Nondestructive Measurement of Nuclear Magnetization by Off-Resonant Faraday Rotation

We report on the nondestructive measurement of nuclear magnetization in $n$-GaAs via cavity enhanced Faraday rotation. In contrast with the existing optical methods, this detection scheme does not require the presence of detrimental out-of-equilibrium electrons. Specific mechanisms of the Faraday rotation are identified for (i) nuclear spins situated within the localized electron orbits, these spins are characterized by fast dynamics, (ii) all other nuclear spins in the sample characterized by much slower dynamics. Our results suggest that even in degenerate semiconductors nuclear spin relaxation is limited by the presence of localized electron states and spin diffusion, rather than by Korringa mechanism.

Figure 1

(a)–(c) Band diagrams with relative absorption probabilities ${\alpha }_{+}$, ${\alpha }_{-}$ for the two opposite light helicities: under ${\sigma }^{-}$ optical pumping (a) and in the presence of nuclear field only, for the transitions involving free (b) and bound (c) electron states. For clarity, only transitions from the heavy hole band are shown. (d) Sketch of the experimental setup. (e) Calculated transmission of the microcavity sample above the stop band (black), measured transmission of the probe beam (red), and photoluminescence (PL, blue). (f) FR scans for two samples, including preparation ($t<0$) and measurement ($t>0$) stage. Total pumping time is 10 min.

Figure 2

(a) Faraday rotation induced by nuclear polarization prepared by ${\sigma }^{-}$ pumping at $B_z=200\mathrm{G}$. Solid lines are fits to the biexponential decay. Inset: Effect of pump helicity on the nuclear FR. Decay times (b) and amplitudes (c) deduced from biexponential fit of the data shown in (a). Solid lines are calculated nuclear spin relaxation times. $T_b$, nuclei under the bound electron orbit; $T_D$, diffusion-limited relaxation; $T_K$, Korringa relaxation. (d) Nuclear repolarization experiment. Preparation during 6 min., ${\sigma }^{-}$ pumping, $B_z=100\mathrm{G}$. At $t=0$ the pump is switched off and alternating field is applied ($\pm 7\mathrm{G}$, right-hand scale). Static FR in the external field $B_z=\pm 7\mathrm{G}$ is shown by dashed lines.

Figure 3

NMR detected by “fast” (a),(b) and “slow” (c),(d) components of the FR at $B_z=200\mathrm{G}$. (a) FR measured after 2 min ${\sigma }^{-}$ pumping in the presence of $B_{\mathrm{rf}}$. Right-hand scale: Values of rf applied during pumping. (b) NMR spectrum reconstructed from a set of FR amplitudes measured as a function of the rf, applied during pumping. (c) FR measured after 5 min ${\sigma }^{-}$ pumping. At $t=60\mathrm{s}$, $B_{\mathrm{rf}}$ is switched on. Right-hand scale: Corresponding frequency profile. (d) The signal shown in (c) presented as a function of the rf, applied during measurement.