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

TL;DR

This paper demonstrates that in a triangular Kitaev-Heisenberg model, Z_2 vortices condense into a lattice at zero temperature, forming a novel vortex crystal due to spin-orbit interactions and geometric frustration.

Contribution

It introduces a new ground-state vortex crystal in a frustrated spin system with spin-orbit coupling, expanding understanding of topological excitations in such materials.

Findings

Z_2 vortex lattice forms at zero temperature

Vortices exhibit soliton-like magnetization modulations

Mechanism involves interplay of frustration and spin-orbit anisotropy

Abstract

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. As the mechanism relies on the interplay of geometric frustration and spin-orbital anisotropies, such vortex mesophases can materialize as a ground-state property in spin-orbit coupled correlated systems with nearly hexagonal topology, as in triangular or strongly frustrated honeycomb iridates.