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The properties of transition metal compounds are largely determined by nontrivial interplay of different degrees of freedom: charge, spin, lattice, but also orbital ones. Especially rich and interesting effects occur in systems with orbital…
Charge, spin, and orbital degrees of freedom underlie the physics of transition metal compounds. Much work has revealed quantum critical points associated with spin and charge degrees of freedom in many of these systems. Here we illustrate…
We investigate the interplay between Coulomb driven orbital order and octahedral distortions in strongly correlated Mott insulators due to orbital dilution, i.e., doping by metal ions without an orbital degree of freedom. In particular, we…
A spin-orbital superexchange Hamiltonian in a Mott insulator with $t_{2g}$ orbital degeneracy is investigated. More specifically, we focus on a spin ferromagnetic state of the model and study a collective behavior of orbital angular…
We investigate the influence of spin-orbit coupling $\lambda$ in strongly-correlated multiorbital systems that we describe by a three-orbital Hubbard-Kanamori model on a Bethe lattice. We solve the problem at all integer fillings $N$ with…
In the present review different effects related to the orbital degrees of freedom are discussed. Leaving aside such aspects as the superexchange mechanism of the cooperative Jahn-Teller distortions and different properties of…
Transition metal oxides are a rich group of materials with very interesting physical properties that arise from the interplay of the charge, spin, orbital, and lattice degrees of freedom. One interesting consequence of this, encountered in…
We study finite temperature properties of a generic spin-orbital model relevant to transition metal compounds, having coupled quantum Heisenberg-spin and Ising-orbital degrees of freedom. The model system undergoes a phase transition,…
Effects of possible orbital order in magnetic properties of two-dimensional spin gap system for CaV$_4$O$_9$ are investigated theoretically. After analyzing experimental data, we show that single orbital models assumed in the literature are…
We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these…
We present a theory for spin excitations in ferromagnetic metallic manganites and demonstrate that orbital fluctuations have strong effects on the magnon dynamics in the case these compounds are close to a transition to an orbital ordered…
We present a general theory of multiorbital spin waves in magnetically ordered metallic systems. Motivated by the itinerant magnetism of iron-based superconductors, we compare the magnetic excitations for two different scenarios: when the…
Spin correlations in metallic and insulating phases of $V_2O_3$ and its derivatives are investigated using magnetic neutron scattering. Metallic samples have incommensurate spin correlations varying little with hole doping. Paramagnetic…
We study the effects of temperature and magnetic field on a two-orbital Hubbard model within dynamical mean field theory. We focus on the quarter filled system, which is a special point in the phase diagram due to orbital degeneracy. At…
Density functional calculations are performed to study the magnetic order of the severely distorted square planar cupric oxide (CuO) and local spin disorder in it in the presence of the transition metal impurities M (= Cr, Mn, Fe, Co and…
Finite temperature orbital state in a ferromagnetic Mott insulator with triply-degenerate $t_{2g}$ orbital is investigated numerically. We employ the quantum Monte Carlo simulation with the loop algorithm. Indications for conventional…
We study the effects of the degeneracy of the $e_g$ orbitals as well as the double exchange interaction with $t_{2g}$ spins in perovskite transition-metal oxides. In addition to the spin field ${\vec S}_i$, the isospin field ${\vec T}_i$ is…
In frustrated spinel antiferromagnets, dilution with non-magnetic ions can be a powerful strategy for probing unconventional spin states or uncovering interesting phenomena. Here, we present X-ray, neutron scattering and thermodynamic…
We use dynamical mean-field theory to study how electronic transport in multi-orbital metals is influenced by correlated (nominally) empty orbitals that are in proximity to the Fermi level. Specifically, we study 2 + 1 orbital and 3 + 2…
The two-orbital degenerate Hubbard model with distinct hopping integrals is studied by combining dynamical mean-field theory with quantum Monte Carlo simulations. The role of orbital fluctuations for the nature of the Mott transition is…