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With the perovskite multiferroic RMnO₃ (R=Gd, Tb, Dy) as guidance, we argue that the Dzyaloshinskii-Moriya interaction (DMI) provides the microscopic mechanism for the coexistence and strong coupling between ferroelectricity and incommensurate magnetism. We use Monte Carlo simulations and zero-temperature exact calculations to study a model incorporating the double-exchange, superexchange, Jahn-Teller, and DMI terms. The phase diagram contains a multiferroic phase between A and E antiferromagnetic phases, in excellent agreement with experiments.
Сергиенко et al. (Thu,) studied this question.