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

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 Hamiltonian and study its low energy sector by constructing several exact-eigenstates in the limit of vanishing Hund's coupling. We find that orbital degrees of freedom modulate the spin-exchange energies, release the infinite spin-degeneracy ...

The common phase diagrams of superconducting iron pnictides show interesting material specificities in the structural and magnetic phase transitions. In some cases the two transitions are separate and second order, while in others they appear to happen concomitantly as a single first order transition. We explore these differences using Monte Carlo simulations of a two-dimensional Hamiltonian with coupled Heisenberg-spin and Ising-orbital degrees of freedom. In this spin-orbit...

Motivated by recent neutron and x-ray observations in V_2O_3, we derive the effective Hamiltonian in the strong coupling limit of an Hubbard model with three degenerate t_{2g} states containing two electrons coupled to spin S = 1, and use it to re-examine the low-temperature ground-state properties of this compound. An axial trigonal distortion of the cubic states is also taken into account. Since there are no assumptions about the symmetry properties of the hopping integrals...

Motivated by recent experiments, we present a comprehensive theoretical study of the geometrically frustrated strongly correlated magnetic insulator Mn$_3$O$_4$ spinel oxide based on a microscopic Hamiltonian involving lattice, spin and orbital degrees of freedom. Possessing the physics of degenerate e$_g$ orbitals, this system shows a strong Jahn-Teller effect at high temperatures. Further, careful attention is paid to the special nature of the superexchange physics arising ...

We report the synthesis and characterization of Li2ZnV3O8, which is a new Zn-doped LiV2O4 system containing only tetravalent vanadium. A Curie-Weiss susceptibility with a Curie-Weiss temperature of <theta>CW ~214 K suggests the presence of strong antiferromagnetic correlations in this system. We have observed a splitting between the zero-field cooled ZFC and field cooled FC susceptibility curves below 6 K. A peak is present in the ZFC curve around 3.5 K suggestive of spin-fre...

We study geometrically frustrated antiferromagnets with magnetoelastic coupling. Frustration in these systems may be relieved by a structural transition to a low temperature phase with reduced lattice symmetry. We examine the statistical mechanics of this transition and the effects on it of quenched disorder, using Monte Carlo simulations of the classical Heisenberg model on the pyrochlore lattice with coupling to uniform lattice distortions. The model has a transition betwee...

CaV$_2$O$_4$ is a spin-1 antiferromagnet, where the magnetic vanadium ions are arranged on quasi-one-dimensional (1D) zig-zag chains with potentially frustrated antiferromagnetic exchange interactions. High temperature susceptibility and single-crystal neutron diffraction measurements are used to deduce the non-collinear magnetic structure, dominant exchange interactions and orbital configurations. The results suggest that at high temperatures CaV$_2$O$_4$ behaves as a Haldan...

Motivated by puzzling aspects of spin-glass behavior reported in frustrated magnetic materials, we theoretically investigate effects of magnetoelastic coupling in geometrically frustrated classical spin models. In particular, we consider bond-disordered Heisenberg antiferromagnets on a pyrochlore lattice coupled to local lattice distortions. By integrating out the lattice degree of freedom, we derive an effective spin-only model, the bilinear-biquadratic model with bond disor...

This review summarizes more than 100 years of research on spinel compounds, mainly focusing on the progress in understanding their magnetic, electronic, and polar properties during the last two decades. Many spinel compounds are magnetic insulators or semiconductors; however, a number of spinel-type metals exists including superconductors and some rare examples of d-derived heavy-fermion compounds. In the early days, they gained importance as ferrimagnetic or even ferromagnet...

We review the mechanism of spin-lattice coupling in relieving the geometrical frustration of pyrochlore antiferromagnets, in particular spinel oxides. The tetrahedral unit, which is the building block of the pyrochlore lattice, undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom are coupled to the antiferromagnetism. By restricting our considerations to distortions which preserve the translational symmetries of the lattice, we present a general the...