Nanosecond X-Ray Photon Correlation Spectroscopy on Magnetic Skyrmions

We report an x-ray photon correlation spectroscopy method that exploits the recent development of the two-pulse mode at the Linac Coherent Light Source. By using coherent resonant x-ray magnetic scattering, we studied spontaneous fluctuations on nanosecond time scales in thin films of multilayered Fe/Gd that exhibit ordered stripe and Skyrmion lattice phases. The correlation time of the fluctuations was found to differ between the Skyrmion phase and near the stripe-Skyrmion boundary. This technique will enable a significant new area of research on the study of equilibrium fluctuations in condensed matter.

Figure 1

Schematic depicting the geometry of the experiment at the LCLS [25], including the monochromator, the MCP detector which is used to sort the relative pulse height amplitude between pulse pairs, the pulse pair separated by time $\tau$, the sample and applied magnetic field, the CCD mask to limit x-ray illumination on the CCD to a small region of interest, and the commercial (Andor) CCD. Inset: a cartoon of a single spin configuration of a chiral magnetic Skyrmion, a single unit of the Skyrmion lattice, and the resonant x-ray scattering from the Skyrmion hexagonal lattice, as measured at the ALS.

Figure 2

Probability to scatter $k$ photons, $P(k)$, for $k=1-4$ photons at the Skyrmion peak measured through coherent soft x-ray resonant scattering in Fig. 2(a)–(d), respectively. The distributions are plotted with $\overline{k}$, the average photons per speckle. The black points are the binned data, the shades of green represent the range of contrast calculations for this range of data, and the red curve is the best fit of the data to Eq. (1).

Figure 3

Contrast vs time delay in the Skyrmion phase at 210 mT. The blue data points are calculated based on a fit to $\alpha (1)$, the ratio between $P(1)$ and $P(2)$, using Eq. (1). A fit to $P(3)$ is shown for comparison (red data points). The orange curve represents a fit to an exponential, yielding a decay time of 4 ns. The (qualitative) oscillatory curve shown in gray is one possible solution for the apparent deviation from a simple exponential decay.

Figure 4

Contrast vs time delay near the Skyrmion-stripe phase transition at 200 mT. Blue data points are calculated based on a fit to $\alpha (1)$, the ratio between $P(1)$ and $P(2)$, using Eq. (1), with the fit for $P(3)$ shown for comparison (red data points). The blue curve represents a decay time consistent with the data, estimated at 300 ps.