Electric-field-induced magnetic easy-axis reorientation in ferromagnetic/ferroelectric layered heterostructures

A phenomenological model is presented for the electric-field-induced reorientation of magnetic easy axis in ferromagnetic (FM)/ferroelectric (FE) layered heterostructures, where the FM layers include either polycrystalline or (001) preferentially oriented films of widely used Fe, CoFe₂O ₄ (CFO), Ni, and Fe₃O₄. The magnetic easy axes could rotate within the film plane at relatively low applied electric fields in CFO, Ni, and Fe₃O₄ films. As the applied electric field increases, the easy axes tend to switch from an in-plane direction to an out-of-plane one in CFO and Ni films. Such electric-field-induced easy-axis reorientations (EARs) can be abrupt and gradual, defined as first-order and second-order transitions, respectively. The influences of residual strain, different electric-field orientations, and nonlinear strain vs electric-field behavior of the FE substrates, on the EARs are also addressed.