Electron Spin Diffusion Research Articles

Spin helices in GaAs quantum wells: Interplay of electron density, spin diffusion, and spin lifetime

To establish a correlation between spin diffusion, spin lifetime, and electron density, we study spin polarization evolution in low-dimensional GaAs semiconductors hosting two-dimensional electron gases by employing time-resolved magneto-optical Kerr effect microscopy. It is shown that for the establishment of the longest spin-lifetime, the variation in the scattering rate with electron density is of more importance than fulfilling the persistent spin helix condition when the Rashba α and Dresselhaus β parameters are balanced. More specifically, regardless of α and β linear dependencies on the electron density, the spin relaxation rate is determined by the spin diffusion coefficient that depends on electron density nonmonotonously. The longest experimental spin-lifetime occurs at an electron density, corresponding to transition from Boltzmann to Fermi–Dirac statistics, which is several times higher than that when the persistent spin helix is expected. These facts highlight the role the electron density may play when considering applications for spintronic devices.

Electron spin relaxation of P1 centers in synthetic diamonds with potential as B1 standards for DNP enhanced NMR

The microwave magnetic field, B1, in the non-resonant structures typically used for DNP-enhanced NMR is relatively small, so calibration via continuous wave (CW) power saturation requires a sample with longer spin lattice relaxation times than the samples used as CW standards in X-band cavities. HPHT diamonds have strong, easily observed EPR signals from P1 centers (nitrogen defects), and are indefinitely stable. This makes HPHT diamonds attractive as secondary standards for calibration of electron B1 field strength in a variety of experimental arrangements. The concentrations of P1 centers is also typically in the 30–200 ppm range, or equivalently 10–60 mM, and therefore the EPR relaxation observed is relevant to DNP enhanced NMR employing free radical polarizing agents at similar concentrations. Pulsed and CW saturation relaxation measurements T1 and T2 are compared at X-band. Under CW conditions the relevant T1T2 product of time constants in our samples at room temperature is found to be dominated by electron–electron spin diffusion, and the product is large enough that saturation will be possible with the B1 of typical DNP systems. The similarity of T1 and T2 values obtained by pulse measurements at X-band and Q-band suggests that the X-band results can be extrapolated to the higher EPR frequencies used for DNP experiments. The electron spin dynamics observed here in HPHT diamond samples identify them as useful model systems to better delineate the interplay of electron spin relaxation, magic angle spinning, and inhomogeneous microwave irradiation as they affect DNP enhancement.

Probing the in-plane electron spin polarization in Ge/ Si0.15Ge0.85 multiple quantum wells

We investigate spin transport in a set of $\text{Ge}/{\text{Si}}_{0.15}{\text{Ge}}_{0.85}$ multiple quantum wells (MQWs) as a function of the well thickness. We exploit optical orientation to photogenerate spin-polarized electrons in the discrete energy levels of the well conduction band at the $\mathrm{\ensuremath{\Gamma}}$ point of the Brillouin zone. After diffusion, we detect the optically oriented spins by means of the inverse spin-Hall effect (ISHE) taking place in a thin Pt layer grown on top of the heterostructure. The employed spin injection/detection scheme is sensitive to in-plane spin-polarized electrons, therefore, by detecting the ISHE signal as a function of the photon energy, we evaluate the spin polarization generated by optical transitions driven by the component of the light wave vector in the plane of the wells. In this way, we also gain insight into the electron spin-diffusion length in the MQWs. The sensitivity of the technique to in-plane spin-related properties is a powerful tool for the investigation of the in-plane component of the spin polarization in MQWs, which is otherwise commonly inaccessible.

Study of Electron Spin Diffusion and Relaxation Dynamics by Diffraction of transient spin grating in an Intrinsic GaAs/AlGaAs Quantum Well

In this paper, the transient spin grating method was used to measure the attenuation rate of the diffraction signals of the intrinsic spin gratings of the intrinsic GaAs/AlGaAs quantum wells in different periods at room temperature, and the electron spin diffusion coefficient Ds = 121±6cm2/s was obtained. The electron spin diffusion coefficients of GaAs/AlGaAs quantum well were in good agreement with that of p-type GaAs/AlGaAs quantum well, indicating that the doping type for GaAs/AlGaAs quantum well has no significant effect on the diffusion rate of spin-polarized electrons. In this paper, the widely used formula of transient spin grating diffraction signal attenuation rate was used to fit the diffraction experimental results of the transient spin grating in the intrinsic GaAs/AlGaAs quantum well. The measured electron spin relaxation time was much shorter than that measured by the saturation absorption method. The reason for the deviation in the measured spin relaxation time was analyzed. The dynamic law of transient spin grating modulation attenuation over time was derived. The decay rate formula was modified, and the modified formula was used to fit the experimental data in the transient spin grating diffraction to obtain the spin relaxation time τs = 123 ps. The result was consistent with the measured electron spin relaxation time by the saturation absorption method.

Doping dependence of the electron spin diffusion length in germanium

We have investigated the electron spin diffusion length at room temperature in bulk n-doped germanium as a function of the doping concentration. To this purpose, we exploit a nonlocal spin injection/detection scheme where spins are optically injected at the direct gap of Ge and electrically detected by means of the inverse spin-Hall effect (ISHE). By optically generating a spin population in the conduction band of the semiconductor at different distances from the spin detector, we are able to directly determine the electron spin diffusion length Ls in the Ge substrate. We experimentally observe that Ls > 20 μm for lightly doped samples and, by taking into account the electron diffusion coefficient, we estimate electron spin lifetime values τs larger than 50 ns. In contrast, for heavily doped Ge substrates, the spin diffusion length decreases to a few micrometers, corresponding to τs ≈ 20 ns. These results can be exploited to refine spin transport models in germanium and reduce the experimental uncertainties associated with the evaluation of Ls from other spin injection/detection techniques.

Spatiotemporal Spin Noise Spectroscopy.

We report on the potential of a new spin noise spectroscopy approach by demonstrating all-optical probing of spatiotemporal spin fluctuations. This is achieved by homodyne mixing of a spatially phase-modulated local oscillator with spin-flip scattered light, from which the frequency and wave vector dependence of the spin noise power is unveiled. As a first application of the method we measure the spatiotemporal spin noise in weakly n-doped CdTe layers, from which the electron spin diffusion constant and spin relaxation rates are determined. The absence of spatial spin correlations is also shown for this particular system.

Weak coupling theory of topological Hall effect

Topological Hall effect (THE) caused by a noncoplanar spin texture characterized by a scalar spin chirality is often described by the Berry phase, or the associated effective magnetic field. This picture is appropriate when the coupling, $M$, of conduction electrons to the spin texture is strong (strong-coupling regime) and the adiabatic condition is satisfied. However, in the weak-coupling regime, where the coupling $M$ is smaller than the electrons' scattering rate, the adiabatic condition is not satisfied and the Berry phase picture does not hold. In such a regime, the relation of the effective magnetic field to the spin texture can be "nonlocal", in contrast to the "local" relation in the strong coupling case. Focusing on the case of continuous but general spin texture, we investigate the THE in various characteristic regions in the weak-coupling regime, namely, (1) diffusive and local, (2) diffusive and nonlocal, and (3) ballistic. In the presence of spin relaxation, there arise two more regions in the "weakest-coupling" regime: (1') diffusive and local, and (2') diffusive and nonlocal. We derived the analytic expression of the topological Hall conductivity (THC) for each region, and found that the condition for the locality of the effective field is governed by transverse spin diffusion of electrons. In region 1, where the spin relaxation is negligible and the effective field is local, the THC is found to be proportional to $M$, instead of $M^3$ of the weakest-coupling regime. In the diffusive, nonlocal regions (2 and 2'), the effective field is given by a spin chirality formed by "effective spins" that the electrons see during their diffusive motion. Applying the results to a skyrmion lattice, we found the THC decreses as the skyrmion density is increased in region 2', reflecting the nonlocality of the effective field, and shows a maximum at the boundary to the "local" region.

Modeling the photo-induced inverse spin-Hall effect in Pt/semiconductor junctions

We show that the photon energy dependence of the photo-induced inverse spin-Hall effect (ISHE) signal at Pt/semiconductor junctions can be reproduced by a model that explicitly accounts for the electron spin diffusion length Ls in the semiconductor. In particular, we consider the Pt/GaAs, Pt/Ge, and Pt/Si systems: although optical spin injection and transport of spin-polarized electrons in the conduction band of these semiconductors are ruled by different mechanisms, a simple one dimensional analytical diffusion model, where Ls is the free parameter, can reproduce the ISHE data in all cases. This highlights the potentialities of the photo-induced ISHE spectra as a tool to directly address fundamental spin transport properties in semiconductors.

Persistent spin helix manipulation by optical doping of a CdTe quantum well

Time-resolved Kerr-rotation microscopy explores the influence of optical doping on the persistent spin helix in a [001]-grown CdTe quantum well at cryogenic temperatures. Electron spin diffusion dynamics reveal a momentum-dependent effective magnetic field providing SU(2) spin-rotation symmetry, consistent with kinetic theory. The Dresselhaus and Rashba spin-orbit coupling parameters are extracted independently from rotating the spin helix with external magnetic fields applied parallel and perpendicular to the effective magnetic field. Most importantly, a non-uniform spatiotemporal precession pattern is observed. The kinetic theory framework of spin diffusion allows for modeling of this finding by incorporating the photocarrier density into the Rashba ($\alpha$) and the Dresselhaus ($\beta_3$) parameters. Corresponding calculations are further validated by an excitation-density dependent measurement. This work shows universality of the persistent spin helix by its observation in a II-VI compound and the ability to fine-tune it by optical doping.

NMR Signal Quenching from Bound Biradical Affinity Reagents in DNP Samples.

We characterize the effect of specifically bound biradicals on the NMR spectra of dihydrofolate reductase from E. coli. Dynamic nuclear polarization methods enhance the signal-to-noise of solid state NMR experiments by transferring polarization from unpaired electrons of biradicals to nuclei. There has been recent interest in colocalizing the paramagnetic polarizing agents with the analyte of interest through covalent or noncovalent specific interactions. This experimental approach broadens the scope of dynamic nuclear polarization methods by offering the possibility of selective signal enhancements and the potential to work in a broad range of environments. Paramagnetic compounds can have other effects on the NMR spectroscopy of nearby nuclei, including broadening of nuclear resonances due to the proximity of the paramagnetic agent. Understanding the distance dependence of these interactions is important for the success of the technique. Here we explore paramagnetic signal quenching due to a bound biradical, specifically a biradical-derivatized trimethoprim ligand of E. coli dihydrofolate reductase. Biradical-derivatized trimethoprim has nanomolar affinity for its target, and affords strong and selective signal enhancements in dynamic nuclear polarization experiments. In this work, we show that, although the trimethoprim fragment is well ordered, the biradical (TOTAPOL) moiety is disordered when bound to the protein. The distance dependence in bleaching of NMR signal intensity allows us to detect numerous NMR signals in the protein. We present the possibility that static disorder and electron spin diffusion play roles in this observation, among other contributions. The fact that the majority of signals are observed strengthens the case for the use of high affinity or covalent radicals in dynamic nuclear polarization solid state NMR enhancement.

Non-local electrical spin injection and detection in germanium at room temperature

Non-local carrier injection/detection schemes lie at the very foundation of information manipulation in integrated systems. This paradigm consists in controlling with an external signal the channel where charge carriers flow between a “source” and a well separated “drain.” The next generation electronics may operate on the spin of carriers in addition to their charge and germanium appears as the best hosting material to develop such a platform for its compatibility with mainstream silicon technology and the predicted long electron spin lifetime at room temperature. In this letter, we demonstrate injection of pure spin currents (i.e., with no associated transport of electric charges) in germanium, combined with non-local spin detection at 10 K and room temperature. For this purpose, we used a lateral spin valve with epitaxially grown magnetic tunnel junctions as spin injector and spin detector. The non-local magnetoresistance signal is clearly visible and reaches ≈15 mΩ at room temperature. The electron spin lifetime and diffusion length are 500 ps and 1 μm, respectively, the spin injection efficiency being as high as 27%. This result paves the way for the realization of full germanium spintronic devices at room temperature.

Long-lived spin polarization in n-doped MoSe2 monolayers

Transition metal dichalcogenide monolayers are highly interesting for potential valleytronic applications due to the coupling of spin and valley degrees of freedom and valley-selective excitonic transitions. However, ultrafast recombination of excitons in these materials poses a natural limit for applications so that a transfer of polarization to resident carriers is highly advantageous. Here, we study the low-temperature spin-valley dynamics in nominally undoped and n-doped MoSe2 monolayers using time-resolved Kerr rotation. In the n-doped MoSe2, we find a long-lived component of the Kerr signal which we attribute to the spin polarization of resident carriers. This component is absent in the nominally undoped MoSe2. The long-lived spin polarization is stable under applied in-plane magnetic fields. Spatially resolved measurements allow us to determine an upper boundary for the electron spin diffusion constant in MoSe2.

Hot electron spin diffusion in n-type GaAs

We use two-color magneto-optical Kerr (MOKE) microscopy to study low-temperature electron spin diffusion in bulk n-type GaAs (n = 1.4 × 1016 cm−3). We show that simple drift-diffusion models do not describe the spin diffusion for above-bandgap optical spin injection correctly. By variation of the excitation energy and lattice temperature we demonstrate that this discrepancy is caused by the influence of the pump-induced local overheating of the electron system with respect to the lattice, which persists over length scales comparable to the spin diffusion length. Consideration of this hot carrier effect is crucial for a reliable extraction of spin propagation parameters from optical experiments.

Time and spatially resolved electron spin detection in semiconductor heterostructures by magneto‐optical Kerr microscopy

We review on time and spatially resolved two‐color pump–probe magneto‐optical Kerr effect (MOKE) microscopy studies of electron spins in bulk n‐GaAs and GaAs (110) quantum wells (QWs) at low lattice temperatures. The influence of photocarrier heating by above‐bandgap optical spin excitation on the spatially resolved magneto‐optical spin detection is considered in detail. We demonstrate that a continuous‐wave (cw) measurement of the local Kerr rotation at a fixed arbitrary probe wavelength in general does not correctly reveal the local spin polarization when hot electrons are present. For bulk GaAs we determine the true lateral electron spin polarization profile from cw measurements of the spatial dependence of the full excitonic Kerr rotation spectrum. For the (110) QWs, we directly obtain the electron spin diffusion coefficient from picosecond real space imaging of the time evolution of an optically excited electron spin packet, which we observe with a spectrally broad probe pulse.

Electron spin diffusion in monolayerMoS2

Electron spin diffusion is investigated in monolayer ${\mathrm{MoS}}_{2}$ in the absence of external electric and magnetic fields. The electron-impurity scattering, which is shown to play a negligible role in spin relaxation in time domain in this material, has a marked effect on the in-plane spin diffusion due to the anisotropic spin precession frequency in the spatial domain. With the electron-impurity and intervalley electron-phonon scatterings separately included in the scattering term, we study the intra- and intervalley diffusion processes of the in-plane spins by analytically solving the kinetic spin Bloch equations. The intravalley process is found to be dominant in the in-plane spin diffusion, in contrast to the case of spin relaxation in time domain, where the intervalley process can be comparable to or even more important than the intravalley one. For the intravalley process, we find that the in-plane spin diffusion is suppressed with the increase of impurity density but effectively enhanced by increasing electron density in both the degenerate and nondegenerate limits. We also take into account the electron-electron Coulomb scattering in the intravalley process. Interestingly, we find that in the nondegenerate limit, the intravalley spin-diffusion length presents an opposite trend in the electron-density dependence compared to the one with only electron-impurity scattering.

Picosecond real-space imaging of electron spin diffusion in GaAs

We use time-resolved two-color Kerr microscopy to study low-temperature electron spin diffusion in bulk GaAs with high spatial and temporal resolution. This method enables direct real-space imaging of the advancing spread of an optically excited electron spin packet by spin diffusion. We observe a high initial expansion rate of the spin packet, which is strongly reduced with increasing time. Comparison with continuous-wave Kerr spectroscopy demonstrates that this decrease is caused by the influence of the transient cooling of hot photocarriers on the electron spin diffusion coefficient.

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.

Hyperfine interaction and its effects on spin dynamics in organic solids

Hyperfine interaction (HFI) and spin-orbit coupling are two major sources that affect electron spin dynamics. Here we present a systematic study of the HFI and its role in organic spintronic applications. For electron spin dynamics in disordered $\ensuremath{\pi}$-conjugated organics, the HFI can be characterized by an effective magnetic field whose modular square is a weighted sum of contact and dipolar contributions. We determine the effective HFI fields of some common $\ensuremath{\pi}$-conjugated organics studied in the literature via first-principles calculations. Most of them are found to be less than 2 mT. While the H atoms are the major source of the HFI in organics containing only the C and H atoms, many organics contain other nuclear spins, such as Al and N in tris-(8-hydroxyquinoline) aluminum, that contribute to the total HFI. Consequently, the deuteration effect on the HFI in the latter may be much weaker than in the former. The HFI gives rise to multiple resonance peaks in electron spin resonance. In disordered organic solids, these individual resonances are unresolved, leading to a broad peak whose width is proportional to the effective HFI field. As electrons hop among adjacent organic molecules, they experience a randomly varying local HFI field, inducing electron spin relaxation and diffusion. This is analyzed rigorously based on master equations. Electron spin relaxation undergoes a crossover along the ratio between the electron hopping rate $\overline{\ensuremath{\eta}}$ and the Larmor frequency $\ensuremath{\Omega}$ of the HFI field. The spin relaxation rate increases (decreases) with $\overline{\ensuremath{\eta}}$ when $\overline{\ensuremath{\eta}}\ensuremath{\ll}\ensuremath{\Omega}$ ($\overline{\ensuremath{\eta}}\ensuremath{\gg}\ensuremath{\Omega}$). A coherent beating of electron spin at $\ensuremath{\Omega}$ is possible when the external field is small compared to the HFI. In this regime, the magnetic field is found to enhance the spin relaxation.

Hot carrier effects on lateral electron spin diffusion inn-type GaAs

We report on spatially resolved two-color pump-probe Hanle--magneto-optical Kerr effect studies of low-temperature electron spin diffusion in bulk $n$-type GaAs (${n}_{D}=1.4\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$). The influence of the lattice temperature on electron spin diffusion is investigated and it is shown that simple drift-diffusion models do not describe the spin diffusion for above-band-gap optical spin injection correctly. Variation of lattice temperature and excitation energy allow us to trace this discrepancy to the influence of the pump-induced local overheating of the electron system with respect to the lattice which persists over length scales comparable to the spin diffusion length. Consideration of this hot carrier effect is crucial for a reliable extraction of spin propagation parameters from optical experiments.

Nonuniform current and spin accumulation in a 1 μm thick n-GaAs channel

The spin accumulation in a n-GaAs channel produced by spin extraction into a (Ga,Mn)As contact is measured by cross-sectional imaging of the spin polarization in GaAs. The spin polarization is observed in a 1 μm thick n-GaAs channel with the maximum polarization near the contact edge opposite to the maximum current density. The one-dimensional model of electron drift and spin diffusion, frequently used, cannot explain this observation. It also leads to incorrect spin lifetimes from Hanle curves with a strong bias and distance dependence. Numerical simulations based on a two-dimensional drift-diffusion model, however, reproduce the observed spin distribution quite well and lead to realistic spin lifetimes.