Spin-wave calculations for magnetic stacks with interface Dzyaloshinskii-Moriya interaction

Hedi Bouloussa, Yves Roussigné, Mohamed Belmeguenai, Andrey Stashkevich, Salim Mourad Chérif, Jiawei Yu, and Hyunsoo Yang

Phys. Rev. B 98, 024428 – Published 31 July 2018

Abstract

We present a complete calculation of spin waves in magnetic stacks, including the interfacial Dzyaloshinskii-Moriya interaction (iDMI) as a boundary condition, and discuss the influence of interlayer coupling and magnetic anisotropy on the spin-wave nonreciprocity. We show that the usual simple approach relating the iDMI strength to the slope of the spin-wave nonreciprocity versus the spin-wave number, in the case of a thin ferromagnetic film in contact with a heavy metal exhibiting a strong-orbit coupling, is not valid in many more complex structures. In the case of stacks made of identical magnetic layers, an analytical method allowed us to check that the effect of iDMI on the entire structure is captured by including the total thickness of the ferromagnetic layers. The experimental data obtained for some systems by means of Brillouin light scattering are analyzed through the presented models.