Magnetic-anisotropy modulation in multiferroic heterostructures by ferroelectric domains from first principles.

First-principles calculations incorporating spin-orbit coupling are presented for a multiferroic material as a ferromagnetic/ferroelectric junction. We simulate the interface effect that cannot be described by the single-phase bulk. The in-plane uniaxial magnetic-anisotropy of CoFeSi is observed when the ferroelectric domain is polarized parallel to the interface, whereas the magnetic anisotropy is significantly different in the plane for the electrical polarization perpendicular to the interface. While the single-phase effect dominates the main part of the modulation of the magnetic anisotropy, symmetry breaking due to the interfacial effect is observed in the ferromagnetic ultrathin films. The origin of the modulated magnetic-anisotropy can be attributed to the shifting of specific energy bands in CoFeSi when the ferroelectric domain is modified.