Transition Metal Oxides Rock Salt and Rutile: Metal-Metal Bonding Chemistry 754 Solid State Chemistry Lecture #25 May 27, 2003

Rock Salt and Rutile: Structure & Properties Octahedral Molecular Orbital Diagram Rock Salt p*(t2g) and s*(eg) Bands M-M Interactions Properties 3d Transition Metal Monoxides Magnetic Superexchange Rutile p*(t2g) Bands, t and t Properties MO2 (M=Ti, V, Cr, Mo, W, Ru) Double Exchange in CrO2

Rock Salt Crystal Structure M y x

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

3d Transition Metal Monoxides AFM = Antiferromagnetic How can we understand this behavior? Metallic conductivity for a fairly ionic Ti2+-O2- bond? Semiconducting behavior for partially filled bands?

Orbital Overlap in the t2g Band G point (kx=ky=kz=0) M M M-O p nonbonding M-M bonding Band Runs Uphill from G  M M point (kx=ky=p/a, kz=0) M M M-O p antibonding M-M nonbonding

Orbital Overlap in the eg Band G point (kx=ky=kz=0) M M Band Runs Uphill from G  M M-O s nonbonding M point (kx=ky=p/a, kz=0) M M M-O s antibonding

Band Structure Calculations SrTiO3 TiO The eg s* band is more narrow in TiO because the Ti-O distance is considerably longer and the overlap is smaller. The t2g p* band is also slightly more narrow in TiO, except for near the G-point, where Ti-Ti bonding lowers the energy and widens the band.

Magnetic Structure MnO, FeO, CoO and NiO are all antiferromagnets with the structure shown below (for MnO). eg t2g = A F M eg t2g = O Mn The electrons align themselves in an antiparallel fashion due to AFM superexchange interactions arising primarily from the ½ filled eg orbitals. The magnetic ordering temperature increases from Mn  Fe  Co  Ni due to increasing covalency (see Magnetism lecture). The magnetic ordering has implications for the electronic transport properties.

Mott-Hubbard Insulators Fe O The AFM coupling of ions is shown for FeO. The ½ filled eg orbitals stabilize AFM coupling. Notice that there is no mechanism for the minority spin electrons (shown in red) to move from one Fe ion to the next without undergoing a spin flip (the t2g orbitals of the same spin are occupied). Consequently the AFM coupling of ions forces a localization of the t2g electrons, even in the absence of a ½ filled or completely filled band. This is essentially the opposite of double-exchange. Such compounds are called Mott-Hubbard insulators. eg  t2g  eg  t2g  M-O-M Interaction is AFM () when both TM have 1/2 filled configurations (d5-d5 or d3-d3)

Rutile Crystal Structure z x y

MO2 with the Rutile Structure

c/a Ratio in Rutile-Type Oxides VO2 (T > 340K) Metallic V-V Even Spacing VO2 (T < 340K) V-V Alternating CrO2 Metallic Cr-Cr Even Spacing RuO2 Metallic Ru-Ru Even Spacing MoO2 Metallic Mo-Mo Alternating

M-M Overlap in the t2g Band M-M s bonding M M-M p antibonding M-M d bonding G point kx=0 ky=0 kz=0 M-M s antibonding M M-M p bonding M-M d antibonding Z point kx=0 ky=0 kz=p/a

Combined M-O & M-M Effects The M-O p* and M-M bonding interactions both make a contribution to the t2g band. The M-O p* interactions are dominant, but the M-M s interactions preturb the picture. The M-M p & d interactions are of minimal importance. As we fill up the t2g band we can roughly think of the following picture in terms of M-M bonding strength. M-M s  d1 TM Ion EF DOS M-M p  d2 TM Ion M-M d/d* M-M p*  d5 TM Ion M-M s*  d6 TM Ion M-O p* M-O p* ~ M-M s > M-M p > M-M d

Tetragonal Structure (TiO2,CrO2,RuO2) M-O s* [4] Delocalized Electrons + M-M s* EF RuO2 M-O p* [2] d eg EF CrO2 + M-M s EF VO2 d t2g EF TiO2 Transition Metal O 2p NB Oxygen 2p M-O p M-O s Z = 2 (M2O4)

Band Structure Calculations SrTiO3 TiO2

Calculated Band Structure (Tetragonal, Z=2) TiO2 VO2 CrO2

Density of States (Tetragonal Structure) TiO2 VO2 CrO2

G point Z point MoO2 Monoclinic Z=4 TiO2 Tetragonal Z=2 a a a a a a M-M Short=Bonding M-M Long=Bonding M-M Short=AB M-M Long=AB Bonding Z point M a M a M a Antibonding M-M Short=Bonding M-M Long=AB M-M Short=AB M-M Long=Bonding

Pierls Distortion a E k E k a a a a a 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 p* interactions. a E k p/a EF E k p/a EF a a a a a

Monoclinic Structure (VO2,MoO2) M-O s* [8] Delocalized Electrons M-O Antibonding M-M s* [2] EF MoO2 d eg M-O p* [8] EF VO2 M-M s [2] d t2g Localized Electrons M-M Bonding O 2p NB Oxygen 2p M-O p M-O s Z = 4 (M4O8)

CrO2 Tetragonal (Z=2) MoO2 Monoclinic (Z=4) Mo-O p* Mo-Mo s

CrO2 and RuO2 Why are alternating long-short M-M contacts, indicative of Metal-Metal bonding not observed in CrO2 and RuO2. The electron count suggests that the M-M s levels should be full and the M-M s* levels empty? There is a competition between localized M-M bonding (prefers dimers) and delocalized electronic transport in the M-O p* band (prefers equal spacing). Favors delocalized transport in the M-O p* band Dominant in CrO2 (poor overlap) RuO2 (electron count) Favors M-M bonding and localized e- Dominant in MoO2 VO2 Intermediate

Double Exchange CrO2 is ferromagnetic. A property which leads to it’s use in magnetic cassette tapes. What stabilizes the ferromagnetic state? t|| tp* Antiferromagnetic: Delocalized transport violates Hund’s Rule. Localized t|| electrons No M-M Bonding M Delocalized t2g p* electrons Ferromagnetic: Delocalized transport of tp* electrons allowed. Localized t|| electrons polarize itinerant (delocalized) t2g p* electrons. Magnetism and conductivity are correlated.