Complex strain evolution of polar and magnetic order in multiferroic BiFeO₃ thin films

Electric-field control of magnetism requires deterministic control of the magnetic order and understanding of the magnetoelectric coupling in multiferroics like BiFeO₃ and EuTiO₃. Despite this critical need, there are few studies on the strain evolution of magnetic order in BiFeO₃ films. Here, in (110)-oriented BiFeO₃ films, we reveal that while the polarization structure remains relatively unaffected, strain can continuously tune the orientation of the antiferromagnetic-spin axis across a wide angular space, resulting in an unexpected deviation of the classical perpendicular relationship between the antiferromagnetic axis and the polarization. Calculations suggest that this evolution arises from a competition between the Dzyaloshinskii-Moriya interaction and single-ion anisotropy wherein the former dominates at small strains and the two are comparable at large strains. Finally, strong coupling between the BiFeO₃ and the ferromagnet Co_0.9Fe_0.1 exists such that the magnetic anisotropy of the ferromagnet can be effectively controlled by engineering the orientation of the antiferromagnetic-spin axis.