Switching of ferrotoroidal domains via an intermediate mixed state in the multiferroic Y-type hexaferrite Ba$_{0.5}$Sr$_{1.5}$Mg$_2$Fe$_{12}$O$_{22}$

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.