Spin waves in a thin film with magnetoelectric coupling at the surfaces

The standing spin waves in a thin ferromagnetic film are calculated when the surface magnetization is influenced by magnetoelectric coupling. At the interfaces, inversion symmetry is broken allowing for an energy term that is linear in the electric polarization in the film. For the two film surfaces, the magnetoelectric coupling is opposite in sign and therefore results in asymmetric pinning of the dynamic magnetization. The magnetoelectric pinning alters the spin wave frequencies and also the power absorbed by the material at these resonances.