Nonreciprocity of Propagation of Exchange-Dipole Spin Waves in Two-Layer Magnetic Films with Crossed Magnetization of the Layers

Abstract

An analytical theory of propagation of exchange-dipole spin waves (SWs) in two-layer dipole-coupled magnetic films is presented in the approximation of uniform dynamic magnetization across the thickness of each layer. Different cases of noncollinear magnetization of the layers in the directions parallel and perpendicular to the direction of wave propagation are considered. For the configurations considered, the spectra and ellipticities of SWs propagating in opposite directions are calculated. It is shown that both the frequency and the ellipticity of forward and backward waves can differ, i.e., the propagation becomes nonreciprocal when at least one of the layers is magnetized in the film plane perpendicular to the propagation direction, including the case when the equilibrium magnetizations of the layers are mutually orthogonal. However, the nonreciprocity in such two-layer waveguides with crossed magnetization is less pronounced than that in the Damon–Eshbach geometry (DEG) with antiparallel magnetization of the layers. This difference is explained by the fact that, in the latter geometry, both the magnitude and chirality of the circularly polarized dynamic magnetic dipole field make nonreciprocal contributions to its interaction energy with the precessing magnetization. At the same time, only one of these contributions is present in crossed magnetization geometries.