Monte Carlo modeling the phase diagram of magnets with the Dzyaloshinskii - Moriya interaction*

We use classical Monte Carlo calculations to model the high-pressure behavior of the phase transition in the helical magnets. We vary values of the exchange interaction constant J and the Dzyaloshinskii-Moriya interaction constant D, which is equivalent to changing spin-spin distances, as occurs in real systems under pressure. The system under study is self-similar at D/J=constant, and its properties are defined by the single variable J/T, where T is temperature. The existence of the first order phase transition critically depends on the ratio D/J. A variation of J
strongly affects the phase transition temperature and width of the fluctuation region (the "hump") as follows from the system self-similarity. The high-pressure behavior of the spin system depends on the evolution of the interaction constants J and D on compression. Our calculations are relevant to the high pressure phase diagrams of helical magnets MnSi and Cu₂OSeO₃.