Nuclear spin cooling by helicity-alternated optical pumping at weak magnetic fields in $n$-GaAs

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Nuclear spin cooling by helicity-alternated optical pumping at weak magnetic fields in $n$ -GaAs

P. S. Sokolov, M. Yu. Petrov, K. V. Kavokin, A. S. Kurdyubov, M. S. Kuznetsova, R. V. Cherbunin, S. Yu. Verbin, N. K. Poletaev, D. R. Yakovlev, D. Suter, and M. Bayer

Phys. Rev. B 96, 205205 – Published 28 November 2017

Abstract

The spin dynamics of localized donor-bound electrons interacting with the nuclear spin ensemble in $n$ -doped GaAs epilayers is studied using nuclear spin polarization by light with modulated circular polarization. We show that the observed buildup of the nuclear spin polarization is a result of competition between nuclear spin cooling and nuclear spin warmup in the oscillating Knight field. The developed model allows us to explain the dependence of nuclear spin polarization on the modulation frequency and to estimate the equilibration time of the nuclear spin system that appears to be shorter than the transverse relaxation time $T_{2}$ determined from nuclear magnetic resonance.

Received 18 July 2017
Revised 2 October 2017

DOI:https://doi.org/10.1103/PhysRevB.96.205205

Physics Subject Headings (PhySH)

Optical pumping Semiconductors Spin polarization Spin pumping Spin relaxation

Doped semiconductors III-V semiconductors

Photoluminescence

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

P. S. Sokolov^1,2, M. Yu. Petrov², K. V. Kavokin^2,3, A. S. Kurdyubov², M. S. Kuznetsova², R. V. Cherbunin², S. Yu. Verbin², N. K. Poletaev³, D. R. Yakovlev^1,3, D. Suter⁴, and M. Bayer^1,3

¹Experimentelle Physik 2, Technische Universität Dortmund, D-44221 Dortmund, Germany
²Spin Optics Laboratory, Saint Petersburg State University, 198504 St. Petersburg, Russia
³Ioffe Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
⁴Experimentelle Physik 3, Technische Universität Dortmund, D-44221 Dortmund, Germany

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Vol. 96, Iss. 20 — 15 November 2017

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Images

Figure 1
(a) PL spectrum (excitation energy $E_{exc} = 1.55$ eV) of $n$ -doped GaAs measured at $B = 0$ T. (b) Spectral dependence of the PL circular polarization degree. (c) Circular polarization degree vs transverse magnetic field (Voigt geometry, $B_{z} = 0)$ measured at alternating helicity of excitation $f_{\mod} = 50$ kHz. The electron spin relaxation time $τ_{s} = 20$ ns is evaluated. (d) Magnetic-field dependencies of the circular polarization degree (Faraday configuration, $B_{x} = 0)$ measured for the $D^{0} X$ transition $(E_{\det} = 1.514$ eV) at fast modulation of the helicity of excitation $f_{\mod} = 200$ kHz (black curve) and $f_{\mod} = 1$ kHz (green curve). The corresponding electron correlation time $τ_{c} = 310$ ps. Solid lines in panels (c) and (d) result from fitting with Eqs. (1) and (2), respectively.
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Figure 2
(a) Manifestation of the additional tiny PR signal in small longitudinal fields (Faraday configuration, $B_{x} = 0)$ measured for the $D^{0} X$ transition $(E_{\det} = 1.514$ eV) at continuous-wave (CW) excitation. (b) Recovery of the PL circular polarization degree by a longitudinal magnetic field in the absence of a transverse magnetic field (circles) and in the presence of $B_{x} = 1$ mT (squares). (c) PR curves measured at different frequencies of modulation in the presence of a transverse magnetic field. Solid lines in panels (b) and (c) result from fitting with a bell-shaped function: $ρ_{c} (B_{z}) = ρ_{sat} - A_{PR} / (1 + B_{z}^{2} / Δ_{B}^{2})$ , with $ρ_{sat}, A_{PR}$ , and $Δ_{B}$ being fitting parameters.
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Figure 3
Calculated Overhauser fields $(B_{N})$ vs $f_{\mod}$ . Solid lines are fits with Lorentzian functions given by Eq. (13), from which the values of the cutoff frequencies $ω_{1 / 2}$ are extracted. The inset shows the Overhauser fields $\log_{10} [B_{N}]$ for different powers of optical excitation.
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Figure 4
(a) Electron mean spin polarization (squares) and its fit with a saturating exponential function: $S_{0} (P_{exc}) = S_{\infty} [1 - exp (- P_{exc} / P_{0})]$ (solid line). The fit parameters are $S_{\infty} = 0.041$ and $P_{0} = 2.6$ mW. (b) Power dependence of the electron correlation time. The solid green line shows a linear fit with $τ_{c} = 320$ ps. (c) Cutoff frequency of the Overhauser field buildup vs excitation power $P_{exc}$ (triangles). The solid line shows a fit of the data with Eq. (14). The inset shows the corresponding nuclear spin correlator ${\hat{G}}_{0}^{'}$ as a result of normalization of $ω_{1 / 2}$ to $S_{0}$ . The solid black line shows a linear fit with ${\hat{G}}_{0}^{'} = 12 μ s$ .
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Figure 5
Normalized real Fourier component of the correlator of the nuclear-nuclear interactions vs frequency for $B = 0$ (dashed line) and $B = 1$ mT (solid lines) calculated for the ${}^{75}{As}$ nuclear species. The filled area defines the range of frequencies $ω < ω_{1 / 2}$ observed in the experiment. The black filled circle represents the value of the correlator determined from experiment [see the inset in Fig. 4]. The thick red line represents the ${\hat{G}}_{ω}^{'}$ calculated for the best fit of $G_{0}^{'}$ $(T_{2} = 55 μ s)$ , and the thin, solid, and dashed black lines are calculated for the spin-spin relaxation time $T_{2} = {(γ_{N} B_{L})}^{- 1} \approx 114 μ s$ .
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