# Tag Archives: Spin Waves

## A First-Rate Experiment: The Damon-Eshbach Mode

One of the things I have tried to do on this blog is highlight excellent experiments in condensed matter physics. You can click the following links for posts I’ve written on illuminating experiments concerning the symmetry of the order parameter in cuprate superconductors, Floquet states on the surface of topological insulators, quantized vortices in superfluid 4He, sonoluminescence in collapsing bubbles and LO-TO splitting in doped semiconductors, just to highlight a few. Some of these experiments required some outstanding technical ingenuity, and I feel it important to document them.

In a similar vein, there was an elegant experiment published in PRL back in 1977 by P. Grunberg and F. Metawe that shows a rather peculiar spectral signature observed with Brillouin scattering in thin film EuO. The data is presented below. For those who don’t know, Brillouin scattering is basically identical to Raman scattering, but the energy scale observed is much lower, typically a fraction of a $cm^{-1}$ ~ 5 $cm^{-1}$ (1 $cm^{-1} \approx$ 30GHz). Brillouin scattering is often used to observe acoustic phonons.

From the image above there is immediately something striking in the data: the peak labeled M2 only shows up on either the anti-Stokes side (the incident light absorbs a thermally excited mode) or the Stokes side (the incident light excites a mode) depending on the orientation of the magnetic field. In his Nobel lecture, Grunberg revealed that they discovered this effect by accident after they had hooked up some wires in the opposite orientation!

Anyway, in usual light scattering experiments, depending on the temperature, modes are observed on both sides (Stokes and anti-Stokes) with an intensity difference determined by Bose-Einstein statistics. In this case, two ingredients, the slab geometry of the thin film and the broken time-reversal symmetry give rise to the propagation of a surface spin wave that travels in only one direction, known as the Damon-Eshbach mode. The DE mode propagates on the surface of the sample in a direction perpendicular to the magnetization, B, of the thin film, obeying a right-hand rule.

When one thinks about this, it is truly bizarre, as the dispersion relation would for the DE mode on the surface would look something like the image below for the different magnetic field directions:

One-way propagation of Damon Eshbach Mode

The dispersion branch only exists for one propagation direction! Because of this fact (and the conservation of momentum and energy laws), the mode is either observed solely on the Stokes or anti-Stokes side. This can be understood in the following way. Suppose the experimental geometry is such that the momentum transferred to the sample, q, is positive. One would then be able to excite the DE mode with the incident photon, giving rise to a peak on the Stokes side. However, the incident photon in the experiment cannot absorb the DE mode of momentum -q, because it doesn’t exist! Similar reasoning applies for the magnetization in the other direction, where one would observe a peak in only the anti-Stokes channel.

There is one more regard in which this experiment relied on a serendipitous occurrence. The thin film was thick enough that the light, which penetrates about 100 Angstroms, did not reach the back side of the film. If the film had been thin enough, a peak would have shown up in both the Stokes and anti-Stokes channels, as the photon would have been able to interact with both surfaces.

So with a little fortune and a lot of ingenuity, this experiment set Peter Grunberg on the path to his Nobel prize winning work on magnetic multilayers. As far as simple spectroscopy experiments go, one is unlikely to find results that are as remarkable and dramatic.