We investigate the magnetic-field-induced $(H\parallel b)$ transition in the reference improper multiferroic $\mathrm{MnW}{\mathrm{O}}_4$ using superspace formalism. The distinct superspace group symmetries are determined from single-crystal neutron diffraction. The study of the full magnetic symmetry of the incommensurate magnetic phases under field provides the keys for understanding its magnetic and ferroelectric behavior up to 12 T. At moderate fields, below the transition, the magnetic modulations of the two Mn sites in the simple cell are independent. At the field-induced transition between multiferroic phases, the electric polarization undergoes a flip from the monoclinic $b$ axis to the $ac$ plane. An additional component in the polarization is predicted along the $c$ axis, due to a point symmetry change from $2_y{1}^{\prime }$ to $m_y{1}^{\prime }$. In contrast with the low-field phase, above the transition the influence of the magnetic field results in the coupling between the magnetic modulations of the two Mn sites of the original monoclinic cell.

• Received 27 September 2014
• Revised 3 March 2015

DOI:https://doi.org/10.1103/PhysRevB.91.104429