Out-of-plane electric polarization in double-fan magnetic phase of Y-type hexaferrite

It has been revealed that a Y-type hexaferrite ${\mathrm{BaSrCo}}_{2}{\mathrm{Fe}}_{11.1}{\mathrm{Al}}_{0.9}{\mathrm{O}}_{22}$ hosts not only an in-plane $({P}_{ab})$ but also an out-of-plane $({P}_{c})$ component of magnetically induced electric polarization in the double-fan magnetic phase. With an increasing in-plane magnetic field, the magnitude of ${P}_{c}$ reaches a maximum at around $2\phantom{\rule{0.28em}{0ex}}\text{T}$ and decreases as approaching the critical field $(3.8\phantom{\rule{0.28em}{0ex}}\text{T})$ of the transition to the collinear ferrimagnetic phase. ${P}_{c}$ has also been verified to show a ${120}^{\ensuremath{\circ}}$-period oscillation as a function of the in-plane magnetic field direction. These results are reproduced by a model combining the inverse Dzyaloshinskii-Moriya interaction and the spin-dependent $pd$ hybridization mechanisms.