Monte Carlo Simulations of the Three-dimensional Heisenberg model with Dzyaloshinskii-Moriya interactions

The three-dimensional Heisenberg model on a simple cubic lattice with Dzyaloshinskii-Moriya (DM) interactions¹ between nearest-neighbor along all directions has been studied using Monte Carlo simulations. The Metropolis algorithm, together with single histogram techniques and finite-size-scaling analysis, have been used to obtain the thermodynamic behavior of the system in the thermodynamic limit. Instead of using fluctuating boundary conditions² , in order to take into account the incommensurability that results from the extra vectorial energetic term, we have determined, a priori, the shift angle at the boundary as a function of the DM interaction. This method has proved to decrease the simulation time significantly. We found that the ordered state has a spiral configuration for all values of non-zero DM interaction with the system undergoing a conventional second-order phase transition. The phase diagram, in the temperature versus DM interaction, has been obtained.

¹I. Dzyaloshinskii, J. Phys. Chem. Solids 4 241 (1958); T. Moriya, Phys. Rev. Lett. 4 228 (1960).

²H. Liu, J. A. Plascak, and D. P. Landau, Phys. Rev. E 97 052118 (2018); G. Albuquerque Silva, J. A. Plascak and D. P. Landau, Phys. Rev. E 106 044116 (2022).