Asymmetric spin wave dispersion due to a saturation magnetization gradient

TL;DR

This paper shows that a gradient in saturation magnetization causes non-reciprocal spin wave propagation and asymmetric dispersion, enabling unidirectional spin wave control for magnonic circuits.

Contribution

It introduces a theoretical and simulation-based demonstration that $M_s$ gradients induce asymmetric dispersion and unidirectional spin wave propagation, advancing magnonic device design.

Findings

$M_s$ gradient causes non-reciprocal spin wave propagation

Asymmetric dispersion relation due to $M_s$ gradient

Potential for unidirectional spin wave propagation

Abstract

We demonstrate using micromagnetic simulations and a theoretical model that a gradient in the saturation magnetization ($M_s$) of a perpendicularly magnetized ferromagnetic film induces a non-reciprocal spin wave propagation and, consequently an asymmetric dispersion relation. The $M_s$ gradient adds a linear potential to the spin wave equation of motion consistent with the presence of a force. We consider a transformation from an inertial reference frame in which the $M_s$ is constant to an accelerated reference frame where the resulting inertial force corresponds to the force from the $M_s$ gradient. As in the Doppler effect, the frequency shift leads to an asymmetric dispersion relation. Additionally, we show that under certain circumstances, unidirectional propagation of spin waves can be achieved which is essential for the design of magnonic circuits. Our results become more relevant in light of recent experimental works in which a suitable thermal landscape is used to dynamically modulate the saturation magnetization.