Coupling spin waves to circuits through PEEC approach

The generation of magnetostatic spin waves in magnetic nanostructures can be obtained by using inductive input antennas having different geometries, e.g. a coplanar wave guide (CWG) or a transmission line. The induced spin waves are manipulated in the magnetic nanostructure and result is read out further by a second inductive antenna. The simulation of this structure must take into account the coupling of the magnetic dynamics in the magnetic nanostructure to the external circuits exciting it. In this paper the partial element equivalent circuits (PEEC), usually applied to the simulation of multiconductor circuits, is coupled to the magnetic spin wave model based on the linearized Landau-Lifschitz-Gilbert equation. The coupling between the PEEC equivalent circuit and the spin wave phenomena is eventually taken into account by means of a magnetization controlled voltage source introduced in each longitudinal branch of the PEEC equivalent circuit. A numerical examples of the proposed approach is presented.