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Longitudinal spin relaxation of donor-bound electrons in direct band-gap semiconductors

Xiayu Linpeng, Todd Karin, M. V. Durnev, Russell Barbour, M. M. Glazov, E. Ya. Sherman, S. P. Watkins, Satoru Seto, and Kai-Mei C. Fu
Phys. Rev. B 94, 125401 – Published 1 September 2016
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  • INTRODUCTION
  • SAMPLES AND EXPERIMENTAL TECHNIQUE
  • EXPERIMENTAL RESULTS
  • THEORY
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • Supplemental Material
    References

    Abstract

    We measure the donor-bound electron longitudinal spin-relaxation time (T1) as a function of magnetic field (B) in three high-purity direct band-gap semiconductors: GaAs, InP, and CdTe, observing a maximum T1 of 1.4, 0.4, and 1.2 ms, respectively. In GaAs and InP at low magnetic field, up to ∼2 T, the spin-relaxation mechanism is strongly density and temperature dependent and is attributed to the random precession of the electron spin in hyperfine fields caused by the lattice nuclear spins. In all three semiconductors at high magnetic field, we observe a power-law dependence T1∝B−ν with 3≲ν≲4. Our theory predicts that the direct spin-phonon interaction is important in all three materials in this regime in contrast to quantum dot structures. In addition, the “admixture” mechanism caused by Dresselhaus spin-orbit coupling combined with single-phonon processes has a comparable contribution in GaAs. We find excellent agreement between high-field theory and experiment for GaAs and CdTe with no free parameters, however a significant discrepancy exists for InP.

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    • Received 18 May 2016

    DOI:https://doi.org/10.1103/PhysRevB.94.125401

    ©2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Spin relaxation
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Xiayu Linpeng1, Todd Karin1, M. V. Durnev2, Russell Barbour1, M. M. Glazov2, E. Ya. Sherman3,4, S. P. Watkins5, Satoru Seto6, and Kai-Mei C. Fu1,7

    • 1Department of Physics, University of Washington, Seattle, Washington 98195, USA
    • 2Ioffe Institute, 194021 St.-Petersburg, Russia
    • 3Department of Physical Chemistry, The University of the Basque Country, 48080 Bilbao, Spain
    • 4IKERBASQUE Basque Foundation for Science, Bilbao, Spain
    • 5Department of Physics, Simon Fraser University, Burnaby, BC, Canada V5A-1S6
    • 6National Institute of Technology, Ishikawa College, Tsubata, Kahoku, Ishikawa 929-0392, Japan
    • 7Department of Electrical Engineering, University of Washington, Seattle, Washington 98195, USA

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    Issue

    Vol. 94, Iss. 12 — 15 September 2016

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    • Figure 1
      Figure 1

      (a) Energy level diagram for the InP donor system. (b) Photoluminescence spectrum of InP. Excitation at 1.549 eV with 50 μW power, for the two above-band-gap excitation spectra (red and blue). σ (π) denote linear collection polarization perpendicular (parallel) to the magnetic field. Resonant excitation spectrum (black) uses excitation at 1.417 eV with 100 μW π-polarized light, with σ-polarized light collected. (c) Pulse sequence for optical pumping. The Ti:sapphire laser is pulsed on and off, repetitively, on the π transition, while PL from the σ transition is detected. The time between pulses significantly exceeds T1. (d) Optical pumping trace for InP with laser power 10 μW. The inset sketches the population transfer process during optical pumping. The amplitude of the exponential curve is proportional to the population in ↑. (e) Pulse sequence for T1 measurement. The detector gate-on time is 2 μs and the laser pulse length is 50 μs. (f) T1 measurement for InP with laser power 10 μW. The data are fit with an exponential plus a background yielding the time constant T1=(0.23±0.1) ms. Error bars denote the standard deviation of the recovery signal in each time bin over the many repetitions of the pulse sequence. The corresponding representative data for GaAs and CdTe are given in Appendix pp2. All experiments used ∼30 μm laser spot size.

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    • Figure 2
      Figure 2

      T1 as a function of Zeeman splitting for the six different samples at 1.5 K. The absolute values of the electron g factors used to convert from B to the Zeeman splitting for GaAs, InP, and CdTe are 0.44, 1.3, and 1.65, respectively. Sample descriptions are given in Table 1. The black dashed lines in the high energy (low energy) side denote a B−3 (B2) dependence for reference. They are offset from the experimental data for clarity. The green dashed line denotes the thermal energy kBT for reference.

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    • Figure 3
      Figure 3

      (a) T1 as a function of the Zeeman splitting for InP-2 at 1.5 K. The arrows show the magnetic field values at which the temperature dependence study was performed. (b)–(d) Temperature dependence of T1 at (b) B=0.48 T, (c) 1.9 T, and (d) 5.7 T. The dotted line denotes |gμB|/kB.

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    • Figure 4
      Figure 4

      T1 as a function of Zeeman splitting for CdTe-1 at T = 1.5 K and T = 5 K. The red and blue lines are mutually fitted by an empirical formula T1=bB4/Fph, where b=2000μs/T4. The red and blue dashed lines denote the energy at 1.5 and 5 K.

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    • Figure 5
      Figure 5

      Schematic of spin-relaxation mechanisms. (a) At low magnetic fields, spin relaxation is dominated by the interaction of the electron spin with lattice nuclear spins. (b) and (c) Relevant for the high-field spin-relaxation mechanism. (b) Energy level structure for unperturbed donor-bound electron in magnetic field, described by zero-field quantum numbers. (c) Dresselhaus spin-orbit coupling mixes states with opposite spin and different angular momentum components. In the admixture mechanism, phonons cause relaxation between the two eigenstates via the components with like spin. The direct spin-phonon interaction causes spin relaxation via the components with opposite spin.

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    • Figure 6
      Figure 6

      Theoretical results for spin-relaxation time T1 via the admixture mechanism, using both analytic and numerical wave functions. Pink and gray dots show the experimental data. For GaAs (a), the theory matches the data reasonably well with no fit parameters. For InP (b) and CdTe (c), the calculated values are multiplied by the factor specified in the figure for ease of comparison. T=1.5K. We note that the numerically calculated T1 which includes only the 2p states is slightly shorter than the full numerical solution. This is due to destructive interference between the orbital states in Eq. (8).

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    • Figure 7
      Figure 7

      Theoretical results for the spin-relaxation time T1 via the direct spin-phonon mechanism for GaAs (a), InP (b), and CdTe (c). Pink and gray dots show the experimental data. T=1.5K. The two dashed lines and two solid lines in (c) represent the analytic and numerical calculation results of T1 using v0=8×105m/s (upper curves) and v0=3×106m/s (lower curves).

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    • Figure 8
      Figure 8

      Magnetophotoluminescence spectra in the Voigt geometry. (a) GaAs-2. The oscillations in photoluminescence intensity with field are attributed to oscillations in magnetoabsorption due to the diamagnetic exciton effect [57], T=2K, excitation and collection are performed in linear polarizations oriented at ±45∘ with respect to the magnetic field direction, 1 mW excitation power at 810 nm. (b) InP-2, T=2.3K,σ-polarization excitation, all polarizations collected, 40 μW above band-gap excitation power. (c) CdTe-2. T=1.6K. π-polarization excitation, σ-polarization collection, 20 μW above band-gap excitation power.

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    • Figure 9
      Figure 9

      (a) Energy level diagram for donor system in CdTe. (b) Photoluminescence spectrum of CdTe at B=3.5T,T=1.5K. Excitation at 1.653 eV with 50 μW for the two above band spectra (red and blue). Excitation at 1.593 with 50 μW for resonant spectrum (black), as shown by the red arrow. (c) Optical pumping trace for CdTe at 3.5 T, 1.5 K. Power 50 μW. Laser pulse lasts 100 μs. (d) T1 measurement for CdTe at 3.5 T, 1.5 K. Power 50 μW. T1=(12.0±0.2)μs. (e) Energy level diagram for donor system in GaAs. (f) Photoluminescence spectrum of GaAs at 7 T, 1.5 K. Excitation at 1.530 eV with 18 μW for the two above band spectra (red and blue). Excitation at 1.517 with 10 μW for resonant spectrum (black), as shown by the red arrow. (g) Optical pumping trace for GaAs at 7 T, 1.5 K. Power 10 μW. Laser pulse lasts 50 μs. (d) T1 measurement for GaAs at 7 T, 1.5 K. Power 10 μW. T1=(313±5)μs. All data are taken with an excitation spot size ∼30 μm.

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    • Figure 10
      Figure 10

      Time-resolved photoluminescence during optical pulse. (a) Collection of D0X emission during resonant D0X excitation (blue curve) and above-band-gap excitation (red curve). A significant increase in emission intensity is observed for above-band-gap excitation. (b) Optical pumping traces for InP-1 at 4 T. Blue curve: Standard optical pumping experiment. Red curve: Prior to the optical pumping pulse, a 50 μs long above-band-gap prepulse is applied. The end of the prepulse is 5 μs before the start of the optical pumping pulse.

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    • Figure 11
      Figure 11

      Energies of excited state orbitals vs dimensionless magnetic field β from numerical simulation of hydrogen atom in magnetic field. The plot shows the energy difference of 18 excited states from the ground state with the same spin projection. States are labeled by their zero-field quantum numbers. Also plotted is the Zeeman splitting energy |g|μB in units of effective Rydberg, the maximum β of the plot being the maximum experimental β obtained for each material. The Zeeman energy can be ignored compared to the orbital energy.

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    • Figure 12
      Figure 12

      The overlap integral between the Gaussian approximation for the wave function, Eq. (E9), and the numerical solution was maximized as a function of β. The ratio of the radial and axial Gaussian sizes is plotted as a function of B. Also shown are the experimental limits of the “high-field” regime where T1 goes as B−ν for the three different materials. Using these limits, reasonable choices of χ are 1.5, 1.7, and 2.2 for GaAs, InP, and CdTe, respectively.

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