Enhanced magnetoelectric effect by spin-orbit coupling in M-type hexaferrite

Magnetoelectric (ME) effect triggered by spiral spin orders in various hexaferrites develops both the theory and application of ME coupling. However, the strength of such ME effect is restricted by the small spin-orbit coupling (SOC) of $3d$ electrons in M-type hexaferrite. Here, we introduce the $5d$ element Ir with large SOC into $\mathrm{Sr}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$. It is found that a low ${\mathrm{Ir}}^{4+}\text{\ensuremath{-}}\mathrm{doping}$ level (about 4.2% of total ${\mathrm{Fe}}^{3+}$ ions) can induce conical spin order in $\mathrm{Sr}{\mathrm{Mg}}_{x}{\mathrm{Ir}}_{x}{\mathrm{Fe}}_{12\ensuremath{-}2x}{\mathrm{O}}_{19}$ ceramics, mainly because ${\mathrm{Ir}}^{4+}$ ions prefer to enter a crucial $4{f}_{2}$ magnetic-interacted site and thus strengthen the local Dzyaloshinskii-Moriya interaction. Spin-order-induced polarization $({P}_{\mathrm{spin}})$ is achieved and displays a synchronous temperature-dependent behavior with the displacive polarization $({P}_{\mathrm{disp}})$. This interesting ME effect is discussed via $d\text{\ensuremath{-}}p$ hybridization emerging at $\mathrm{Fe}{\mathrm{O}}_{5}$ trigonal bipyramids. Moreover, ${P}_{\mathrm{spin}}$ response decreases step by step during the periodical ME test, reflecting the controllable helicity and the possible multilevel states. These results demonstrate the impact of the $5d$ element with strong SOC on the formation of conical spin order and the enhancement of ME effect in M-type hexaferrite, and also reveal the interconnectedness between ${P}_{\mathrm{spin}}$ and ${P}_{\mathrm{disp}}$.