Helicity, anisotropies and their competition in a multiferroic magnet: insight from the phase diagram

Motivated by the complex phase diagram of MnWO4, we investigate competition between anisotropy, magnetic field, and helicity for the anisotropic next-nearest-neighbor Heisenberg model. Apart from two competing exchanges, which favor a spiral magnetic structure, the model features the bi-axial single-ion anisotropy. The model is treated in the real-space mean-field approximation and the phase diagram containing various incommensurate and commensurate states is obtained for different field orientations. We discuss similarities and differences of the theoretical phase diagram and the experimental diagram of MnWO4.