Transcript Slide 1
Low-temperature properties 1 of the t2g Mott insulators Interatomic exchange-coupling constants by 2nd-order perturbation theory in t t2g1 + t2g1 = t2g0 + t2g2 Orbital and Magnetic Orders Superexchange: JAF ~ 4t2/U tx=ty=48 meV tz=105 meV tz=38 meV tx=ty=99 meV 3D AF F Jse 5.0 3.0 -0.7 -4.7 High-temperature orthorhombic phase 0 meV 53 meV 92 meV 0 meV 80 meV 207 meV Mott transition and suppression of orbital fluctuations in t2g2 perovskites LaVO3 YVO3 t2g2 LaVO3 770 K (orthorhombic PI phase) YVO3 1 2 3 Much stronger orbital fluctuations for the t2g2 La and Y vanadates than for the t2g1 titanates because of 1) Hunds rule and 2) less AB(O) covalency Empty crystal-field orbital, |3), in the monoclinic phase Vanadate t2g2 conclusions The missing piece in the Sr2RhO4 puzzle Sr2RhO4 is a K2NiF4-structured 4d (t2g)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, 026408 (2008) Ru 4d (t2g)4 (Ca1-xSrx)RuO4: The relatively small size and strong covalency of Ca cause the RuO6 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. Sr2RuO4 is a 2D Fermi liquid whose Fermi surface agrees well with LDA and has a mass enhancement of 3. It becomes superconducting below 1K. From Haverkort et al. PRL 026406 (2008) K2NiF4 Ru o Ca or Sr Ruddlesden-Popper (Ca,Sr)n+1RunO3n+1 where n=1, 2, 3, (t2g)5 (t2g)4 From Haverkort et al. PRL 026406 (08) Alternating rotation of octahedra and cell doubling in xy-plane gaps the broad, overlapping xy and x2-y2 bands for a filling of 5 t2g electrons. But still unusually bad agreement between ARPES and LDA ζeff 2-parameter fit + ζeff / εF + εF ζeff = 2.15 ζ why? Since Sr2RhO4 is paramagnetic at low temperature, HF mean field approximation We had: , leading to: where the polarization, p, should be determined selfconsistently. For each Bloch state, so the polarization function is: 2-parameter fit ζeff + ζeff / εF + εF ζeff = 2.2 ζ, why? The missing piece: