Longitudinal Spin Relaxation Time Research Articles

Hole Spin Coherence in InAs/InAlGaAs Self‐Assembled Quantum Dots Emitting at Telecom Wavelengths

Measurements of the longitudinal and transverse spin relaxation times of holes in an ensemble of vertically tunnel‐coupled self‐assembled InAs/InAlGaAs quantum dots (QDs), emitting in the telecom spectral range, are reported. The spin coherence is determined using the spin mode‐locking method in the inhomogeneous ensemble of QDs. Modeling the signal allows us to extract the hole spin coherence time to be in the range of μs. The longitudinal spin relaxation time μs is measured using the spin inertia method. The parameters investigated allow us to suggest that the main relaxation mechanism at low magnetic fields is related to the electron–hole spin exchange.

Method to quickly estimate T1 value by suppressing spin exchange relaxation and magnetic field gradient relaxation in atomic sensors

The accuracy of atomic sensor is determined by the transverse nuclear spin relaxation time (T2). As the longitudinal nuclear spin relaxation time (T1) is the upper limit of T2, it becomes an important metric for evaluating the merits of alkali vapor cells. However, the conventional method for measuring T1 of pulse delay takes dozens of minutes, which will increase the effect of random errors during the testing process. In order to solve this problem, a method to quickly estimate the value of T1 is proposed by suppressing the influence of spin exchange relaxation and magnetic field gradient relaxation terms on T2. Experimental results indicate that the accuracy is maintained at above 95%, and the testing time is reduced to less than 5%.

Coherent Carrier Spin Dynamics in FAPbBr3 Perovskite Crystals.

Coherent spin dynamics of electrons and holes are studied in hybrid organic-inorganic lead halide perovskite FAPbBr3 bulk single crystals using the time-resolved Kerr ellipticity technique at cryogenic temperatures. The Larmor spin precession of the carrier spins in a magnetic field is monitored to measure the Landé g-factors of electrons (+2.44) and holes (+0.41). These g-factors are highly isotropic. The measured spin dephasing times amount to a few nanoseconds, and the longitudinal hole spin relaxation time is 470 ns. The important role of the strong hyperfine interaction between carrier spins and nuclear spins is demonstrated via dynamic nuclear polarization. At low temperatures, electron and hole spin relaxation predominantly occurs via the hyperfine interaction, whose importance significantly decreases at temperatures above 12 K. We overview the spin dynamics in various lead halide perovskite crystals and polycrystalline films and conclude on their common features provided by charge carrier localization at cryogenic temperatures.

Coherent Spin Dynamics of Electrons in CdSe Colloidal Nanoplatelets

Coherent spin dynamics of electrons in CdSe colloidal nanoplatelets are investigated by time-resolved pump–probe Faraday rotation at room and cryogenic temperatures. We measure electron spin precession in a magnetic field and determine g-factors of 1.83 and 1.72 at low temperatures for nanoplatelets with a thickness of 3 and 4 monolayers, respectively. The dephasing time of spin precession T2* amounts to a few nanoseconds and has a weak dependence on temperature, while the longitudinal spin relaxation time T1 exceeds 10 ns even at room temperature. Observations of single and double electron spin–flips confirm that the nanoplatelets are negatively charged. The spin–flip Raman scattering technique reveals g-factor anisotropy by up to 10% in nanoplatelets with thicknesses of 3, 4, and 5 monolayers. In the ensemble with a random orientation of nanoplatelets, our theoretical analysis shows that the measured Larmor precession frequency corresponds to the in-plane electron g-factor. We conclude that the experimentally observed electron spin dephasing and its acceleration in the magnetic field are not provided by the electron g-factor anisotropy and can be related to the localization of the resident electrons and fluctuations of the localization potential.

Rapid measurement of longitudinal nuclear spin relaxation time based on the in-situ longitudinal magnetometer in Rb–Xe comagnetometers

The longitudinal relaxation time T1 of Xe nuclear spins is an important parameter to determine the performance of Rb–Xe comagnetometers. The industry standard delayed pulse method is time-consuming, and requires multiple π pulses and π/2 pulses. In this work, a direct measurement method for obtaining T1 based on the in-situ longitudinal magnetometer is introduced with the measurement period shortened to 3-5 T1. The proposed method requires only a single π pulse, reducing the measurement time by approximately more than 90%. By solving the Bloch equation, the working principle of the longitudinal magnetometer and the measurement method is demonstrated. The experiment shows that the longitudinal magnetometer achieves a linear working range greater than 60 nT, and the difference in measurement results of T1 through different methods at different temperatures and pump beam power is less than 3%. In addition, the longitudinal magnetometer introduced in this method has broad prospects for measuring the basic physical quantities in comagnetometers.

Optically Active Spin Defects in Few-Layer Thick Hexagonal Boron Nitride.

Optically active spin defects in hexagonal boron nitride (hBN) are promising quantum systems for the design of two-dimensional quantum sensing units offering optimal proximity to the sample being probed. In this Letter, we first demonstrate that the electron spin resonance frequencies of boron vacancy centers (V_{B}^{-}) can be detected optically in the limit of few-atomic-layer thick hBN flakes despite the nanoscale proximity of the crystal surface that often leads to a degradation of the stability of solid-state spin defects. We then analyze the variations of the electronic spin properties of V_{B}^{-} centers with the hBN thickness with a focus on (i)the zero-field splitting parameters, (ii)the optically induced spin polarization rate and (iii)the longitudinal spin relaxation time. This Letter provides important insights into the properties of V_{B}^{-} centers embedded in ultrathin hBN flakes, which are valuable for future developments of foil-based quantum sensing technologies.

Detection of Paramagnetic Spins with an Ultrathin van der Waals Quantum Sensor.

Detecting magnetic noise from small quantities of paramagnetic spins is a powerful capability for chemical, biochemical, and medical analysis. Quantum sensors based on optically addressable spin defects in bulk semiconductors are typically employed for such purposes, but the 3D crystal structure of the sensor inhibits sensitivity by limiting the proximity of the defects to the target spins. Here we demonstrate the detection of paramagnetic spins using spin defects hosted in hexagonal boron nitride (hBN), a van der Waals material that can be exfoliated into the 2D regime. We first create negatively charged boron vacancy (VB-) defects in a powder of ultrathin hBN nanoflakes (<10 atomic monolayers thick on average) and measure the longitudinal spin relaxation time (T1) of this system. We then decorate the dry hBN nanopowder with paramagnetic Gd3+ ions and observe a clear T1 quenching under ambient conditions, consistent with the added magnetic noise. Finally, we demonstrate the possibility of performing spin measurements, including T1 relaxometry using solution-suspended hBN nanopowder. Our results highlight the potential and versatility of the hBN quantum sensor for a range of sensing applications and make steps toward the realization of a truly 2D, ultrasensitive quantum sensor.

Properties of Donor Qubits in ZnO Formed by Indium-Ion Implantation

Shallow neutral donors (D$^{0}$) in ZnO have emerged as a promising candidate for solid-state spin qubits. Here, we report on the formation of D$^{0}$ in ZnO via implantation of In and subsequent annealing. The implanted In donors exhibit optical and spin properties on par with $\textit{in situ}$ doped donors. The inhomogeneous linewidth of the donor-bound exciton transition is less than 10 GHz, comparable to the optical linewidth of $\textit{in situ}$ In. Longitudinal spin relaxation times ($T_1$) exceed reported values for $\textit{in situ}$ Ga donors, indicating that residual In implantation damage does not degrade $T_1$. Two laser Raman spectroscopy on the donor spin reveals the hyperfine interaction of the donor electron with the spin-9/2 In nuclei. This work is an important step toward the deterministic formation of In donor qubits in ZnO with optical access to a long-lived nuclear spin memory.

Coherent Spin Dynamics of Electrons in Two-Dimensional (PEA)2PbI4 Perovskites.

The versatile potential of lead halide perovskites and two-dimensional materials is merged in the Ruddlesden-Popper perovskites having outstanding optical properties. Here, the coherent spin dynamics in Ruddlesden-Popper (PEA)2PbI4 perovskites is investigated by picosecond pump-probe Kerr rotation in an external magnetic field. The Larmor spin precession of resident electrons with a spin dephasing time of 190 ps is identified. The longitudinal spin relaxation time in weak magnetic fields measured by the spin inertia method is as long as 25 μs. A significant anisotropy of the electron g-factor with the in-plane value of +2.45 and out-of-plane value of +2.05 is found. The exciton out-of-plane g-factor of +1.6 is measured by magneto-reflectivity. This work contributes to the understanding of the spin-dependent properties of two-dimensional perovskites and their spin dynamics.

Measurement of longitudinal nuclear spin relaxation time in NMR gyroscope by real-time monitoring

In the atomic cell of a nuclear magnetic resonance gyroscope, a transverse bias field is applied to enable the in situ alkali magnetometer to sense the variations in the longitudinal magnetic field. During a single relaxation process of the noble gas, the longitudinal relaxation time is obtained by monitoring and fitting the signal of the magnetometer in real-time. The relaxation times measured using our method are nearly identical to those obtained using the conventional delayed pulse method, but in contrast, our method saves ∼90% of the time. By using the new method, fast and accurate batch testing for a large number of atomic cells can be achieved to optimize the manufacturing of the cells, which is helpful in speeding up the development of gyroscopes.

Submillisecond Spin Relaxation in CsPb(Cl,Br)3 Perovskite Nanocrystals in a Glass Matrix.

Lead halide perovskite nanocrystals in a glass matrix are a promising platform for optoelectronic applications due to their excellent optical properties combined with outstanding stability against the environment. We reveal the potential of this system for spintronics by studying the electron spin properties of CsPb(Cl,Br)3 nanocrystals in a fluorophosphate glass matrix. Using optical spin orientation and spin depolarization with a radio frequency field, we measure longitudinal spin relaxation time, T1, reaching several hundreds of microseconds at low temperatures. This time T1 corresponds to a spin state with a small g factor, which we attribute to a weakly exchange-coupled electron-hole pair with antiparallel spins.

Ensemble spin relaxation of shallow donor qubits in ZnO

We present an experimental and theoretical study of the longitudinal electron spin relaxation (${T}_{1}$) of shallow donors in the direct band-gap semiconductor ZnO. ${T}_{1}$ is measured via resonant excitation of the Ga donor-bound exciton. ${T}_{1}$ exhibits an inverse-power dependence on magnetic field ${T}_{1}\ensuremath{\propto}{B}^{\ensuremath{-}n}$, with $4\ensuremath{\le}n\ensuremath{\le}5$, over a field range of 1.75 T to 7 T. We derive an analytic expression for the donor spin-relaxation rate due to spin-orbit (admixture mechanism) and electron-phonon (piezoelectric) coupling for the wurtzite crystal symmetry. Excellent quantitative agreement is found between experiment and theory suggesting the admixture spin-orbit mechanism is the dominant contribution to ${T}_{1}$ in the measured magnetic field range. Temperature and excitation-energy dependent measurements indicate a donor density dependent interaction may contribute to small deviations between experiment and theory. The longest ${T}_{1}$ measured is 480 ms at 1.75 T with increasing ${T}_{1}$ at smaller fields theoretically expected. This work highlights the extremely long longitudinal spin-relaxation time for ZnO donors due to their small spin-orbit coupling.

Dipolar spin relaxation of divacancy qubits in silicon carbide

Divacancy spins implement qubits with outstanding characteristics and capabilities in an industrial semiconductor host. On the other hand, there are still numerous open questions about the physics of these important defects, for instance, spin relaxation has not been thoroughly studied yet. Here, we carry out a theoretical study on environmental spin-induced spin relaxation processes of divacancy qubits in the 4H polytype of silicon carbide (4H-SiC). We reveal all the relevant magnetic field values where the longitudinal spin relaxation time T1 drops resonantly due to the coupling to either nuclear spins or electron spins. We quantitatively analyze the dependence of the T1 time on the concentration of point defect spins and the applied magnetic field and provide an analytical expression. We demonstrate that dipolar spin relaxation plays a significant role both in as-grown and ion-implanted samples and it often limits the coherence time of divacancy qubits in 4H-SiC.

Coherent Spin Dynamics of Electrons and Holes in CsPbBr3 Colloidal Nanocrystals.

The spin dynamics in CsPbBr3 lead halide perovskite nanocrystals are studied by picosecond pump-probe Faraday rotation in an external magnetic field. Coherent Larmor precession of electrons and holes with spin dephasing times of ∼600 ps is detected in a transversal magnetic field. The longitudinal spin relaxation time in weak magnetic fields reaches 80 ns at a temperature of 5 K. In this regime, the carrier spin dynamics is governed by nuclear spin fluctuations characterized by an effective hyperfine field strength of 25 mT. The Landé factors determining the carrier Zeeman splittings are ge = +1.73 for electrons and gh = +0.83 for holes. A comparison with a CsPbBr3 polycrystalline film and bulk single crystals evidences that the spatial confinement of electrons and holes in the nanocrystals only slightly affects their g factors and spin dynamics.

Measurement of a129Xe transverse relaxation rate without the influence of Rb polarization-induced magnetic gradient.

We demonstrate the measurement of the transverse spin relaxation rate of Xe without the influence of the Rb polarization-induced magnetic field gradient. The optical pumping beam and probe beam turn on and off repeatedly during the measurement to reduce the relaxation originating from the Rb polarization-induced magnetic field gradient. During the absence of the optical pumping beam, the nuclear spin of the noble gas atom does not experience the alkali-polarization-induced magnetic field gradient so that the transverse spin relaxation rate (1/T2) decreases. When the duty cycle reaches zero, the measured transverse relaxation time T2 approaches the longitudinal spin relaxation time T1. Our method helps in roughly estimating the longitudinal spin relaxation time with a single measurement of the free induction decay.

Optical spin control and coherence properties of acceptor bound holes in strained GaAs

Hole spins in semiconductors are a potential qubit alternative to electron spins. In nuclear-spin-rich host crystals like GaAs, the hyperfine interaction of hole spins with nuclei is considerably weaker than that for electrons, leading to potentially longer coherence times. Here we demonstrate optical pumping and coherent population trapping for acceptor-bound holes in a strained GaAs epitaxial layer. We find $\mu$s-scale longitudinal spin relaxation time T$_1$ and an inhomogeneous dephasing time T$_2^*$ of $\sim$7~ns. We attribute the spin relaxation mechanism to a combination effect of a hole-phonon interaction through the deformation potentials and a heavy-hole light-hole mixing in an in-plane magnetic field. We attribute the short T$_2^*$ to g-factor broadening due to strain inhomogeneity. T$_1$ and T$_2^*$ are quantitatively calculated based on these mechanisms and compared with the experimental results. While the hyperfine-mediated decoherence is mitigated, our results highlight the important contribution of strain to relaxation and dephasing of acceptor-bound hole spins.

A modified analytical model of the alkali-metal atomic magnetometer employing longitudinal carrier field* *Project supported by the Hunan Graduate Research and Innovation Project (Grant No. CX2018B009), the Natural Science Foundation of Hunan (Grant No. 2018JJ3608), the Research Project of National University of Defense Technology (Grant Nos. ZK170204 and ZZKY-YX-07-02), and the National Natural Science Foundation of China (Grant Nos. 61671458

Alkali-metal atomic magnetometers employing longitudinal carrier magnetic field have ultrahigh sensitivity to measure transverse magnetic fields and have been applied in a variety of precise-measurement science and technologies. In practice, the magnetometer response is not rigorously proportional to the measured transverse magnetic fields and the existing fundamental analytical model of this magnetometer is effective only when the amplitudes of the measured fields are very small. In this paper, we present a modified analytical model to characterize the practical performance of the magnetometer more definitely. We find out how the longitudinal magnetization of the alkali metal atoms vary with larger transverse fields. The linear-response capacity of the magnetometer is determined by these factors: the amplitude and frequency of the longitudinal carrier field, longitudinal and transverse spin relaxation time of the alkali spins and rotation frequency of the transverse fields. We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method and simulation experiments are conducted to verify the validity and correctness of the proposed modified model. This model can be helpful for measuring larger fields more accurately and configuring a desirable magnetometer with proper linear range.

Longitudinal spin relaxation time of donor-bound electrons in a CdTe quantum well

We study the magnetic-field dependence of the longitudinal spin relaxation time ${T}_{1}$ of donor-bound electrons placed in the middle of an 8-nm CdTe quantum well with different doping concentrations in the range from $1\ifmmode\times\else\texttimes\fi{}{10}^{9}$ to $2.9\ifmmode\times\else\texttimes\fi{}{10}^{11}$ $\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ and at low temperature. We use an extended photoinduced Faraday rotation technique, which expands the usual domain of the measured decays from tens of ns to $\ensuremath{\mu}\mathrm{s}$. As in high-purity bulk semiconductors, a maximum relaxation time of around ${T}_{1}\ensuremath{\sim}10\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ is observed for a residually doped sample at low magnetic field of $B=0.08\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. For higher doping concentrations, the magnetic-field dependence of ${T}_{1}$ shows a nonmonotonic behavior: first a rapid increase, followed by a plateau or a decrease of ${T}_{1}$. The fast increase of ${T}_{1}$ at low magnetic fields is explained by the inhibition of the mechanisms identified at zero field---hyperfine and anisotropic exchange interactions---while the behavior at high magnetic field can be succesfully explained by a mechanism proposed by Lyubinskiy and associated to electron hops [I. S. Lyubinskiy, JETP Lett. 88, 814 (2008)]. A good agreement between experiment and theory is found for samples below the metal-insulator transition, when Dresselhaus terms of spin-orbit coupling are considered to be the dominant ones in the Hamiltonian describing the system.

Temperature dependence of the longitudinal spin relaxation time T1 of single nitrogen-vacancy centers in nanodiamonds

We report the experimental study of the temperature-dependence of the longitudinal spin relaxation time $T_1$ of single Nitrogen-Vacancy (NV) centers hosted in nanodiamonds. To determine the relaxation mechanisms at stake, measurements of the $T_1$ relaxation time are performed for a set of individual NV centers both at room and cryogenic temperatures. The results are consistant with a temperature-dependent relaxation process which is attributed to a thermally-activated magnetic noise produced by paramagnetic impurities lying on the nanodiamond surface. These results confirm the existence of surface-induced spin relaxation processes occurring in nanodiamonds, which are relevant for future developments of sensitive nanoscale NV-based quantum sensors.

Optical detection of electron spin dynamics driven by fast variations of a magnetic field: a simple method to measure T_1, T_2, and T_2^* in semiconductors

We develop a simple method for measuring the electron spin relaxation times T_1, T_2 and T_2^* in semiconductors and demonstrate its exemplary application to n-type GaAs. Using an abrupt variation of the magnetic field acting on electron spins, we detect the spin evolution by measuring the Faraday rotation of a short laser pulse. Depending on the magnetic field orientation, this allows us to measure either the longitudinal spin relaxation time T_1 or the inhomogeneous transverse spin dephasing time T_2^*. In order to determine the homogeneous spin coherence time T_2, we apply a pulse of an oscillating radiofrequency (rf) field resonant with the Larmor frequency and detect the subsequent decay of the spin precession. The amplitude of the rf-driven spin precession is significantly enhanced upon additional optical pumping along the magnetic field.