Nonreciprocity of spin waves in a double layer ferromagnet with Dzyaloshinskii-Moriya interactions
In this paper, boundary conditions for Landau-Lifshitz equations at the interface between two ferromagnets with different Dzyaloshinskii-Moriya interactions are derived. We calculated and verified the analytical expression for the energy flux density continuity for the spin-wave propagation through the interface between two ferromagnets with/without Dzyaloshinskii-Moriya interactions considering the boundary conditions mentioned. Analytical expressions for reflection, transmission coefficients and the nonreciprocity factor are calculated in the case of spin-wave propagation through a double layer ferromagnet with/without Dzyaloshinskii-Moriya interactions in the first/second layer. Two principally different types of nonreciprocity effects for spin waves are revealed in such a double layer system. The material parameters of a double layer ferromagnet with/without Dzyaloshinskii-Moriya interactions in the first/second layer are found for which the extremely high nonreciprocity factor (>10) is expected according to the results of calculations. The results of the paper deepen the knowledge about the spin-wave propagation control in magnonic devices.