Magnetoelectric multiferroics are materials which exhibit coexistence between certain types of long-range magnetic order and a ferroelectric order. Monoclinic structure MnWO4 is such a multiferroic material. When a magnetic field is applied along three principal directions, this material exhibits different commensurate and incommensurate ordered magnetic phases, some of them are also ferroelectric. The three principal directions are the easy axis (x), the hard axis (z), and the intermediate axis (y), which is parallel to the crystallographic b direction.
We extend earlier work [1] and present a quantitative theoretical analysis of MnWO4 temperature -- magnetic field phase diagram. Our analysis uses the mean field approximation based on a magnetic Heisenberg Hamiltonian with a single-ion anisotropy. We constructed a semi-phenomenological Landau theory, with a few adjustable parameters, which gives a good fit to all the experimental transition lines as well as to the measured magnetic and ferroelectric order parameters.

References
[1] S. Matityahu, O. Entin-Wohlman and A. Aharony, Phys. Rev. B 85, 174408 (2012).