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The effect of uniaxial tensile strain on spin coherence in n-type GaAs epilayers is probed using time-resolved Kerr rotation, photoluminescence, and optically detected nuclear magnetic resonance spectroscopies. The band gap, electron spin lifetime, electron g factor, and nuclear quadrupole splitting are simultaneously imaged over millimeter scale areas of the epilayers for continuously varying values of strain. All-optical nuclear magnetic resonance techniques allow access to the strain-induced nuclear quadrupolar resonance splitting in field regimes not easily addressable using conventional optically detected nuclear magnetic resonance. ©2006 American Institute of Physics

Contents

• BODY OF ARTICLE
• REFERENCES
• FIGURES
• FOOTNOTES

Strain is an important material parameter in band-structure engineering and has been extensively^1,2,3 studied in III-V semiconductors. Recent work,^4,5,6 has shown that electron spins in GaAs and related compounds respond to strain dramatically. In particular, the manipulation of the spin-orbit coupling in GaAs via strain may be used for the development of all-electrical spintronic devices.⁵

Here we employ a mechanical three-point bending vise to controllably and reproducibly tune the tensile strain from 0.0%–0.2% in situ, a typical range for strain engineered heterostructures. This geometry creates a continuous variation in the magnitude of the strain which can be spatially imaged. We observe significant changes to the electron spin and charge dynamics in bulk n-type GaAs samples. Additionally, we investigate the effect of strain on the nuclear quadrupolar resonances (NQR) of each atomic species present in GaAs using all-optical nuclear magnetic resonance (NMR).^7,8,9

A series of samples¹⁰ was grown using molecular beam epitaxy consisting of a semi-insulating (100) GaAs substrate, 100  nm undoped GaAs buffer layer, 400  nm Al_0.7Ga_0.3As, and a final 500  nm n-type GaAs active layer. The doping ranges from 2×10¹⁶  to  1×10¹⁸  cm^–3, with the majority of data taken on samples doped between 4  and  6×10¹⁶  cm^–3 to maximize electron spin lifetimes.¹¹ A longer electron spin lifetime is advantageous for the all-optical NMR measurement.⁷

The samples are held in a variable temperature magneto-optical cryostat and probed using time-resolved Kerr rotation (TRKR),^4,5,7,8,9,12 photoluminescence (PL), and all-optical NMR spectroscopies. All measurements are performed at T=5  K unless otherwise specified. Excitation is provided by a pulsed Ti:sapphire laser with a repetition rate of 76  MHz and energies of 1.525  eV for the Kerr studies and 1.614  eV for the PL experiments. The magnetic field is applied parallel to [011] (Fig. 1). Pump and probe pulses are focused on the sample with a spot diameter of ~50  µm and powers of 1  mW and 100  µW, respectively. The pump beam is modulated between left and right circular polarizations with a photoelastic modulator (PEM) at 50  kHz to reduce¹³ the dynamic nuclear polarization (DNP),^14,15 while the probe beam is linearly polarized and chopped at 1.16  kHz for lock-in detection. Using a mechanical delay line, the delay time t between the two pulses can be tuned from 0  to  6  ns. The reflected probe polarization is rotated by an angle _K, which is proportional to the electron spin polarization along the propagation direction. _K as a function of delay time can be fit by e^–t/T  cos(_L/2), where t is the pulse delay time, T is the inhomogeneous transverse spin lifetime, and _L is the Larmor precession frequency of the electron spins.

Figure 1.

The sample is held against the upper support with a weak adhesive layer at room temperature and cooled to T=5  K without applying strain. After thermal stability is achieved, strain is applied by forcing the wedge [Fig. 1(a)] against the back of the sample. This creates an approximately uniaxial strain along the x direction that is compressive at the rear and tensile at the front of the sample with a neutral axis at the center. Three-point bending with simply supported edges will create strain that is proportional to the displacement along the loading axis. Area scans are obtained by moving the objective lens using two piezodriven linear translators whose minimum step size is 0.2  µm. Frequencies and lifetimes near the edge of the sample in the stressed state were consistent with measurements taken before straining, indicating that the edge restraints and adhesive were not introducing significant additional strain into the sample. The onset of the strain can be seen as a change in the electron precession frequency, as in Fig. 1(b), and can be reproducibly tuned to higher and lower levels. For the majority of this work, after the initial straining, the sample is held below 30  K to avoid introducing additional strain. All of the data presented in this letter are from the same sample in a single strained state, but the effects were reproduced in a number of samples¹⁰ across the abovementioned doping range.

In Fig. 1(b), typical TRKR data can be seen from the unstrained (open circle) and strained (solid line) areas of the sample. Data from the region with highest strain show a significant change in both the spin lifetime and precession frequency. There is an increase in the electron precession frequency due to the strain's effect on the electron g factor.¹⁶ The magnitude of the change in the electron precession frequency in this case is 70±5  MHz, corresponding to a 5% shift towards more negative values of the effective g factor. Suppression of the spin lifetime compared to the unstrained value is brought about by increased spin splitting in the conduction band.¹⁷

Spatially resolved PL reveals how the band gap changes over the sample area. In Fig. 2(b), spectra from several excitonic recombination peaks are visible. The blue (red) line is a double Lorentzian fit to the data from the unstrained (strained) area of the sample. The higher energy peak is recombinant luminescence from the neutral donor bound (D⁰,X), ionized donor bound (D⁺,X), and free excitons (X),^18,19 while the lower energy peak is composed of luminescence from recombination on carbon impurities, in particular the donor-acceptor transition (D⁰,C) and conduction band to the C acceptor (e,C),^18,19 amongst others. The application of tensile strain raises the valence band edge, visible as a redshift of the peaks to lower energy. Spatial variation of the energy shifts is shown in Fig. 2(a). Comparing the observed spectra with previous measurements of acceptor peak shifts versus strain,²⁰ we estimate the maximum strain to be less than 0.16% in this sample.²¹ Integration of an in situ interferometer would allow a more precise estimate of the in-plane strain.

Figure 2.

Figure 2(c) shows three line cuts from the images in Fig. 2(a). Symbols from each line cut are pictured in their respective images. The chosen straining geometry allows for a variety of strain levels to be addressed without changing the physical setup. Due to a small asymmetry in the sample jig, a two dimensional stress variation exists in the epilayer. This variation can be seen in the spatially resolved maps of PL, precession frequency, and lifetime in Fig. 2(a).

All-optical NMR utilizes resonant depolarization of the nuclear spins that have been polarized via DNP to detect the electric quadrupolar resonances of the nuclei, which are sensitive to the local electric fields at atomic sites.² This technique is capable²² of addressing as few as 10⁸ nuclear spins, and in contrast to detection of NQR with rf probes,^23,24,25 measurements can be performed within a large range of magnetic fields. In experiments using polarization resolved PL Refs. 26,27 to detect NQR, small magnetic fields are typically used (1  T) because the electron spin polarization (and thus the polarization detectable via PL) goes as (B)1/(1+(_LT)²).²⁸ _L is nearly linear in magnetic field, thus the observed polarization is diminished as the applied field increases. Previous high field measurements^24,25 of NQR and traditional optically detected nuclear magnetic resonance (ODNMR)^23,26,27 use a rf coil for excitation and/or detection of the NMR signal. While these methods offer the possibility for pulse sequence manipulation, nonreliance on DNP, and wider temperature ranges, they are often complex to implement.

Measuring the Kerr rotation under continuous illumination as a function of laboratory time shows a change in electron precession frequency larger than that affected by the application of strain. This is the result of the additional effective magnetic field created by the DNP which is significant despite the presence of the PEM in the optical path. The DNP has a saturation time of 45–60  min at these temperatures. Figure 3(c) shows the evolution of the nuclear field as a function of laboratory time for three positions of increasing strain. The presence of DNP allows for the use of all-optical NMR to probe the behavior of the nuclei. Of the three species present, ⁶⁹Ga, ⁷¹Ga, and ⁷⁵As, the ⁷⁵As has the strongest resonance transitions. This is due both to ⁷⁵As being the most abundant isotope as well as to the fact that the hyperfine coupling is strongest between the electron and the ⁷⁵As atom.¹⁴ For this reason, the majority of the study was confined to that species.

Figure 3.

NQR are detected⁹ by measuring the Kerr rotation signal at a fixed delay of 1200  ps while sweeping the in-plane magnetic field. As the applied field is swept through the resonant field for each species, its nuclear magnetization is destroyed by the alternating field of the pulsed laser. This causes a swift decrease in the total effective magnetic field felt by the electrons and a correspondingly abrupt change in the Kerr rotation signal. Fixing the pump-probe delay beyond 1  ns and at a point of high derivative of the Kerr rotation allows the precession frequency shift caused by the removal of the nuclear field to be more easily detected. A sweep rate of 5  mT/min provides time for the nuclear polarization to accumulate. Figure 3(a) shows typical field scans from strained (solid line) and unstrained (open circle) areas of the sample. B₀ (5.21  T for ⁷⁵As) is centered between the two transitions. Two events⁹ are visible in the data for each strain, corresponding to transitions from m=±3/2 to m=1/2 states. A surprising observation is the significant range over which their separation continues to increase, leading to a 60  mT splitting at the highest applied strain. This corresponds to a splitting in nuclear precession frequency between the two quadrupolar transitions of ~150  kHz, significantly larger then previous studies.^26,27 By tuning the strain we are able to manipulate the nuclear precession frequency splitting between these two transitions in a reproducible and controllable fashion over a range of 10–150  kHz. Figures 3(b)3(d) show the quadrupolar transition fields as a function of position along the X and Y directions, respectively. The asymmetry in the sample vise can be seen clearly in the Y axis figure.

The simplicity and sensitivity of the techniques used here present an attractive method for imaging strain fields in more complicated heterostructures. The data show that strain-induced modification of the spin-orbit coupling can be detected in the electronic and nuclear spin dynamics. These techniques along with the incorporation of rapid mechanical modulation of strain in very high frequency structures²⁹ may provide a pathway to active control of spin states in high frequency spintronic devices.

The authors would like to thank Y. K. Kato, M. Poggio, and J. Speck for their helpful insight and comments. This work was supported by the AFOSR, the DARPA/DMEA, and the NSF.

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Full figure

Fig. 1. (Color) (a) Schematic of the experimental setup and stress geometry. The laser is directed along the growth axis (z axis). A threaded rod (1) pushes the wedge (2) past the chip breaker (3), forcing it against the back of the sample. Strain is produced (4) in the plane of the sample, compressive in the rear and tensile in the active layer (black region). (b) Kerr rotation as a function of delay time for the strained (solid line) and unstrained (open circle) areas of the sample (T=5  K). The Kerr rotation _K is proportional to the conduction electron polarization along z. _L can be obtained from the period of the oscillations in the Kerr rotation, T from the curve decay. First citation in article

Full figure

Fig. 2. (Color) (a) Top down, spatial maps of donor-bound exciton group PL, C exciton group PL, effective g factor, and T over the entire sample. Symbols from line cuts in (c) pictured on images. (b) PL from strained (square) and unstrained (circle) areas of the sample. Overlaid are Lorentzian fits used to extract peak shifts. (c) Line cuts along X of C group PL energy (solid square), effective g factor (open square), and T (open circle) from spatially resolved maps in Fig. 2(a). For the PL, the maximum shift on the center is ~10  meV. The TRKR and PL measurements are performed at T=5  K. First citation in article

Full figure

Fig. 3. (Color) (a) NMR transitions for maximum (solid line) and minimum (open circle) strain. Arrows highlight resonant nuclear depolarization at (from left to right) B=–29, –4, +4, and +29  mT. (b) X dependence of the NQR field along the sample. Pictured in the center is a schematic of the line cut orientation. Transitions are plotted in nuclear frequency shift (left) and magnetic field (right). (c) Dynamically polarized nuclear field vs laboratory time for varying strains. The square symbol is for the lowest strain; triangle is for the highest (T=10  K). (d) Y dependence of NQR field. Unless noted, all measurements are performed at T=5  K. First citation in article

^aElectronic mail: awsch@physics.ucsb.edu

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