NMR in the solid phase of two-dimensional electrons at high magnetic fields

We report on a magnetic resonance study in the electron solid phase of a low-disorder $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ sample at very high magnetic fields using a resistively detected NMR technique. An anomalous dispersivelike line shape is observed at the onset of the electron solid in the vicinity of the Landau filling $\nu =\frac{2}{9},\frac{1}{5}$ fractional quantum Hall state, reminiscent of the line shape observed near filling factor $\nu \sim 1$. In contrast to this filling factor region, the spin-lattice relaxation time $T_1$ in the electron solid is found to be very long, and does not correlate with either $R_{xx}$ or the Landau filling factor. The dispersivelike line shapes observed in this regime suggests that the intricate interplay between the nuclear spin and the electronic transport may be modified by the formation of the electron solid.

Figure 1

(Color online) Magnetoresistance $R_{xx}$ versus the magnetic field $H_0$ at $T\sim 40\mathrm{mk}$. Filling factors of interest are indicated by arrows. A schematic of the NMR experiment is shown in the upper left corner. The shaded area shows the filling factor ranges where an electron solid is expected to form.

Figure 2

(Color online) Lower panel: magnetoresistance $R_{xx}$ vs the filling factor $\nu$ around the electron solid region at $T\sim 40\mathrm{mK}$. The filled circles and letters denote the filling factors where the resistively detected NMR spectrum was obtained. The filling factors where in addition relaxation time experiments were performed are shown with inverted triangles. Upper panel: the line shape obtained for the filling factors $a–e$ is shown with a normalized frequency axis as to allow direct comparison of the data (see text).

Figure 3

(Color online) Upper panel: resistively detected nuclear spin relaxation experiment. The inset shows the NMR spectrum with the off- (f1) and on-resonance (f2) frequencies. Lower panel: Spin-lattice relaxation rate $(1∕T_1)$ for ${}^{75}\mathrm{As}$ versus the filling factor $\nu$ between and near the $\nu =\frac{1}{5}$ and $\nu =\frac{2}{9}$ FQHE states.