We derived an analytic expression of refractive index for dipole-exchange spin waves (DESWs) in a laterally confined heterogeneous magnetic thin-film system and also derived Snell's law for DESWs by employing a dispersion relation and a specific boundary condition at a heterogeneous magnetic interface. These analytical results mimic well the macroscopic behaviors of propagation, reflection and refraction of DESWs, as obtained from micromagnetic simulations, for example, on a specific yttrium-iron-garnet ( Y 3 Fe 5 O 12) and permalloy ( Ni 80 Fe 20) interface.
Snell’s Law for Spin Waves