Nonreciprocity of spin waves in a double layer ferromagnet with Dzyaloshinskii-Moriya interactions

TL;DR

This paper derives boundary conditions and analytical expressions for spin-wave propagation in double layer ferromagnets with Dzyaloshinskii-Moriya interactions, revealing two types of nonreciprocity effects and conditions for high nonreciprocity.

Contribution

It introduces new boundary conditions and analytical formulas for spin-wave nonreciprocity in ferromagnetic bilayers with Dzyaloshinskii-Moriya interactions, advancing magnonic device control.

Findings

Two types of nonreciprocity effects identified.

High nonreciprocity factor (>10) achievable with specific parameters.

Analytical expressions for reflection and transmission coefficients derived.

Abstract

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.