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 $\mathbf{D}$ 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 $\mathbf{D}$ 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 $H\ne 0$, the GS in the perpendicular $\mathbf{D}$ case shows no skyrmions. However, in the case of in-plane $\mathbf{D}$ with $H\ne 0$, 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.

16 pages, 10 figures, submitted to JMMM

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Cited by in corpus (4)

• Spontaneous antiferromagnetic skyrmion/antiskyrmion lattice and spiral spin liquid states in the frustrated triangular lattice
• Quantum Spin-Wave Theory for non-collinear Spin Structures, a Review
• Spin Excitation Continuum in the Exactly Solvable Triangular-Lattice Spin Liquid CeMgAl11O19
• Quantum Spin Liquids in Weak Mott Insulators with a Spin-Orbit Coupling