Evidence for Skyrmion Crystallization from NMR Relaxation Experiments

A resistively detected NMR technique was used to probe the two-dimensional electron gas in a $\mathrm{GaAs}/\mathrm{AlGaAs}$ quantum well. The spin-lattice relaxation rate $(1/T_1)$ was extracted at near complete filling of the first Landau level by electrons. The nuclear spin of ${}^{75}\mathrm{As}$ is found to relax much more efficiently with $T\to 0$ and when a well developed quantum Hall state with $R_{xx}\simeq 0$ occurs. The data show a remarkable correlation between the nuclear spin relaxation and localization. This suggests that the magnetic ground state near complete filling of the first Landau level may contain a lattice of topological spin texture, i.e., a Skyrmion crystal.

Figure 1

Magnetotransport $R_{xx}$ for the two-dimensional electron system. The bottom $x$ axis shows the applied magnetic field and the upper $x$ axis the corresponding filling factors. A schematic of the NMR experiment is shown in the upper left corner. The inset at the center of the graph shows an example of resistively detected NMR resonance for the ${}^{75}\mathrm{As}$ nucleus and at filling factor $\nu =0.86$.

Figure 2

Nuclear spin-lattice relaxation time $T_1$ for ${}^{75}\mathrm{As}$ at various electronic temperatures $T_e$ and filling factors, $\nu$. The thin dotted lines are guides to the eye. The inset shows a typical experiment from which $T_1$ is determined (see text). The solid line is a fit to a single exponential.

Figure 3

Nuclear spin-lattice relaxation rate $(1/T_1)$ for ${}^{75}\mathrm{As}$ versus $R_{xx}$ at the same filling factors as in Fig. 2. The straight line is a linear fit to the $\nu =0.86$ data. $T_m$ (defined in the text) is shown in the inset (filled circles) versus the partial filling factor, $|\nu -1|$. The solid line is a guide to the eye, and the dotted line an extrapolation to $T=0$. The dash-dotted line is a theoretical estimate for the classical transition temperature of a Skyrme crystal [8] (see text).