We study realizations of spirals and skyrmions in two-dimensional antiferromagnets with a triangular lattice on an inversion-symmetry-breaking substrate. As a possible material realization, we investigate the adsorption of transition-metal atoms (Cr, Mn, Fe, or Co) on a monolayer of ${\mathrm{MoS}}_2$, ${\mathrm{WS}}_2$, or ${\mathrm{WSe}}_2$ and obtain the exchange, anisotropy, and Dzyaloshinskii-Moriya interaction parameters using first-principles calculations. Using energy minimization and parallel-tempering Monte Carlo simulations, we determine the magnetic phase diagrams for a wide range of interaction parameters. We find that skyrmion lattices can appear even with weak Dzyaloshinskii-Moriya interactions, but their stability is hindered by magnetic anisotropy. However, a weak easy plane magnetic anisotropy can be beneficial for stabilizing the skyrmion phase. Our results suggest that Cr/${\mathrm{MoS}}_2$, Fe/${\mathrm{MoS}}_2$, and Fe/${\mathrm{WSe}}_2$ interfaces can host spin spirals formed from the ${120}^{\circ }$ antiferromagnetic states. Our results further suggest that for interfaces, such as Fe/${\mathrm{MoS}}_2$, the Dzyaloshinskii-Moriya interaction is strong enough to drive the system into a three-sublattice skyrmion lattice in the presence of experimentally feasible external magnetic field.

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• Antiferromagnetism
• Magnetic texture
• Skyrmions
• Topological materials