Penetration depth model for optical alignment of nuclear spins in GaAs

A framework for predicting bulk NMR quantities in semi-insulating GaAs under optical alignment conditions is developed by combining literature penetration depth data with simple kinetic equations. The model accounts for the major photoconductivity and NMR intensity variations with photon energy, including the peak near $1.5\mathrm{eV}$. With the fitting parameters fixed, the photon-flux dependence of the NMR intensity is predicted quantitatively up to an energy shift. At the highest fluxes, we see the NMR intensity level off, suggesting that it is possible to completely fill the relevant electronic reservoir. The model also quantitatively fits the time dependence of the light-induced hyperfine shift. The experimental and modeling results have implications toward understanding the microscopic mechanism, and are consistent with nuclear polarization via bound electrons. Finally, the model makes experimentally testable predictions for the photon energy and flux dependences of the spin temperature and hyperfine shift of the NMR line.

Figure 1

(Color online) Comparison of two optical phenomena near the band gap of GaAs, (A) ${}^{69}\mathrm{Ga}$ NMR enhancement (Ref. 4) and (B) photoconductance, both with linear polarized light, $9.4\mathrm{T}$, and $\sim 10\mathrm{K}$.

Figure 2

Absorption coefficients for GaAs at low temperature for three different magnetic fields used as an input to our model.

Figure 3

(A) Conductance versus penetration depth for several laser intensities (in $\mathrm{W}∕{\mathrm{cm}}^2$) with the thickness fixed at $0.35\mathrm{mm}$, and (B) for several thicknesses with the laser intensity fixed at $1\mathrm{W}∕{\mathrm{cm}}^2$. (C) Optimal penetration depth versus laser intensity (more precisely $C_1{\varphi }_o$) for various thicknesses.

Figure 4

(Color online) Experimental and theoretical photoconductances overlaid, separate in inset, for $350\mu \mathrm{m}$ thick GaAs at $10\mathrm{T}$ field, $10\mathrm{K}$, and $70\mathrm{mW}$ laser power.

Figure 5

${}^{69}\mathrm{Ga}$ OPNMR signal for $350\mu \mathrm{m}$ thick GaAs at $10\mathrm{T}$ field, $10\mathrm{K}$, and $320\mathrm{mW}$ laser power. Experimental points are squares. Overlaid are predictions from an oversimplified free electron model (Theory 1) and a free electron model accounting for the energy-dependent electron-spin polarization (Theory 2).

Figure 6

Theoretical steady-state departure of the electron-spin polarization from equilibrium (relative to the initially excited departure) versus photon energy, for various laser powers.

Figure 7

(A) Comparison of the theoretical and experimental ${}^{71}\mathrm{Ga}$ OPNMR signal growth for short irradiation times at $1.503\mathrm{eV}$, $320\mathrm{mW}$, and $9.4\mathrm{T}$. (B) Theoretical ${}^{71}\mathrm{Ga}$ signal growth at $1.55\mathrm{eV}$, $320\mathrm{mW}$, and several different magnetic fields. Curves corresponding to 4 and $10\mathrm{T}$ are multiplied by factors of 2.8 and 12.2, respectively, to easily see the difference in curvatures at different magnetic fields.

Figure 8

Predicted decay of (A) laser intensity, (B) donor occupation fraction, (C) electron-spin polarization, and (D) ${}^{71}\mathrm{Ga}$ nuclear-spin polarization with depth into the crystal. Curves are shown for three photon energies (in eV, same for all four plots), for $320\mathrm{mW}$ of laser power, and for $20\mathrm{s}$ of irradiation, at $10\mathrm{T}$ field and $10\mathrm{K}$.

Figure 9

Theoretical ${}^{69}\mathrm{Ga}$ OPNMR signal versus photon energy, assuming the shallow-donor polarization mechanism, overlaid onto experimental data from Ref. 4.

Figure 10

Experimental dependence of ${}^{71}\mathrm{Ga}$ NMR signal on laser power for $1.501\mathrm{eV}$ (open squares) and $1.506\mathrm{eV}$ (filled squares) photon energies. Theoretical curves, shifted in energy by $6\mathrm{meV}$, are overlaid.

Figure 11

Reproduction of the data in Fig. 10, but at higher laser intensities (narrower beam). ${}^{71}\mathrm{Ga}$ NMR data are shown for photon energies of 1.504, 1.507, and $1.512\mathrm{eV}$. Similar-looking saturation curves were also observed at 1.509 and $1.511\mathrm{eV}$.

Figure 12

(A) Average $z$ component of ${}^{71}\mathrm{Ga}$ nuclear angular momentum, in units of $\hslash$, for nuclei contributing to the NMR signal. (B) Light-induced hyperfine shift of the ${}^{71}\mathrm{Ga}$ NMR line. Predictions are shown as a function of photon energy, after $2\mathrm{s}$ of irradiation, for two different laser powers, and for both circularly polarized helicities, at $10\mathrm{T}$ and $10\mathrm{K}$.

Figure 13

(A) Average $z$ component of ${}^{71}\mathrm{Ga}$ nuclear angular momentum, in units of $\hslash$, for nuclei contributing to the NMR signal. (B) Light-induced hyperfine shift of the ${}^{71}\mathrm{Ga}$ NMR line. Predictions are shown as a function of laser power, after $2\mathrm{s}$ of irradiation, for three different photon energies: $1.502\mathrm{eV}$ (short dashes), $1.515\mathrm{eV}$ (long dashes), and $1.558\mathrm{eV}$ (solid line), and for both circularly polarized helicities, at $10\mathrm{T}$ and $10\mathrm{K}$.

Figure 14

Light-induced shift of the ${}^{71}\mathrm{Ga}$ NMR frequency versus time of irradiation with $1.509\mathrm{eV}$, $123\mathrm{mW}$, and circularly polarized light. Theoretical curves are overlaid onto the data.