Low-temperature properties of the t 2g 1 Mott insulators of the t 2g 1 Mott insulators Interatomic exchange-coupling constants by 2nd-order perturbation theory in t t 2g 1 + t 2g 1 = t 2g 0 + t 2g 2 Orbital and Magnetic Orders Superexchange: J AF ~ 4t 2 /U t x =t y =99 meV t z =105 meV t x =t y =48 meV t z =38 meV 3D AF F J se 0 meV 53 meV 80 meV 92 meV 207 meV High-temperature orthorhombic phase LaVO 3 YVO3YVO3YVO3YVO3 Mott transition and suppression of orbital fluctuations in t 2g 2 perovskites LaVO 3 YVO 3 t 2g K (orthorhombic PI phase) Much stronger orbital fluctuations for the t 2g 2 La and Y vanadates than for the t 2g 1 titanates because of 1) Hunds rule and 2) less AB(O) covalency 1 2 3 Empty crystal-field orbital, |3), in the monoclinic phase Vanadate t 2g 2 conclusions The missing piece in the Sr 2 RhO 4 puzzle Sr 2 RhO 4 Sr 2 RhO 4 is a K 2 NiF 4 -structured 4d (t 2g ) 5 paramagnetic metal Transition-metal oxides have interesting properties because they have many lattice and electronic (orbital, charge, and spin) degrees of freedom, coupled by effective interactions (electron-phonon, hopping t, Coulomb repulsion U, and Hunds-rule coupling J). When some of the interactions are of similar magnitude, competing phases may exist in the region of controllable compositions, fields, and temperatures. The interactions tend to remove low-energy degrees of freedom, e.g. to reduce the metallicity Guo-Qiang Liu, V.N. Antonov, O. Jepsen, and OKA, PRL 101, (2008) Ca or Sr o Ru Ru 4d (t 2g ) 4 (Ca 1-x Sr x )RuO 4 : The relatively small size and strong covalency of Ca cause the RuO 6 to rotate and tilt. For x increasing from 0 to 1 these distortions go away and the properties go from insulating to metallic and from magnetic (AF/F metamagn) to paramagnetic at low T. Sr 2 RuO 4 is a 2D Fermi liquid whose Fermi surface agrees well with LDA and has a mass enhancement of 3. It becomes superconducting below 1K. K 2 NiF 4 From Haverkort et al. PRL (2008) Ruddlesden-Popper (Ca,Sr) n+1 Ru n O 3n+1 where n=1, 2, 3, xyx 2 -y 2 Alternating rotation of octahedra and cell doubling in xy-plane gaps the broad, overlapping xy and x 2 -y 2 bands for a filling of 5 t 2g electrons. From Haverkort et al. PRL (08) (t 2g ) 4 (t 2g ) 5 ARPES LDA But still unusually bad agreement between and 2-parameter fit + eff / F + F eff eff = 2.15 eff = 2.15 why? Since Sr 2 RhO 4 is paramagnetic at low temperature, HF mean field approximation We had: where the polarization, p, should be determined selfconsistently., leading to: For each Bloch state, so the polarization function is: 2-parameter fit + eff / F eff = 2.2 , why? + F eff The missing piece: