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The mixed spin 3- spin 3/2 Ising model has been simulated using cooling algorithm on cellular automaton (CA). The simulations have been made in the interval -6<=D<=6 for J=1 for the square lattices with periodic boundary conditions. The…
In CaIrO3 electronic correlation, spin-orbit coupling, and tetragonal crystal field splitting are predicted to be of comparable strength. However, the nature of its ground state is still object of debate, with contradictory experimental and…
We have shown that the V4+ ion with 1 d electron can have almost non-magnetic ground state under the action of the octahedral crystal field in the presence of the spin-orbit coupling and off-cubic distortions. Such the situation occurs in…
We investigate the role of orbital degeneracy in the double exchange (DE) model. In the $J_{H}\to\infty$ limit, an effective generalized ``Hubbard'' model incorporating orbital pseudospin degrees of freedom is derived. The model possesses…
Competition and cooperation between electron correlation and relativistic spin-orbit coupling give rise to diverse exotic quantum phenomena in solids. An illustrative example is spin-orbit entangled quantum liquids, which exhibit remarkable…
Hyperkagome iridate, Na$_4$Ir$_3$O$_8$, has been regarded as a promising candidate material for a three-dimensional quantum spin liquid. Here the three-dimensional network of corner-sharing triangles forms the hyperkagome lattice of…
We summarize some characteristic features of the frustrated magnetic interactions in spin-orbital models adequate for cubic transition metal oxides with orbital degeneracy. A generic tendency towards dimerization, found already in the…
$\alpha$-RuCl$_3$ has been extensively studied recently because of potential bond-dependent Kitaev magnetic exchange interactions and the resulting quantum spin liquid phase that can be realized therein. It has been known that the covalency…
We investigate the spin state of LaCoO3 using state-of-the-art photoemission spectroscopy and ab initio band structure calculations. The GGA+U calculations provide a good description of the ground state for the experimentally estimated…
We compare the effective spin-orbital super\-exchange triggered by magnetic $3d$ impurities with $d^3$ and $d^2$ configurations and either no orbital degree of freedom (orbital dilution) or hole replacing a doublon (charge dilution) in a…
Here we report on the low-energy excitations within the paramagnetic spin-orbit insulator Sr$_3$Ir$_2$O$_7$F$_2$ studied via resonant inelastic X-ray scattering, \textit{ab initio} quantum chemical calculations, and model-Hamiltonian…
We discuss the ground state properties of a spin 1/2 magnetic ion with threefold $t_{2g}$ orbital degeneracy on a highly frustrated pyrochlore lattice, like Ti$^{3+}$ ion in B-spinel MgTi$_2$O$_4$. We formulate an effective spin-orbital…
The electronic structure of the perovskite La$_{1-x}$Sr$_x$CoO$_3$ has been obtained as a function of Sr substitution and volume from a series of generalized-gradient-corrected, full-potential, spin-density-functional band structure…
The semi-metallic behavior of the perovskite iridate SrIrO3 shifts the end-member of the strongly spin-orbit (SO) coupled Ruddlesden-Popper series Srn+1IrnO3n+1 away from the Mott insulating regime and the half-filled pseudospin Jeff=1/2…
We argue that in LaCoO3 exists the fine electronic structure associated with the atomic-like states of the Co3+ ions and caused by the crystal-field and intra-atomic spin-orbit interactions. This low-energy fine electronic structure has to…
Transition metal oxides exhibit various competing phases and exotic phenomena depending on how their reaction to the rich degeneracy of the $d$-orbital. Large spin-orbit coupling (SOC) reduces this degeneracy in a unique way by providing a…
We study a doubly-degenerate orbital model on a honeycomb attice. This is a model for orbital states in multiferroic layered iron oxides. The classical and quantum models are analyzed by spin-wave approximation, Monte-Carlo simulation and…
Spin-orbit coupling (SOC) often gives rise to interesting electronic and magnetic phases in an otherwise ordinary pool of paramagnetic heavy metal oxides. In presence of strong SOC, assumed to be working in $j$-$j$ coupling regime, 5$d^4$…
For many years a spin-state transition at $T \approx 100 K$ and insulator - metal transition (IMT) at $T_{IMT} \approx 600 K$ in LaCoO$_3 $ remains a mystery. Small low-spin - high-spin spin gap $\Delta _S = E\left( {HS} \right) - E\left(…
The concept of the entanglement between spin and orbital degrees of freedom plays a crucial role in understanding various phases and exotic ground states in a broad class of materials, including orbitally ordered materials and spin liquids.…