Field-induced ferroelectric and commensurate spin state in mutiferroic HoMn${}_2$O${}_5$

Neutron diffraction measurements under high magnetic fields have been performed for the multiferroic compound HoMn${}_2$O${}_5$. At zero field, high-temperature incommensurate magnetic (HT-ICM) – commensurate magnetic (CM) – low-temperature incommensurate magnetic (LT-ICM) orders occur with decreasing temperature, where ferroelectric polarization arises only in the CM phase. Upon applying a magnetic field, the LT-ICM phase completely disappears and the CM phase is induced at the lowest temperature. This field-induced CM state is completely associated with the field-induced electric polarization in this material [Higashiyama {\it et al}., Phys. Rev. B {\bf 72}, 064421 (2005).], strongly indicating that the commensurate spin state is essential to the ferroelectricity in the multiferroic $R$Mn${}_2$O${}_5$ system.