Orbital and magnetic transitions in geometrically-frustrated vanadium spinels -- Monte Carlo study of an effective spin-orbital-lattice coupled model --

The surprising inversion of the orbital- and magnetic-order transition temperatures in the RVO3 series with increasing the rare-earth radius makes the series unique among orbitally-ordered materials. Here, augmenting dynamical mean-field theory with a decomposition of the order parameter into irreducible tensors, we show that this anomalous behavior emerges from an unusual hierarchy of interactions. First, increasing the rare-earth radius, orbital physics comes to be controll...

We investigate the frustrated magnetic interactions in cubic transition metal oxides with orbital degeneracy. The $e_g$ orbitals order easier and their ordering explains the $A$-type antiferromagnetic phase in KCuF$_3$ and LaMnO$_3$. In $t_{2g}$ systems the magnetic order changes at a transition from an orbital liquid to orbital ordered states. The fluctuations of $t_{2g}$ orbitals play a prominent role in LaVO$_3$ and YVO$_3$, where they compete with the Jahn-Teller effect a...

We investigate ground-state properties and quantum phase transitions in the one-dimensional S=1 spin-orbital model relevant to cubic vanadates. Using the density matrix renormalization group, we compute the ground-state energy, the magnetization and the correlation functions for different values of the Hund's coupling $J_H$ and the external magnetic field. It is found that the magnetization jumps at a certain critical field, which is a hallmark of the field-induced first-orde...

We study quantum phase transitions induced by the on-site spin-orbit interaction lambda(L.S) in a toy model of vanadium chains. In the lambda->0 limit, the decoupled spin and orbital sectors are described by a Haldane and an Ising chain, respectively. The gapped ground state is composed of a ferro-orbital order and a spin liquid with finite correlation lengths. In the opposite limit, strong spin-orbital entanglement results in a simultaneous spin and orbital-moment ordering, ...

We show that the recently proposed S=2 bond model with orbital degrees of freedom for insulating V$_{2}$O$_{3}$ not only explains the anomalous magnetic ordering, but also other mysteries of the magnetic phase transition. The model contains an additional orbital degree of freedom that exhibits a zero temperature quantum phase transtion in the Ising universality class.

Magnetic correlations in all four phases of pure and doped vanadium sesquioxide V_2O_3 have been examined by magnetic thermal neutron scattering. While the antiferromagnetic insulator can be accounted for by a Heisenberg localized spin model, the long range order in the antiferromagnetic metal is an incommensurate spin-density-wave, resulting from a Fermi surface nesting instability. Spin dynamics in the strongly correlated metal are dominated by spin fluctuations in the Ston...

Starting from the Mott insulator picture for cubic vanadates, we derive and investigate the model of superexchange interactions between V$^{3+}$ ions, with nearly degenerate $t_{2g}$ orbitals occupied by two electrons each. The superexchange interactions are strongly frustrated and demonstrate a strong interrelation between possible types of magnetic and orbital order. We elucidate the prominent role played by fluctuations of $yz$ and $xz$ orbitals which generate ferromagneti...

We study the influence of the spin lattice distortion on the properties of frustrated magnetic systems and consider the applicability of the spin-1/2 frustrated square lattice model to materials lacking tetragonal symmetry. We focus on the case of layered vanadium phosphates AA'VO(PO4)2 (AA' = Pb2, SrZn, BaZn, and BaCd). To provide a proper microscopic description of these compounds, we use extensive band structure calculations for real materials and model structures and supp...

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 degenerate Hubbard model, is confirmed for $t_{2g}$ but not for $e_g$ systems. In the $t_{2g}$ case the quantum orbital fluctuations are more pronounced and contribute to a stronger competition between different magnetic and orbital states. Ther...

The chromium spinels MgCr2O4 and ZnCr2O4 are prime examples of the highly frustrated pyrochlore lattice antiferromagnet. Experiment has carefully established that both materials, upon cooling, distort to lower symmetry and order magnetically. We study the nature of this process by a combination of density-functional-theory based energy mapping and classical Monte Carlo simulations. We first computationally establish precise Heisenberg Hamiltonian parameters for the high tempe...