Related papers: Spin--orbital interaction for face-sharing octahed…
We analyze the role of local geometry in the spin and orbital interaction in transition metal compounds with orbital degeneracy. We stress that the tendency observed for the most studied case (transition metals in O$_6$ octahedra with one…
The Kugel-Khomskii Hamiltonian for cubic titanates describes spin and orbital superexchange interactions between $d^1$ ions having three-fold degenerate $t_{2g}$ orbitals. Since orbitals do not couple along "inactive" axes, perpendicular to…
Orbitally degenerate systems provide a promising platform for realizing novel quantum phases driven by spin-orbital exchange interactions, as described by the Kugel-Khomskii model. Spinel vanadates, in which orbital degrees of freedom…
We derive a spin-orbital Hamiltonian for a triangular lattice of e_g orbital degenerate (Ni^{3+}) transition metal ions interacting via 90 degree superexchange involving (O^{2-}) anions, taking into account the on-site Coulomb interactions…
This paper contains the details of Phys. Rev. Lett. 73, 2919 (1994) and, to a lesser extent, Phys. Rev. Lett. 72, 3710 (1994). We treat a Hubbard model which includes all the 3d states of the Cu ions and the 2p states of the O ions. We also…
A one-dimensional model of coupled spin-1/2 spins and pseudospin-1/2 orbitals with nearest-neighbor interaction is rigorously shown to exhibit spin-orbital separation by means of a non-local unitary transformation. On an open chain, this…
Transition metal compounds with the $(t_{2g})^4$ electronic configuration are expected to be nonmagnetic atomic singlets both in the weakly interacting regime due to spin-orbit coupling, as well as in the Coulomb dominated regime with…
In the quest for materials hosting Kitaev spin liquids, much of the efforts have been focused on the fourth- and fifth-row transition metal compounds, which are spin-orbit coupling assisted Mott insulators. Here, we study the structural and…
The alloy Ca$_{2-x}$Sr$_x$RuO$_4$ exhibits a complex phase diagram with peculiar magnetic metallic phases. In this paper some aspects of this alloy are discussed based on a mean field theory for an effective Kugel-Khomskii model of…
Mott insulators with both spin and orbital degeneracy are pertinent to a large number of transition metal oxides. The intertwined spin and orbital fluctuations can lead to rather exotic phases such as quantum spin-orbital liquids. Here we…
We report $\textit{ab-initio}$ density functional theory calculation and Raman scattering results to explore the electronic structure of Ba$_5$CuIr$_3$O$_{12}$ single crystals. This insulating iridate, consisting of face-sharing IrO$_6$…
Interesting magnetic properties and spin-exchange interactions along various possible pathways in half-integral spin quantum magnetic tetramer system: A$_{2}$PO$_{4}$OH (A = Co, Cu) are investigated. Interplay of structural distortion and…
Using ab initio wave-function-based calculations, we provide valuable insights with regard to the magnetic exchange in 5$d$ and 4$d$ oxides with face-sharing ligand octahedra, BaIrO$_3$ and BaRhO$_3$. Surprisingly strong antiferromagnetic…
Superexchange calculation is performed for multi-orbital band models with broken inversion symmetry. Orbital-changing hopping terms allowed by the symmetry breaking electric field lead to a new kind of orbital exchange term closely…
We develop a microscopic theory of multipole interactions and orderings in 5$d^2$ transition metal ion compounds. In a cubic environment, the ground state of 5$d^2$ ions is a non-Kramers $E_g$ doublet, which is nonmagnetic but hosts…
Spin-orbital entanglement in the ground state of a one-dimensional SU(2)$\otimes$SU(2) spin-orbital model is analyzed using exact diagonalization of finite chains. For $S=1/2$ spins and $T=1/2$ pseudospins one finds that the quantum…
We theoretically investigate magnetic properties in the low-temperature phase with the formation of eight-site clusters, octamers, in the spinel compound CuIr$_2$S$_4$. The octamer state was considered to be a spin-singlet state induced by…
The magnetic anisotropy af a rectangular Cu-O-Cu bond is investigated in second order of the spin-orbit interaction. Such a bond is characteristic for cuprates having edge sharing CuO_2 chains, and exists also in the Cu_3O_4 plane or in…
Several realistic spin-orbital models for transition metal oxides go beyond the classical expectations and could be understood only by employing the quantum entanglement. Experiments on these materials confirm that spin-orbital entanglement…
While the enhancement of the spin-space symmetry from the usual $\mathrm{SU}(2)$ to $\mathrm{SU}(N)$ is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here we propose a new…