Control of multiferroic order by magnetic field in frustrated helimagnet MnI${}_2$. Theory

We provide a theoretical description of frustrated multiferroic $\mathrm{M}\mathrm{n}{\mathrm{I}}_2$ with a spiral magnetic ordering in magnetic field $\mathbf{h}$. We demonstrate that subtle interplay of exchange coupling, dipolar forces, hexagonal anisotropy, and the Zeeman energy account for the main experimental findings observed recently in this material (Kurumaji, et al., Phys.\ Rev.\ Lett.\ {\bf 106}, 167206 (2011)). We describe qualitatively the non-trivial evolution of electric polarization $\mathbf{P}$ upon $\mathbf{h}$ rotation, changing $\mathbf{P}$ direction upon $h$ increasing, and disappearance of ferroelectricity at $h>h_c$, where $h_c$ is smaller than the saturation field.