Two Distinct Ferroelectric Phases in Multiferroic Y-type Hexaferrite Ba$_{2}$Mg$_{2}$Fe$_{12}$O$_{22}$

The magnetic phase diagram of the $Y$-type hexaferrite Ba$_{2}$Mg$_{2}$Fe$_{12}$O$_{22}$ has been studied using single-crystal neutron diffraction. The result indicates successive phase transitions where the magnetic modulation wave number changed discontinuously, when a magnetic field is applied and the temperature is varied. For the low-temperature spin-driven ferroelectric state, we have found a 6-fold structure with q=(0 0 1/2) in weak magnetic fields and a 2-fold structure with q=(0 0 3/2) in strong magnetic fields, between which a first-order transition intervenes accompanied by a hysteresis.