Nonreciprocal Spin-Wave Propagation in a Ferromagnet With Stepwise Interfacial Dzyaloshinskii–Moriya Interaction

In this article, boundary conditions for Landau–Lifshitz equations at the interface between two ferromagnets with different interfacial Dzyaloshinskii–Moriya interactions (iDMIs) are derived. We calculated and verified the analytical expression for the energy flux density continuity for the spin-wave (SW) propagation through the ferromagnet with stepwise iDMI considering the boundary conditions mentioned. Analytical expressions for reflection, transmission coefficients, and the nonreciprocity factor are calculated in the case of SW propagation through a ferromagnet with the stepwise iDMI. Two different types of nonreciprocity effects for SW propagation through a ferromagnet with the stepwise interface Dzyaloshinskii–Moriya interaction are revealed for opposite orientations of Dzyaloshinskii–Moriya vector. The material parameters of a ferromagnet and the stepwise iDMIs are found for which the extremely high nonreciprocity factor (>10) is expected according to the results of calculations. The results of this article deepen the knowledge about the SW propagation control in magnonic devices.