| I will report our recent theoretical results on the effects of spin-orbit coupling in the Mott insulators. First, I discuss a family of hexagonal layered iridates A2IrO3 (A=Li,~Na) and show that they are described by the Hamiltonian that interpolates between Heisenberg and an exactly solvable Kitaev models. Such a model exhibits rich phase behavior, with an extended spin-liquid phase near the Kitaev limit, an unusual stripy order, and a conventional Neel state. I next show that the spin-orbit coupling in a system of d1-ions on a square lattice may drive a magnetically hidden order in which the order parameter responsible for a time-reversal symmetry breaking is a magnetic octupole. I suggest that such an octupolar order is realized in the layered perovskite Sr2VO4. |
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