Dispersion relation of nutation surface spin waves in ferromagnets

TL;DR

This paper theoretically investigates nutation surface spin waves in ferromagnets, revealing their unique dispersion, slower velocities, backward nature, and the influence of inertia on precession spin wave frequencies.

Contribution

It introduces the concept of nutation surface spin waves and calculates their dispersion relations considering inertia effects in ferromagnetic thin films.

Findings

Nutation surface spin waves propagate at terahertz frequencies.

These waves are slower and backward compared to conventional spin waves.

Inertia decreases the frequency of precession spin waves depending on material properties.

Abstract

Inertia effects in magnetization dynamics are theoretically shown to result in a different type of spin waves, i.e. nutation surface spin waves, which propagate at terahertz frequencies in in-plane magnetized ferromagnetic thin films. Considering the magnetostatic limit, i.e. neglecting exchange coupling, we calculate dispersion relation and group velocity, which we find to be slower than the velocity of conventional (precession) spin waves. In addition, we find that the nutation surface spin waves are backward spin waves. Furthermore, we show that inertia causes a decrease of the frequency of the precession spin waves, namely magnetostatic surface spin waves and backward volume magnetostatic spin waves. The magnitude of the decrease depends on the magnetic properties of the film and its geometry.