Suppression of Standing Spin Waves in Low-Dimensional Ferromagnets

We examine the experimental absence of standing spin wave modes in thin magnetic films, by means of atomistic spin dynamics simulations. Using Co on Cu(001) as a model system, we demonstrate that by increasing the number of layers, the optical branches predicted from adiabatic first-principles calculations are strongly suppressed, in agreement with spin-polarized electron energy loss spectroscopy measurements reported in the literature. Our results suggest that a dynamical analysis of the Heisenberg model is sufficient in order to capture the strong damping of the standing modes.

Figure 1

(a) Adiabatic magnon spectra for 8 ML $\mathrm{Co}/\mathrm{Cu}(001)$. Note the optical branches. (b) Comparison between the acoustic branches for systems of different thickness with the SPEELS data reported for 8 ML Co on Cu(001) [3].

Figure 2

Dynamical structure factor $S(\mathbf{q},\omega )$ obtained from ASD simulations of 8 ML $\mathrm{Co}/\mathrm{Cu}(001)$. Top left: Magnon spectrum calculated at 1 K, with $\alpha =3\times {10}^{-4}$. Bottom left: Magnon spectrum calculated at 300 K, with $\alpha =0.05$. Right: Profile of $S(\mathbf{q},\omega )$, in which the peaks associated with the optical branches are more easily visible.

Figure 3

Magnons in an atomic chain, plotted in the $xy$ plane. (a) Long wavelength acoustic magnons; (b) acoustic magnons at the BZ boundary; and (c) optical mode of long wavelength magnons for a system with a two atom basis. In each case the unit cell is outlined by a dashed box.

Figure 4

Dynamical structure factor $S(\mathbf{q},\omega )$ measured over the first and second Brillouin zones, for $\mathrm{Co}/\mathrm{Cu}(001)$ systems consisting of 2, 3, and 8 monolayers.