Heisenberg-Kitaev physics in magnetic fields

α-RuCl₃ is a Mott insulator in the regime of strong spin-orbit coupling. In this material, the effective degrees of freedom are localized spins on a two-dimensional honeycomb lattice. They interact via strongly direction-dependent exchange couplings and, under a suitable external perturbation, may realize Kitaev's celebrated honeycomb spin model. When subject to a magnetic field, recent experiments in fact appear to suggest a field-induced quantum spin liquid characterized by fractionalized Majorana excitations. I will describe and explain the behavior of the relevant extended Heisenberg-Kitaev spin models in applied magnetic fields. Our results reveal surprisingly rich phase diagrams, with non-trivial intermediate phases including vortex crystals and other multi-Q states. I will discuss possible origins of large magnetic anisotropies as observed experimentally, and highlight different mechanisms to stabilize zigzag magnetic order and their distinct field responses.

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