  We report a detailed study of the magnetic field switching of
ferrotoroidal/multiferroic domains in the Y-type hexaferrite compound
Ba$_{0.5}$Sr$_{1.5}$Mg$_2$Fe$_{12}$O$_{22}$. By combining data from SQUID
magnetometry, magneto-current measurements, and resonant X-ray scattering
experiments, we arrive at a complete description of the deterministic
switching, which involves the formation of a temperature-dependent mixed state
in low magnetic fields. This mechanism is likely to be shared by other members
of the hexaferrite family, and presents a challenge for the development of
high-speed read-write memory devices based on these materials.
