Z_2-vortex lattice in the ground state of the triangular Kitaev-Heisenberg model

Understand

The triangular-lattice Heisenberg antiferromagnet (HAF) is known to carry topological Z_2 vortex excitations which form a gas at finite temperatures.

• Here we show that the spin-orbit interaction, introduced via a Kitaev term in the exchange Hamiltonian, condenses these vortices into a triangular $Z_2$ vortex crystal at zero temperature.
• The cores of the Z_2 vortices show abrupt, soliton-like magnetization modulations and arise by a special intertwining of three honeycomb superstructures of ferromagnetic domains, one for each of the three sublattices of the 120-degree state of the pure HAF.
• This is a new example of a nucleation transition, analogous to the spontaneous formation of magnetic domains, Abrikosov vortices in type-II syperconductors, blue phases in cholesteric liquid crystals, and skyrmions in chiral helimagnets.