Spontaneous fluctuations in a magnetic Fe/Gd skyrmion lattice

Magnetic skyrmions are topological spin textures that exhibit classical or quantum quasiparticle behavior. A substantial amount of research has occurred in this field, both because of their unique electromagnetic properties and potential application for future nonvolatile memory storage applications, as well as fundamental questions on their topology and unique magnetic phases. Here, we investigate the fluctuation properties of a magnetic Fe/Gd skyrmion lattice, using short-pulsed x rays. We first measure spontaneous fluctuations of the skyrmion lattice phase and find an inherent, collective mode showing an underdamped oscillation with a relaxation of a couple of nanoseconds. Further observations track the response towards the continuous phase transition and a “critical-like” slowing down of fluctuations is observed well before the critical point. These results suggest that the skyrmion lattice phase never fully freezes into a static crystal. This constant state of fluctuation indicates that the physics of topological magnetic phases may have more in common with high-temperature superconductors with disorder.

Figure 1

The skyrmion lattice phase. (a) The magnetic field-temperature phase diagram of Fe/Gd [11]. (b) The average resonant scattering of the biskyrmion lattice phase right as the lattice solidifies (195 mT), time-averaged over about 40 s, or about $4.7\times {10}^3$ x-ray pulse pairs. The symmetry breaking of the sixfold symmetric pattern is caused by the biskyrmion units, or bound skyrmion pairs. (c) $S(q,0)$ for the skyrmion lattice order at $q=Q_s$, measured with resonant soft x-ray scattering tuned to the Gd $M_5$ edge. The integral of the intensity over the symmetrical skyrmion peaks only is shown with magnetic field, demonstrating the magnetic field conditions to create a stable skyrmion lattice phase at room temperature. The inset in (c) shows a closeup of the plot near the phase transition and designates the calculated Levanyuk-Ginzburg region (blue area), discussed below.

Figure 2

The skyrmion low-energy mode in Fe/Gd. (a) The normalized $S(q,t)$ shown here for the skyrmion lattice peaks where $q$ is given by $Q_s$ for a field of $H=210$ mT or $\left|h\right|=0.22$ [green circle in Fig. 1]. A damped oscillatory decay is observed for a low-energy mode of the skyrmion lattice for $f=0.25$ GHz. (b) The contrast data are evaluated for the time separation of 1.0 ns and plotted as a function of the pulse energy of the first pulse, amplitude $a_1$. This curve $C(q,a_1)$ shows no systematic changes with increasing pulse energy.

Figure 3

Intermediate scattering functions for skyrmion fluctuations. (a) $S(q,t)$ for a magnetic field of $\left|h\right|=0.18$ (blue) shows dynamics with a relaxation time of $\sim$20 ns with a fit to exponential behavior. (b) $S(q,t)$ for skyrmion fluctuations at $\left|h\right|=0.12$ (beige) shows no fluctuations in the observed range, with the gray dashed line indicating the $\left|h\right|=0.18$ data [also plotted in (c)] for comparison. (c) $S(q,t)$, or effectively $S(q,0)$, for the same phase region at $\left|h\right|=0.12$, which is defined by single-shot data. For this curve, since single-shot data are inherently $t=0$, the time axis represents the machine configuration of the electron accelerator for producing the time delay which was used when single shots were filtered from the two-pulse data. This single-pulse curve is used for normalizing any differences due to coherence or machine parameter changes with time delay. For all $S(q,t)$ curves in (a)–(c), single-pulse data were also collected for a given magnetic field, and plotted as square symbols broken from the rest of the curve as a guide to the eye. (d) The timescales $1/\tau$ of the skyrmion phase in units of GHz plotted with reduced field $h$. The colored symbols correspond to the data plotted with the same color in Figs. 2 and 3, as well as with the field points in Fig. 1.