Reversibility of spin-induced electric polarization in multiferroic hexaferrites

Hexaferrites with noncollinear conical magnetic structures are among the most interesting and promising single-phase multiferroics. One puzzle remaining unsolved is why the spin-induced electric polarization can be either reversible or nonreversible by applying magnetic fields. We have unraveled a solution to this puzzle by a systematic study in the multiferroic hexaferrite ${\mathrm{Ba}}_{0.3}{\mathrm{Sr}}_{1.7}{\mathrm{Co}}_{2}{\mathrm{Fe}}_{11}{\mathrm{AlO}}_{22}$ where the electric polarization is reversible at low temperatures but nonreversible at high temperatures. Neutron diffraction results reveal that the rotation of spin cones with applied $ab$-plane magnetic field takes distinct paths at 150 and 305 K: in-plane and out-of-plane rotation, respectively. A theoretical analysis based on the spin current model confirms that the reversal of electric polarization is caused by the in-plane rotation. Our study clarifies the mechanism underlying the reversibility of spin-induced electric polarization in multiferroic hexaferrites.