Generalized calculation of magnetic coupling constants for Mott-Hubbard insulators: Application to ferromagnetic Cr compounds

Using a Rayleigh-Schr\"odinger perturbation expansion of multi-band Hubbard models, we present analytic expressions for the super-exchange coupling constants between magnetic transition metal ions of arbitrary separation in Mott-Hubbard insulators. The only restrictions are i) all ligand ions are closed shell anions and ii) all contributing interaction paths are of equal length. For short paths, our results essentially confirm the Goodenough-Kanamori-Anderson rules, yet in general there does not exist any simple rule to predict the sign of the magnetic coupling constants. The most favorable situation for ferromagnetic coupling is found for ions with less than half filled d shells, the (relative) tendency to ferromagnetic coupling increases with increasing path length. As an application, the magnetic interactions of the Cr compounds Rb$_2$CrCl$_4$, CrCl$_3$, CrBr$_3$ and CrI$_3$ are investigated, all of which except CrCl$_3$ are ferromagnets.Comment: 13 pages, 6 eps figures, submitted to Phys Rev

Spin-orbital physics for p orbitals in alkali RO_2 hyperoxides --- generalization of the Goodenough-Kanamori rules

We derive a realistic spin-orbital model at finite Hund's exchange for alkali hyperoxides. We find that, due to the geometric frustration of the oxygen lattice, spin and orbital waves destabilize both spin and p-orbital order in almost all potential ground states. We show that the orbital order induced by the lattice overrules the one favoured by superexchange and that this, together with the large interorbital hopping, leads to generalized Goodenough-Kanamori rules. They (i) lift the geometric frustration of the lattice, and (ii) explain the observed layered C-type antiferromagnetic order in alkali hyperoxides. This is confirmed by a spin-wave dispersion with no soft-mode behavior presented here as a prediction for future experiments.Comment: 7 pages, 5 figures; accepted in EP

Magnetic Order and Dynamics in an Orbitally Degenerate Ferromagnetic Insulator

Neutron scattering was used to determine the spin structure and the magnon spectrum of the Mott--Hubbard insulator YTiO$_3$. The magnetic structure is complex, comprising substantial G-type and A-type antiferromagnetic components in addition to the predominant ferromagnetic component. The magnon spectrum, on the other hand, is gapless and nearly isotropic. We show that these findings are inconsistent with the orbitally ordered states thus far proposed for YTiO$_3$ and discuss general implications for a theoretical description of exchange interactions in orbitally degenerate systems.Comment: to appear in Phys. Rev. Let

Local Electronic and Magnetic Studies of an Artificial La2FeCrO6 Double Perovskite

Through the utilization of element-resolved polarized x-ray probes, the electronic and magnetic state of an artificial La2FeCrO6 double perovskite were explored. Applying unit-cell level control of thin film growth on SrTiO3 (111), the rock salt double perovskite structure can be created for this system, which does not have an ordered perovskite phase in the bulk. We find that the Fe and Cr are in the proper 3+ valence state, but, contrary to previous studies, the element-resolved magnetic studies find the moments in field are small and show no evidence of a sizable magnetic moment in the remanent state.Comment: 3 pages, 4 figure

Spin--orbital physics in transition metal oxides

We present the main features of the spin-orbital superexchange which describes the magnetic and optical properties of Mott insulators with orbital degrees of freedom. In contrast to the SU(2) symmetry of spin superexchange, the orbital part of the superexchange obeys the lower cubic symmetry of the lattice and is intrinsically frustrated. This intrinsic frustration and spin-orbital entanglement induce enhanced quantum fluctuations, and we point out a few situations where this leads to disordered states. Strong coupling between the spin and orbital degrees of freedom is discussed on the example of the $R$VO$_3$ perovskites, with $R$ standing for rare-earth ion, La,...,Lu. We explain the observed evolution of the orbital $T_{\rm OO}$ and N\'eel $T_{N1}$ transition temperature in the $R$VO$_3$ series with decreasing ionic radius $r_R$. A few open problems and the current directions of research in the field of spin-orbital physics are pointed out.Comment: 19 pages, 5 figure