jahn-Teller Distortion
All Fe atoms equivalent
Localized t2g electrons
Delocalized eg electrons
Metallic to at least 4 K
Chemistry 754 - Solid State Chemistry
Cubic Band Structure Calculations
Energy (vs. O 2s)
CaMnO3 (a = 3.81 A)
SrFeO3 (a = 3.86 A)
LaMnO3 (a = 4.03 A)
20
20
20
15
15
15
10
10
10
X
R
G
M
k
R
X
R
M
G
R
X
R
M
Chemistry 754 - Solid State Chemistry
k
k
G
R
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)
Octahedral tilting and decreased
covalency both narrow the s* (eg) band.
This leads to electron localization and a
cooperative Jahn-Teller Distortion
155.11(5)
SrFeO3  180
Chemistry 754 - Solid State Chemistry
LaMnO3-Cooperative Jahn Teller Dist.
dx2-y2
eg
dx2-y2 (s*) 
dz2(s*) 
t2g(p*) 
dz2
t2g
Mn3+
Symmetric
MnO6
Mn3+
t2g
EF
dx2-y2 (s*) 
dz2(s*) 
t2g(p*) 
Jahn-Teller
Distortion
DOS
Orthorhombic Structure
Pronounced Jahn-Teller
Distortion
All Mn atoms equivalent
Localized t2g & eg electrons
Semiconductor
Chemistry 754 - Solid State Chemistry
CaFeO3-Charge Disproportionation
Fe-O Distances
CaFeO3
2  1.919(2) Å
2  1.927(2) Å
2  1.919(1) Å
Ca
SrFeO3  6  1.92 Å
Fe-O-Fe Angles
CaFeO3
158.1(1)
158.4(2)
Octahedral tilting narrows s* (eg)
band, leads to electron localization!
SrFeO3  180
Chemistry 754 - Solid State Chemistry
Soft Mode Condensation (290 K)
eg
eg
t2g
t2g
eg
eg
Fe3+
t2g
Fe5+
Oxygen shift alters crystal field splitting
Localizes the eg electrons
Drives Metal to Semiconductor Chemistry
Transition
754 - Solid State Chemistry
t2g