Frustrated antiferromagnetic triangular lattice with Dzyaloshinskii–Moriya interaction: Ground states, spin waves, skyrmion crystal, phase transition

Abstract

We study in this article a triangular lattice with Heisenberg spins interacting with each other via an antiferromagnetic exchange interaction J and a Dzyaloshinskii–Moriya (DM) interaction D, between nearest-neighbors (NN). We consider two cases: the first case in which the DM vector D is perpendicular to the lattice plane and the second case where it lies in the plane. A magnetic field H is applied perpendicular to the spin plane in both cases. The ground state (GS) of this system is calculated by minimizing the energy using the very fast steepest-descent method in the two cases. In the case of perpendicular D with H=0, the GS is periodic. We analytically determine the GS configuration which is characterized by two well-defined angles. We calculate the spin-wave spectrum in this case which shows that for small wave vectors the spin waves are forbidden in the system. When H≠0, the GS in the perpendicular D case shows no skyrmions. However, in the case of in-plane D with H≠0, we find a crystal of skyrmions at T=0 composed of three interpenetrating skyrmion sublattice crystals, in agreement with low-T spin textures found in earlier works. We show by Monte Carlo simulations that this skyrmion crystal is stable at finite temperatures below a critical temperature.