Resistively detected NMR of the $\nu =1$ quantum Hall state: A tilted magnetic field study

Previous resistively detected NMR (RDNMR) studies on the $\nu \approx 1$ quantum Hall state have reported a “dispersionlike” line shape and extremely short nuclear-spin-lattice relaxation times, observations which have been attributed to the formation of a skyrme lattice. Here we examine the evolution of the RDNMR line shape and nuclear-spin relaxation for Zeeman:Coulomb energy ratios ranging from 0.012 to 0.036. According to theory, suppression of the skyrme crystal, along with the associated Goldstone mode nuclear-spin-relaxation mechanism, is expected at the upper end of this range. However, we find that the anomalous line shape persists at high Zeeman energy, and only a modest decrease in the RDNMR-detected nuclear-spin-relaxation rate is observed.

Figure 1

Longitudinal magnetoresistance traces acquired at $\theta =0°$ (top), where $\nu =1$ occurs at 5.25 T and in the tilted field with $\theta =68°$, where $\nu =1$ occurs at 13.9 T. In the $\theta =0°$ orientation, $R_{xx}$ was measured using two different excitation currents: 10 and 100 nA. The bath temperature was maintained at or below $\sim 20\text{mK}$. The circle on the lower trace indicates the location at which the spectrum in Fig. 2c was recorded.

Figure 2

(a) ${}^{75}\text{A}\text{s}$ RDNMR spectra acquired at bath temperatures of 31, 58, 85, 116, and 173 mK at 5.185 T and 100 nA ($\theta =0°$, $\nu =0.89$, and $\eta =0.012$). Off-resonance resistances at these temperatures were 200, 250, 545, 1250, and $2870\Omega$, respectively. (b) ${}^{75}\text{A}\text{s}$ RDNMR spectrum acquired at 4.0 T ($\theta =0°$ and $\nu =1.125$), showing a single peak with negative resistance change. The spectrum was recorded at a sweep rate of 166 Hz/s. (c) RDNMR spectrum of ${}^{75}\text{A}\text{s}$ at 16 T ($\nu =0.86$, $\theta =68°$, and $\eta =0.036$). The solid curve represents the fit to a superposition of Gaussian line-shape functions.

Figure 3

(a) Representative saturation-recovery traces at 5.42 T at 38 and 85 mK. Inset: raw $R_{xx}\left(t\right)$ traces obtained on the LF and HF components. (b) Temperature dependences of the ${}^{75}\text{A}\text{s}$ $T_1$ at the magnetic fields and filling factors indicated. The 5.42 T data were collected at slightly lower density during a separate cool down.