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

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.

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 M O A

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 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

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

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

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

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

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 t2g(p*)  eg(s*)  t2g(p*)  CaMnO3 is a Mott-Hubbard Insulator, rather than a metal!

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

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

Cubic Band Structure Calculations

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

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

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!

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