Spontaneous Magnetic Superdomain Wall Fluctuations in an Artificial Antiferromagnet

Collective dynamics often play an important role in determining the stability of ground states for both naturally occurring materials and metamaterials. We studied the temperature dependent dynamics of antiferromagnetically ordered superdomains in a square artificial spin lattice using soft x-ray photon correlation spectroscopy. We observed an exponential slowing down of superdomain wall motion below the antiferromagnetic onset temperature, similar to the behavior of typical bulk antiferromagnets. Using a continuous time random walk model we show that these superdomain walls undergo low-temperature ballistic and high-temperature diffusive motions.

Figure 1

(a) SEM image of a square ASL sample with a schematic of the block-spin lattice and AFM-ordered block spins. (b) ASL diffraction pattern ($T=335\mathrm{K}$) in reciprocal lattice coordinates $(H,K)=\mathbf{(}{Q}_x/(2\pi /a),Q_y/(2\pi /b)\mathbf{)}$, where $a=b=\text{lattice}$ constant (600 nm). Detector intensity is plotted on a log scale in arbitrary units (note color scale). A half-integer AFM Bragg peak is clearly visible at the center of the box bounded by black dotted lines. (c) Temperature dependence of detector intensity along a cut through time-averaged AFM Bragg peak. Inset shows the integrated intensity and peak width obtained from a Lorentzian fit.

Figure 2

(a) Speckles observed for a single AFM Bragg peak at three different temperatures. At 335 K we observe a single AFM superdomain, and growth of speckle number with increasing temperature. (b) Waterfall plots showing the time evolution of speckle positions for various temperatures. Each horizontal line represents a cut through an AFM peak capturing the intensity vs pixel position at some time $t$. One pixel is approximately 0.005 in K. Intensities are normalized to the maximum intensity for each temperature as given in Fig. 1. Spontaneous domain wall fluctuations are observed at all temperatures, but decrease in number with reduced temperature.

Figure 3

(a) Intermediate scattering function $|F{|}^2$ calculated for speckle patterns at different temperatures. Solid lines are random walk fits to the initial decay. Temperature dependence of (b) time cost, ${\tau }_{\mathrm{DW}}$, and (c) exponent $\alpha$ in the model. [Inset in (b)] Random walk model schematic.

Figure 4

(a) Temperature dependence of decay time ${\tau }_F$, compared with ${\tau }_{\mathrm{DW}}$. (b) Compressed exponent $\gamma$.