Theory of Surface-Spin Pinning in Ferromagnetic Resonance

Abstract

A theory is presented which, in conjunction with previous theories, explains for the first time all notable experimental results on exchange and magnetostatic modes in thin films, including surface and bulk modes. Roughly speaking, a surface inhomogeneity thinner than $\sim {\left(\frac{1}{2}\Lambda \right)}^{\frac{1}{2}}$ gives little pinning, while one thicker than $\sim {\left(\frac{1}{2}\Lambda \right)}^{\frac{1}{2}}$ pins the low-order modes. The results, obtained by considering the change of $M_z$ in the surface region, reconcile the different boundary conditions used for thin-film exchange modes and for magnetostatic modes.