Giant Magnetoelastic-Coupling Driven Spin-Lattice Liquid State in Molybdate Pyrochlores.

We propose the idea of a spin-lattice liquid, in which spin and lattice degrees of freedom are strongly coupled and remain disordered and fluctuating down to low temperatures. We show that such a state arises naturally from a microscopic analysis of a class of molybdate pyrochlore compounds, and is driven by a giant magnetoelastic effect. Finally, we argue that this could explain some of the experimental features of Y_{2}Mo_{2}O_{7}.

Emergent SU(4) Symmetry in α-ZrCl_{3} and Crystalline Spin-Orbital Liquids.

While the enhancement of spin-space symmetry from the usual SU(2) to SU(N) is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here, we propose a new mechanism by which SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d^{1} transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)-breaking hopping between the J_{eff}=3/2 quartets.

A spin-orbital-entangled quantum liquid on a honeycomb lattice.

The honeycomb lattice is one of the simplest lattice structures. Electrons and spins on this simple lattice, however, often form exotic phases with non-trivial excitations. Massless Dirac fermions can emerge out of itinerant electrons, as demonstrated experimentally in graphene, and a topological quantum spin liquid with exotic quasiparticles can be realized in spin-1/2 magnets, as proposed theoretically in the Kitaev model.

Spin-Orbit Dimers and Noncollinear Phases in d^{1} Cubic Double Perovskites.

We formulate and study a spin-orbital model for a family of cubic double perovskites with d^{1} ions occupying a frustrated fcc sublattice. A variational approach and a complementary analytical analysis reveal a rich variety of phases emerging from the interplay of Hund's rule and spin-orbit coupling. The phase digram includes noncollinear ordered states, with or without a net moment, and, remarkably, a large window of a nonmagnetic disordered spin-orbit dimer phase.

Zigzag magnetic order in the iridium oxide Na2IrO3.

We explore the phase diagram of spin-orbit Mott insulators on a honeycomb lattice, within the Kitaev-Heisenberg model extended to its full parameter space. Zigzag-type magnetic order is found to occupy a large part of the phase diagram of the model, and its physical origin is explained as due to interorbital t(2g)-e(g) hopping. The magnetic susceptibility, spin wave spectra, and zigzag order parameter are calculated and compared to the experimental data, obtaining thereby the spin coupling constants in Na(2)IrO(3) and Li(2)IrO(3).