Spin-waves in thin films with Dzyaloshinskii-Moriya interaction

H T Diep,Sahbi El Hog,Henryk Puszkarski

doi:10.1063/1.5006268

Abstract

Using the Green’s function method, we calculate the spin-wave (SW) spectrum in a thin film with quantum Heisenberg spins interacting with each other via an exchange interaction J and a Dzyaloshinskii-Moriya interaction of magnitude D. Due to the competition between J and D, the ground state is non collinear. We show that for large D, the first mode in the SW spectrum is proportional to the in plane wave-vector k at the limit k tending to zero. For small D, it is proportional to k2. We show that the surface modes may occur depending on the surface exchange interaction. We calculate the layer magnetizations at temperature T and the transition temperature as a function of the film thickness.

Highlights

In thin films, due to the existence of surfaces, the spin-wave (SW) spectrum is modified with respect to the bulk spectrum
The fact that the DM interaction affects only the first mode can be verified by experiments which measure spin-wave spectra such as neutron scattering.[16]
For SW higher-energy modes, there has been an experimental breakthrough with the spin polarized electron energy loss spectroscopy (SPEELS): this technique allows us to detect very high-energy surface magnons, up to 240 meV in ultrathin ferromagnetic films.[17]

Summary

INTRODUCTION

Due to the existence of surfaces, the spin-wave (SW) spectrum is modified with respect to the bulk spectrum. Due to the lack of neighbors at surface there exist low-energy localized surface modes which reduce the magnetization and the transition temperature.[1] Much has been theoretically understood on simple systems where spin configurations are collinear. In frustrated systems such as helimagnets or frustrated systems, the spin configuration is not collinear, making the calculation harder when including the surface. We have calculated the SW spectrum in some frustrated[2,3] and in helimagnetic thin films.[4,5]. Discussion on experimental connection and concluding remarks are given in Sect.

MODEL AND GROUND STATE

THIN FILM

DISCUSSION AND EXPERIMENTAL