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.
Highlights
From the classical point of view, spin waves are collective excitations of magnetically ordered materials, that is, waves of precession of the magnetization [1,2], for example in thin magnetic films [3,4,5], layered magnetic structures [6,7], periodic magnetic crystals [8,9], and nanometer-sized structures [10]
Waves having predominantly inertial nature appear in ferromagnetic thin films, which we call here nutation surface spin waves
Note that the n-magnetostatic surface spin waves (MSSWs) are conventional precession spin waves whose dispersion is modified by inertia effects due to nutation [Figs. 2(b) and 2(e)], while nutation surface spin waves are solely due to nutation which occurs on top of the background precession
Summary
From the classical point of view, spin waves are collective excitations of magnetically ordered materials, that is, waves of precession of the magnetization [1,2], for example in thin magnetic films [3,4,5], layered magnetic structures [6,7], periodic magnetic crystals [8,9], and nanometer-sized structures [10]. Waves having predominantly inertial nature appear in ferromagnetic thin films, which we call here nutation surface spin waves Since these waves have terahertz frequencies (compared to typically GHz frequencies of other spin wave modes), they can be plotted as a small deviation on top of a “frozen” precession motion [Fig. 1(b)]. Note that the n-MSSWs are conventional precession spin waves whose dispersion is modified by inertia effects due to nutation [Figs. 2(b) (bottom) and 2(e)], while nutation surface spin waves are solely due to nutation which occurs on top of the background precession
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