Chemistry Solid State Chemistry Transition Metal Oxide Rock Salt and Rutile: Metal-Metal Bonding Chemistry 754 Solid State Chemistry Lecture 23 May 22, 2002

Chemistry Solid State Chemistry Rock Salt and Rutile: Structure & Properties Octahedral Molecular Orbital DiagramOctahedral Molecular Orbital Diagram Rock Salt  *(t 2g ) and  *(e g ) BandsRock Salt  *(t 2g ) and  *(e g ) Bands M-M InteractionsM-M Interactions Properties 3d Transition Metal MonoxidesProperties 3d Transition Metal Monoxides Magnetic SuperexchangeMagnetic Superexchange Rutile  *(t 2g ) Bands, t  and t Rutile  *(t 2g ) Bands, t  and t  Properties MO 2 (M=Ti, V, Cr, Mo, W, Ru)Properties MO 2 (M=Ti, V, Cr, Mo, W, Ru) Double Exchange in CrO 2Double Exchange in CrO 2

Chemistry Solid State Chemistry Rock Salt Crystal Structure OM x y

Chemistry Solid State Chemistry Generic Octahedral MO Diagram a 1g (  ) t 1u (  ) e g (  ) t 2g (  ) t 1g & t 2u a 1g (  ) t 1u (  ) t 2g (  ) e g (  ) nd e g (d x2-y2, d z2 ) (n+1)d t 2g (d xy, d xz, d yz ) (n+1)s (n+1)p O 2p  (6) - t 2g, t 1u O 2p NB  (6)-t 1g, t 2u O 2p  (6) a 1g, t 1u, e g Transition Metal Oxygen

Chemistry Solid State Chemistry Simplified Band Structure nd e g (d x2-y2, d z2 ) (n+1)d t 2g (d xy, d xz, d yz ) (n+1)s (n+1)p O 2p  O 2p  (6) a 1g, t 1u, e g Transition Metal Oxygen M-O  M-O  O 2p NB M-O  [3] M-O  [2]  [4] Bands of interest

Chemistry Solid State Chemistry 3d Transition Metal Monoxides AFM = Antiferromagnetic

Chemistry Solid State Chemistry Orbital Overlap in the t 2g Band  point (k x =k y =k z =0) M M MM M M M MM M  point (k x =k y =  /a, k z =0) M-O  nonbonding M-M bonding M-O  antibonding M-M nonbonding Band Runs Uphill from  

Chemistry Solid State Chemistry Orbital Overlap in the e g Band  point (k x =k y =k z =0)  point (k x =k y =  /a, k z =0) M-O  nonbonding Band Runs Uphill from   M M M M M M M M M M M-O  antibonding

Chemistry Solid State Chemistry Band Structure Calculations SrTiO 3 TiO

Chemistry Solid State Chemistry Magnetic Structure What is the magnetic structure of MnO, FeO, CoO and NiO? Why do the electrons align themselves in an antiparallel fashion? Why does the Neel temperature (magnetic ordering temperature) increase from Mn  Fe  Co  Ni? AFMAFM egeg t 2g = egeg = Mn O

Chemistry Solid State Chemistry Magnetic Superexchange M-O-M Interaction is AFM (  ) when both TM have 1/2 filled configurations (d 5 -d 5 or d 3 -d 3 ) Mn O Mn Mn O V e g  t 2g  e g  t 2g  e g  t 2g  e g  t 2g  e g  t 2g  e g  t 2g  e g  t 2g  e g  t 2g  M-O-M Interaction is FM (  ) when 1/2 filled configuration overlaps with empty configuration (d 5 -d 3 ) e g superexchange is stronger than t 2g SE because of greater overlap.

Chemistry Solid State Chemistry Rutile Crystal Structure z x y

Chemistry Solid State Chemistry MO 2 with the Rutile Structure

Chemistry Solid State Chemistry c/a Ratio in Rutile-Type Oxides VO 2 (T > 340K) Metallic V-V Even Spacing VO 2 (T < 340K) Metallic V-V Alternating MoO 2 Metallic Mo-Mo Alternating RuO 2 Metallic Ru-Ru Even Spacing CrO 2 Metallic Cr-Cr Even Spacing

Chemistry Solid State Chemistry M-M Overlap in the t 2g Band M-M  bonding M M M M M M M M M M-M  antibonding M-M  bonding  point k x =0 k y =0 k z =  /a M-M  antibonding M M M M M M M M M M-M  bonding M-M  antibonding  point k x =0 k y =0 k z = 

Chemistry Solid State Chemistry Combined M-O & M-M Effects The M-O  * and M-M bonding interactions both make a contribution to the t 2g band.The M-O  * and M-M bonding interactions both make a contribution to the t 2g band. The M-O  * interactions are dominant, but the M-M  interactions preturb the picture.The M-O  * interactions are dominant, but the M-M  interactions preturb the picture. As we fill up the t 2g band we can roughly think of the following picture in terms of M-M bonding strength.As we fill up the t 2g band we can roughly think of the following picture in terms of M-M bonding strength. M-M  d 1 TM Ion EFEF DOS M-M  d 2 TM Ion M-M   M-M  d 5 TM Ion M-M  d 6 TM Ion M-O   M-O  * ~ M-M  > M-M  > M-M 

Chemistry Solid State Chemistry + M-M  Tetragonal Structure (TiO 2,CrO 2, RuO 2 ) d e g d t 2g Oxygen 2p Transition Metal M-O  M-O  O 2p NB M-O  [2] M-O  [4] + M-M  Z = 2 (M 2 O 4 ) E F TiO 2 E F VO 2 E F CrO 2 E F RuO 2 Delocalized Electrons

Chemistry Solid State Chemistry Band Structure Calculations SrTiO 3 TiO 2

Chemistry Solid State Chemistry TiO 2 VO 2 CrO 2 Calculated Band Structure (Tetragonal, Z=2)

Chemistry Solid State Chemistry TiO 2 VO 2 CrO 2 Density of States (Tetragonal Structure)

Chemistry Solid State Chemistry M M M M a M M M M a M M M M a M M M M a M M M M a M M M M a TiO 2 Tetragonal Z=2 MoO 2 Monoclinic Z=4  point  point Bonding Antibonding M-M Short=Bonding M-M Long=Bonding M-M Short=AB M-M Long=AB M-M Short=Bonding M-M Long=AB M-M Short=AB M-M Long=Bonding

Chemistry Solid State Chemistry Pierls Distortion The dimerization which occurs in the rutile structure and it’s effects on the band structure are similar to the Pierls distortion we discussed for a 1D chain of Hydrogen atoms, except that it occurs on top of the M-O  * interactions. a a a a a a E k 0  /a EFEF E k 0 EFEF

Chemistry Solid State Chemistry M-O  M-O  O 2p NB M-M  [2] M-O  [8] M-O  [8] M-M  [2] d e g d t 2g Z = 4 (M 4 O 8 ) E F VO 2 E F MoO 2 Oxygen 2p Monoclinic Structure (VO 2,MoO 2 ) Delocalized Electrons M-O Antibonding Localized Electrons M-M Bonding

Chemistry Solid State Chemistry MoO 2 Monoclinic (Z=4) CrO 2 Tetragonal (Z=2) Mo-Mo  Mo-O  

Chemistry Solid State Chemistry CrO 2 and RuO 2 Why are alternating long-short M-M contacts, indicative of Metal-Metal bonding not observed in CrO 2 and RuO 2. The electron count suggests that the M-M  levels should be full and the M-M  * levels empty? There is a competition between localized M-M bonding and delocalized electronic transport in the M-O  * band. Favors M-M bonding and localized e Favors M-M bonding and localized e - Dominant in MoO 2 Favors delocalized transport in the M-O  * band Dominant in CrO 2 (poor overlap) RuO 2 (electron count) VO 2 Intermediate

Chemistry Solid State Chemistry Double Exchange CrO 2 is ferromagnetic. A property which leads to it’s use in magnetic cassette tapes. What stabilizes the ferromagnetic state? Localized t || electrons No M-M Bonding M M M M M M Delocalized t 2g  * electrons Ferromagnetic: Delocalized transport of t  * electrons allowed. t || t*t*t*t* t*t*t*t* Antiferromagnetic: Delocalized transport violates Hund’s Rule. Localized t || electrons polarize itinerant (delocalized) t 2g  * electrons. Magnetism and conductivity are correlated.