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.