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

Investigating the classical Kitaev-Heisenberg Hamiltonian on a triangular lattice, we establish the presence of an incommensurate non-coplanar magnetic phase, which is identified as a lattice of $Z_2$ vortices. The vortices, topological point defects in the SO(3) order parameter of the nearby Heisenberg antiferromagnet, are not thermally excited but due to the spin-orbit coupling and arise at temperature $T\to 0$. This $Z_2$-vortex lattice is stable in a parameter regime relevant to iridates. We show that in the other, strongly anisotropic, limit a robust nematic phase emerges.