Theory of nonreciprocal spin waves excitation in spin-Hall oscillators with Dzyaloshinkii-Moriya interaction

TL;DR

This paper develops a two-dimensional analytical model to describe nonreciprocal spin wave excitation in spin-Hall oscillators with interfacial Dzyaloshinskii-Moriya interaction, predicting threshold currents and mode profiles.

Contribution

It introduces a novel analytical framework for understanding spin wave excitation in the presence of i-DMI, validated by micromagnetic simulations.

Findings

Spin wave frequency exhibits quadratic red shift with i-DMI strength.

Threshold current shows weak dependence on i-DMI at small/moderate values.

Analytical results are confirmed by micromagnetic simulations.

Abstract

A two-dimensional analytical model for the description of the excitation of nonreciprocal spin waves by spin current in spin-Hall oscillators in the presence of the interfacial Dzyaloshinskii-Moriya interaction (i-DMI) is developed. The theory allows one to calculate the threshold current for the excitation of spin waves, as well as the frequencies and spatial profiles of the excited spin wave modes. It is found, that the frequency of the excited spin waves exhibits a quadratic red shift with the i-DMI strength. At the same time, in the range of small and moderate values of the i-DMI constant, the averaged wave number of the excited spin waves is almost independent of the i-DMI, which results in a rather weak dependence on the i-DMI of the threshold current of the spin wave excitation. The obtained analytical results are confirmed by the results of micromagnetic simulations.