Anomalous-Filling-Factor-Dependent Nuclear-Spin Polarization in a 2D Electron System

Spin-related electronic phase transitions in the fractional quantum Hall regime are accompanied by a large change in resistance. Combined with their sensitivity to spin orientation of nuclei residing in the same plane as the 2D electrons, they offer a convenient electrical probe to carry out nuclear magnetometry. Despite conditions which should allow both electronic and nuclear-spin subsystems to approach thermodynamic equilibrium, we uncover for the nuclei a remarkable and strongly electronic filling-factor-dependent deviation from the anticipated thermal nuclear-spin polarization.

Figure 1

Location of the $2/3$-spin transition as a function of filling ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$ at which the sample is allowed to relax. Right insets: Sample cross section and evolution of the composite fermion Landau levels with density or $B$ field at fixed $\nu =2/3$. Left inset: Time sequence for current (in nA), $B$ field, and filling factor (gate voltage). For each value of ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$, $B$ is swept discontinuously from 3 to 9 T in 0.1 T steps. The gate voltage tracks $B$ during sweep operations to maintain fixed filling ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$ at all times. After a new field value has been set, the 2DES is left to relax for 180 s. Subsequently, the gate voltage is adjusted for a short excursion to ${\nu }_{{\mathrm{R}}_{\mathrm{S}\mathrm{D}}}=0.66$ and simultaneously the current is turned on. $R_{\mathrm{S}\mathrm{D}}$ is recorded after 2 s to account for time constants of the signal recovery scheme. The current is turned off and the original filling ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$ restored. $B$ is run up to the next value and the entire procedure is repeated up to 9 T. The field value at which $R_{\mathrm{S}\mathrm{D}}({\nu }_{{\mathrm{R}}_{\mathrm{S}\mathrm{D}}}=0.66)$ reaches a minimum (spin transition) is plotted at abscissa ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$. To acquire the next data point, the sample is kept at the upcoming value of ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$ while ramping down the field back to 3 T. ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$ is scanned downwards in 0.01 steps from 1.1 to 0.25 and upwards from 1.1 to 1.8. The bottom color panels are the outcome of a prolonged measurement sequence. They visualize the spin transition for selected values of ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$ by plotting $R_{\mathrm{S}\mathrm{D}}$ for the full $B$-field range and the filling factor interval covering the $2/3$ and $3/5$ FQH states. The color scale for $R_{\mathrm{S}\mathrm{D}}$ spans values from $0.38h/e^2$ (blue) to $1.55h/e^2$ (red). Here also, a 180 s pause at ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$ precedes the collection of every single data point making up these graphs. For some values of ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$, either a broad minimum or two separate minima are observed in $R_{\mathrm{S}\mathrm{D}}({\nu }_{R_{\mathrm{S}\mathrm{D}}}=0.66)$. This is pointed out by placing multiple dots at the same abscissa, connected either by a solid black line or a dashed black line, respectively. The color panel for ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}=0.78$ illustrates this issue.

Figure 2

Example of determining the location of the spin transition for ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}=0.52$. The inset depicts the path traced in the $(B,\nu )$ plane in the course of collecting the $R_{\mathrm{S}\mathrm{D}}$ values. The corresponding time sequence is plotted in Fig. 1. For the entire experiment, $99.3\%$ of the time is spend at ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$.

Figure 3

Temperature dependence of the transition field $B_{\mathrm{t}\mathrm{r}}$ for selected ${\nu }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$. Sample and temperature sensor are in close proximity and both submerged in the ${\mathrm{H}\mathrm{e}}^3/{\mathrm{H}\mathrm{e}}^4$ mixture. The data were taken during a separate cooldown. This accounts for the small discrepancy with the $B_{\mathrm{t}\mathrm{r}}$ fields plotted in Fig. 1.