Tunable magnetic anisotropy in multiferroic oxides

Room-temperature electric-field control of magnetism is actively sought to realize electric-field assisted changes in perpendicular magnetic anisotropy (PMA), which is important to magnetic random access memories (MRAMs) and future spin-orbit based logic technologies. Traditional routes to achieve such control rely on heterostructures of ferromagnets and/or ferroelectrics, exploiting interfacial effects, including strain generated by the substrate, or electric-field induced changes in the interfacial electronic structures. Here we present design rules based on $d$-orbital splitting in an octahedral field and crystallographic symmetries for electric-field control of PMA utilizing hybrid improper ferroelectricity by scaffolding simple perovskite oxides into ultrashort period superlattices, ${(\mathrm{AB}{\mathrm{O}}_{3})}_{1}/{({\mathrm{A}}^{\ensuremath{'}}\mathrm{B}{\mathrm{O}}_{3})}_{1}$, and in multiferroic ${\mathrm{AA}}^{\ensuremath{'}}{\mathrm{BB}}^{\ensuremath{'}}{\mathrm{O}}_{6}$ double perovskites. We validate the strategy using first principles calculations and a single-ion anisotropic model. We find a change in the magnetic anisotropy from the in-plane to the out of plane direction in ${(\mathrm{BiFe}{\mathrm{O}}_{3})}_{1}/{(\mathrm{LaFe}{\mathrm{O}}_{3})}_{1}$ and a 50% decrease of the magnetization along the out of plane direction in $\mathrm{LaYNiMn}{\mathrm{O}}_{6}$, when a polar to nonpolar phase transition occurs with strain. The origin of the PMA control is due to the structural tunable competitions among the ${t}_{2g}$ and ${e}_{g}$ orbital interactions on the magnetic ions arising from relativistic spin-orbital interactions that are susceptible to changes in the oxygen octahedral tilts across the field-tunable transition. Our results allow us to search rapidly for other promising multiferroics materials with voltage-controlled magnetic anisotropy for applications in low-energy information storage and logic devices.