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 ${\text{Ba}}_{2}{\text{Mg}}_{2}{\text{Fe}}_{12}{\text{O}}_{22}$ 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 sixfold structure with $\mathbit{q}=(0\text{ }0\text{ }1/2)$ in weak magnetic fields and a twofold structure with $\mathbit{q}=(0\text{ }0\text{ }3/2)$ in strong magnetic fields between which a first-order transition intervenes accompanied by a hysteresis.