Abstract
The classical nearest neighbor Kitaev-Heisenberg model on the triangular lattice is known to host $\mathbb{Z}_2$ spin-vortices forming a crystalline superstructure in the ground state. The $\mathbb{Z}_2$ vortices in this system can be understood as distortions of the local $120^\circ$ N\'eel parent order of the Heisenberg-only Hamiltonian. Here, we explore possibilities of stabilizing further types of $\mathbb{Z}_2$ vortex phases in Kitaev-Heisenberg models including those which rely on more complicated types of non-collinear parent orders such as tetrahedral states. We perform extensive scans through large classes of Kitaev-Heisenberg models on different lattices employing a two-step methodology which first involves a mean-field analysis followed by a stochastic iterative minimization approach. When allowing for longer-range Kitaev couplings we identify several new $\mathbb{Z}_2$ vortex phases such as a state based on the $120^\circ$ N\'eel order on the triangular lattice which shows a coexistence of different $\mathbb{Z}_2$ vortex types. Furthermore, perturbing the tetrahedral order on the triangular lattice with a suitable combination of first and second neighbor Kitaev interactions we find that a kagome-like superstructure of $\mathbb{Z}_2$ vortices may be stabilized where vortices feature a counter-rotating winding of spins on different sublattices. This last phase may also be extended to honeycomb lattices where it is related to cubic types of parent orders. In total, this analysis shows that $\mathbb{Z}_2$ vortex phases appear in much wider contexts than the $120^\circ$ N\'eel ordered systems previously studied.
Highlights
Topological defects are local perturbations of an otherwise homogeneous system which cannot be removed by any continuous operation
We have studied the generation of Z2-vortex phases and vortex crystals in Kitaev-Heisenberg models, in various geometries and parent orders beyond the 120◦ Néel state
We have probed large classes of systems, following a two step approach: Using an analytical mean-field method, we first searched for the characteristic peak shift in reciprocal space which allowed us to reduce the number of systems to a few candidate models
Summary
Topological defects are local perturbations of an otherwise homogeneous system which cannot be removed by any continuous operation. A prototypical microscopic situation inducing topological defects arises when a two-dimensional system consists of local U(1) degrees of freedom such as the phase field of a superconducting film or the in-plane spin direction of an XY magnet. In this case, a vortex is formed if the U(1)-phase winds an integer number of times around the center of the perturbation, leading to a classification of defects in terms of a Z-quantized vorticity [12,16].
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