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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.

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

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  1. Transition Metal Oxide Perovskites:Band Structure, Electrical and Magnetic Properties Chemistry 754 Solid State Chemistry Lecture #24 May 27, 2003

  2. 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.

  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 Structure M 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 M-O p Transition Metal M-O s

  7. 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

  8. 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

  9. 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-

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

  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. eg(s*)  EF DOS Spin Polarized Band Structure 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. 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

  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. 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

  18. 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!

  19. 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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