The magnetic phase diagram of the Y -type hexaferrite Ba2 Mg2 Fe12 O22 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 q= (001/2) in weak magnetic fields and a twofold structure with q= (003/2) in strong magnetic fields between which a first-order transition intervenes accompanied by a hysteresis. © 2009 The American Physical Society.