Asymmetric spin wave dispersion due to a saturation magnetization gradient

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.

References in corpus (6)

• Realization of XNOR and NAND spin-wave logic gates
• The 2014 Magnetism Roadmap
• Interfacial Dzyaloshinskii-Moriya interaction in perpendicularly-magnetized Pt/Co/AlO${}_x$ ultrathin films measured by Brillouin light spectroscopy
• Asymmetric spin-wave dispersion due to Dzyaloshinskii-Moriya interaction in an ultrathin Pt/CoFeB film
• Magnonics: Spin Waves Connecting Charges, Spins and Photons
• Scattering of exchange spin waves from regions of modulated magnetization