Electron Spin Dynamics Research Articles

Radical pair intersystem crossing: Quantum dynamics or incoherent kinetics?

Magnetic field effects on radical pair reactions arise due to the interplay of coherent electron spin dynamics and spin relaxation effects, a rigorous treatment of which requires the solution of the Liouville-von Neumann equation. However, it is often found that simple incoherent kinetic models of the radical pair singlet-triplet intersystem crossing provide an acceptable description of experimental measurements. In this paper, we outline the theoretical basis for this incoherent kinetic description, elucidating its connection to exact quantum mechanics. We show, in particular, how the finite lifetime of the radical pair spin states, as well as any additional spin-state dephasing, leads to incoherent intersystem crossing. We arrive at simple expressions for the radical pair spin state interconversion rates to which the functional form proposed recently by Steiner et al. [J. Phys. Chem. C 122, 11701 (2018)] can be regarded as an approximation. We also test the kinetic master equation against exact quantum dynamical simulations for a model radical pair and for a series of PTZ•+-Phn-PDI•- molecular wires.

Fourth-order spin correlation function in the extended central spin model

Spin-noise spectroscopy has developed into a very powerful tool to access the electron spin dynamics. While the spin-noise power spectrum in an ensemble of quantum dots in a magnetic field is essentially understood, we argue that the investigation of the higher-order cumulants promises to provide additional information not accessible by the conventional power-noise spectrum. We present a quantum-mechanical approach to the correlation function of the spin-noise power operators at two different frequencies for small spin bath sizes and compare the results with a simulation obtained from the classical spin dynamics for large number of nuclear spins. This bispectrum is defined as a two-dimensional frequency cut in the parameter space of the fourth-order spin correlation function. It reveals information on the influence of the nuclear-electric quadrupolar interactions on the long-time electron spin dynamics dominated by a magnetic field. For large bath sizes and spin lengths the quantum-mechanical spectra converge to those of the classical simulations. The broadening of the bispectrum across the diagonal in the frequency space is a direct measure of the quadrupolar interaction strength. A narrowing is found with increasing magnetic field indicating a suppression of the influence of quadrupolar interactions in favor of the nuclear Zeeman effect.

Electron spin dynamics in mesoscopic GaN nanowires

The electron spin dynamics in spontaneously formed GaN nanowires (NWs) on Si(111) is investigated by time-resolved magneto-optical Kerr-rotation spectroscopy for temperatures from 15 to 260 K. A strong increase in the electron spin relaxation time by more than an order of magnitude is found as compared to bulk GaN. The temperature dependence of spin relaxation is characterized by two regimes, which are explained by a model taking into account the coexistence of two different mechanisms. As a result, the spin lifetime is limited by hyperfine interaction of localized electron spins with nuclear spins at low temperatures. The mesoscopic electron confinement in the NWs leads to a dominance of Dyakonov-Perel spin relaxation driven by interface-induced contributions at high temperatures, resulting in a slow-down, but not complete suppression of spin relaxation as compared to bulk GaN. These findings underline the important role of the high surface-to-volume ratio in NWs.

Electron spin dynamics in Ce3+ : YAG crystals: Hyperfine interaction of 4f and 5d electrons

The electron spin dynamics of $\mathrm{C}{\mathrm{e}}^{3+}$ ions in YAG crystals is studied by time-resolved photoluminescence spectroscopy with an alternating left and right circularly polarized continuous-wave laser modulation technique. The electron spin relaxation due to hyperfine interaction with randomly oriented nuclear spins can be efficiently suppressed by a weak external longitudinal magnetic field. The suppression of the hyperfine-induced spin relaxation makes the electron spin polarization increase from 0.001 to 0.016 for the lowest $4f$ state, and from 0.08 to 0.32 for the lowest $5d$ state. The suppression magnetic fields for the $4f$ electrons are several times weaker than that for the $5d$ electrons, dependent on the crystal orientation. The dispersion of the local hyperfine field distribution $\mathrm{\ensuremath{\Delta}}B$ is isotropic and equal to 4.0 mT for the $5d$ electrons, and anisotropic for the $4f$ electrons with $\mathrm{\ensuremath{\Delta}}{B}_{[001]}=0.8\phantom{\rule{0.16em}{0ex}}\mathrm{mT},\mathrm{\ensuremath{\Delta}}{B}_{[110]}=1.1\phantom{\rule{0.16em}{0ex}}\mathrm{mT},\mathrm{\ensuremath{\Delta}}{B}_{[1\overline{1}0]}=2.4\phantom{\rule{0.16em}{0ex}}\mathrm{mT}$. The hyperfine coupling strength for the $4f$ electrons is \ensuremath{\sim}4 times weaker than that for the $5d$ electrons.

Nuclear spin dynamics influenced and detected by electron spin polarization in CdTe/(Cd,Mg)Te quantum wells

Nuclear spin coherence and relaxation dynamics of all constituent isotopes of an n-doped CdTe/(Cd,Mg)Te quantum well structure are studied employing optically detected nuclear magnetic resonance. Using time-resolved pump-probe Faraday ellipticity, we generate and detect the coherent spin dynamics of the resident electrons. The photogenerated electron spin polarization is transferred into the nuclear spin system, which becomes polarized and acts back on the electron spins as the Overhauser field. Under the influence of resonant radio frequency pulses, we trace the coherent spin dynamics of the nuclear isotopes $^{111}$Cd, $^{113}$Cd, and $^{125}$Te. We measure nuclear Rabi oscillations, the inhomogeneous dephasing time $T_2^*$, the spin coherence time $T_2$, and the longitudinal relaxation time $T_1$. Furthermore, we investigate the influence of the laser excitation and the corresponding electron spin polarization on the nuclear spin relaxation time and find a weak extension of this time induced by interaction with the electron spins.

Surface-mediated spin dynamics probed by optical-pump-probe scanning tunneling microscopy.

In current materials science and technologies, surface effects on carrier and spin dynamics in functional materials and devices are of great importance. In this paper, we present the surface-sensitive probing of electron spin dynamics, performed by optical-pump-probe scanning tunneling microscopy (OPP-STM). Time-resolved spin lifetime information on a manganese (Mn)-deposited GaAs(110) surface was successfully obtained for the first time. With increasing Mn density via in situ evaporation, a nonlinear change in the spin lifetime in the picosecond range was clearly observed, while directly confirming the Mn density by STM. In comparison with the results obtained by the conventional OPP method, we have also demonstrated that the observed nonlinear spin lifetime behavior was surface-mediated, which can be characterized using only the surface-sensitive OPP-STM technique.

Nuclear-spin-pattern control of electron-spin dynamics in a series of V(iv) complexes.

Achieving control of phase memory relaxation times (T m) in metal ions is an important goal of molecular spintronics. Herein we provide the first evidence that nuclear-spin patterning in the ligand shell is an important handle to modulate T m in metal ions. We synthesized and studied a series of five V(iv) complexes with brominated catecholate ligands, [V(C6H4-n Br n O2)3]2- (n = 0, 1, 2, and 4), where the 79/81Br and 1H nuclear spins are arranged in different substitutional patterns. High-field, high-frequency (120 GHz) pulsed electron paramagnetic resonance spectroscopic analysis of this series reveals a pattern-dependent variation in T m for the V(iv) ion. Notably, we show that it is possible for two molecules to have starkly different (by 50%) T m values despite the same chemical composition. Nuclear magnetic resonance analyses of the protons on the ligand shell suggest that relative chemical shift (δ), controlled by the patterning of nuclear spins, is an important underlying design principle. Here, having multiple ligand-based protons with nearly identical chemical shift values in the ligand shell will, ultimately, engender a short T m for the bound metal ion.

Insights into the Efficient Intersystem Crossing of Bodipy-Anthracene Compact Dyads with Steady-State and Time-Resolved Optical/Magnetic Spectroscopies and Observation of the Delayed Fluorescence

Spin-orbit charge transfer-induced intersystem crossing (SOCT-ISC) is of particular interest for preparation of heavy atom-free triplet photosensitizers. Up to now, examples for SOCT-ISC dyads are limited and electron donor/acceptor SOCT-ISC dyads showing strong visible-light harvesting are rare. Herein, we studied the photophysics of a series of Bodipy-anthracene (BDP-An) compact dyads, especially the triplet state electron spin dynamics with the time-resolved electron paramagnetic resonance (TREPR) spectroscopy. The electronic coupling matrix elements (VDA*) between the 1CT (charge transfer) state and 1LE (locally excited) state are in the range 773–1545 cm–1. For one dyad, we observed three triplet states simultaneously with TREPR, that is triplet states confined on the anthracene (3An) and the Bodipy (3BDP) moieties as well as a 3CT state. Based on the electron spin polarization of these three triplet states and the optical experiments, the SOCT-ISC mechanism is confirmed and the radical pair-ISC mechanism as the main ISC channel was excluded. Triplet–triplet annihilation-induced delayed fluorescence was observed for the dyads, which is rare for Bodipy fluorophores.

Signatures of long-range spin-spin interactions in an (In,Ga)As quantum dot ensemble

We present an investigation of the electron spin dynamics in an ensemble of singly-charged quantum dots subject to an external magnetic field and laser pumping with circularly polarized light. The spectral laser width is tailored such that different groups of quantum dots are coherently pumped. Surprisingly, the dephasing time $T^*$ of the electron spin polarization depends only weakly on the laser spectral width. These findings can be consistently explained by a cluster theory of coupled quantum dots with a long range electronic spin-spin interaction. We present a numerical simulation of the spin dynamics based on the central spin model that includes a quantum mechanical description of the laser pulses as well as a time-independent Heisenberg interaction between each pair of electron spins. We discuss the individual dephasing contributions stemming from the Overhauser field, the distribution of the electron $g$-factors and the electronic spin-spin interaction as well as the spectral width of the laser pulse. This analysis reveals the counterbalancing effect of the total dephasing time when increasing the spectral laser width. On one hand, the deviations of the electron $g$-factors increase. On the other hand, an increasing number of coherently pumped electron spins synchronize due to the spin-spin interaction. We find an excellent agreement between the experimental data and the dephasing time in the simulation using an exponential distribution of Heisenberg couplings with a mean value $\overline{J}\approx 0.26\,\mathrm{\mu eV}$.

Ferromagnetic model system with spin-orbit coupling: Dynamical gap and effective spin-flip scattering

Abstract We investigate ultrafast magnetization dynamics due to electron-phonon interaction in a ferromagnetic Rashba model, which includes spin-orbit coupling and a Stoner mean-field splitting. By computing the reduced spin-density matrix including explicitly spin-independent electron-phonon scattering at the level of Boltzmann-type scattering integrals, we investigate the influence of a time-dependent Stoner mean field on the magnetization dynamics. We find that the dynamical gap increases the magnetization quenching on short timescales and slows down the remagnetization process. We further show how the noncollinear dynamics of electronic spins in the band structure with internal spin orbit fields can be approximated by effective spin-flip scattering matrix elements.

Multi-frequency rapid-scan HFEPR

Gaining access to electron spin dynamics at (sub-)THz frequencies is highly challenging. However, this information is highly relevant for the understanding and development of spin polarization agents in dynamic nuclear polarization methods and single-molecule magnets for quantum computation. Here we demonstrate the first rapid-scan EPR experiment in 200 GHz frequency region. A voltage controlled oscillator (VCO) generated fast sinusoidal frequency sweeps with scan rates up to 3×105 THz/s after the frequency multiplication, which is equal to 107 T/s in field representation. Such high scan rates provide access to extremely short relaxation times T2=2π×sweeprate-0.5≈1 ns. The absence of a microwave cavity allowed us to perform multi-frequency experiments in the 170–250 GHz range. A further advantage of a cavity-less approach is the possibility to use vast sweeps, which in turn, allows the deconvolution using a linear sweep function. The deconvoluted spectra obtained with this method are identical to the slow-rate spectrum. We find spin-spin relaxation times of several nanoseconds for pure LiPc samples in this frequency range. These values cannot be obtained by means of conventional pulsed EPR methods.

Electronic structure and spin dynamics of ACo2As2(A=Ba,Sr,Ca)

The electronic structures, charge and spin dynamics of the cobalt pnictide compounds ACo2As2 (A=Ba, Sr, Ca) in the paramagnetic state are investigated by using density functional theory combined with dynamical mean-field theory. In contrast to their iron counterparts, these cobalt pnictide compounds have three-dimensional electronic structures and strong ferromagnetic low-energy spin excitations. The Co 3d eg orbitals dominate the electronic states around the Fermi level and have stronger electronic correlation strength than the Co 3d t2g orbitals. The overall electronic correlation strength is much weaker than that in the iron arsenides, however, the most strongly correlated Co 3d x2-y2 orbital, especially in CaCo2As2, has electronic correlation strength comparable to Fe 3d t2g orbitals in iron arsenides. ACo2As2 (A=Ba, Sr, Ca) shows similar electronic structures where a conduction band of primarily Co 3d x2-y2 orbital character is close to a Van Hove singularity around the Brillouin-zone corner, which promotes ferromagnetic low-energy spin excitations. Originated from its increased nearest-neighbor Co-Co distance and significantly reduced As height from the Co plane, the strong electronic correlation strength and close proximity to the Van Hove singularity of the Co 3d x2-y2 orbital in CaCo2As2 is responsible for its unique A-type antiferromagnetic order observed in experiments. In comparison, despite substantial ferromagnetic low-energy spin excitations, BaCo2As2 and SrCo2As2 remain paramagnetic down to very low temperature because the Co 3d x2-y2 orbital has weaker electronic correlation strength and is further away from the Van Hove singularity.

Theory of radiative electron polarization in strong laser fields

Radiative polarization of electrons and positrons through the Sokolov-Ternov effect is important for applications in high-energy physics. Radiative spin-polarization is a manifestation of quantum radiation reaction affecting the spin-dynamics of electrons. We recently proposed that an analogue of the Sokolov-Ternov effect could occur in the strong electromagnetic fields of ultra-high-intensity lasers, which would result in a build-up of spin-polarization in femtoseconds. In this paper we develop a density matrix formalism for describing beam polarization in strong electromagnetic fields. We start by using the density matrix formalism to study spin-flips in non-linear Compton scattering and its dependence on the initial polarization state of the electrons. Numerical calculations show a radial polarization of the scattered electron beam in a circularly polarized laser, and we find azimuthal asymmetries in the polarization patterns for ultra-short laser pulses. A degree of polarization approaching 9 % is achieved after emitting just a single photon. We develop the theory by deriving a local constant crossed field approximation (LCFA) for the polarization density matrix, which is a generalization of the well known LCFA scattering rates. We find spin-dependent expressions that may be included in electromagnetic charged-particle simulation codes, such as particle-in-cell plasma simulation codes, using Monte-Carlo modules. In particular, these expressions include the spin-flip rates for arbitrary initial polarization of the electrons. The validity of the LCFA is confirmed by explicit comparison with an exact QED calculation of electron polarization in an ultrashort laser pulse.

Tailoring multilayer quantum wells for spin devices

The electron spin dynamics in multilayer GaAs/AlGaAs quantum wells, containing high-mobility dense two-dimensional electron gases, have been studied using time-resolved Kerr rotation and resonant spin amplification techniques. The electron spin dynamics was regulated through the wave function engineering and quantum confinement in multilayer quantum wells. We observed the spin coherence with a remarkably long dephasing time T2* > 13 ns for the structure doped beyond metal-insulator transition. Dyakonov-Perel spin relaxation mechanism, as well as the inhomogeneity of electron g-factor, was suggested as the major limiting factors for the spin coherence time. In the metallic regime, we found that the electron-electron collisions become dominant over microscopic scattering on the electron spin relaxation with the Dyakonov-Perel mechanism. Furthermore, the data analysis indicated that in our structure, due to the spin relaxation anisotropy, Dyakonov-Perel spin relaxation mechanism is efficient for the spins oriented in-plane and suppressed along the quantum well growth direction resulting in the enhancement of T2*. Our findings, namely, long-lived spin coherence persisting up to about room temperature, spin polarization decay time with and without a magnetic field, the spin-orbit field, single electron relaxation time, transport scattering time, and the electron-electron Coulomb scattering time highlight the attractiveness of n-doped multilayer systems for spin devices.

Quantum Interference Controls the Electron Spin Dynamics in n -GaAs

Manifestations of quantum interference effects in macroscopic objects are rare. Weak localization is one of the few examples of such effects showing up in the electron transport through solid state. Here we show that weak localization becomes prominent also in optical spectroscopy via detection of the electron spin dynamics. In particular, we find that weak localization controls the free electron spin relaxation in semiconductors at low temperatures and weak magnetic fields by slowing it down by almost a factor of two in $n$-doped GaAs in the metallic phase. The weak localization effect on the spin relaxation is suppressed by moderate magnetic fields of about 1 T, which destroy the interference of electron trajectories, and by increasing the temperature. The weak localization suppression causes an anomalous decrease of the longitudinal electron spin relaxation time $T_1$ with magnetic field, in stark contrast with well-known magnetic field induced increase in $T_1$. This is consistent with transport measurements which show the same variation of resistivity with magnetic field. Our discovery opens a vast playground to explore quantum magneto-transport effects optically in the spin dynamics.

Discretization of the total magnetic field by the nuclear spin bath in fluorine-doped ZnSe

The coherent spin dynamics of fluorine donor-bound electrons in ZnSe induced by pulsed optical excitation is studied in a perpendicular applied magnetic field. The Larmor precession frequency serves as a measure for the total magnetic field exerted onto the electron spins and, surprisingly, does not increase linearly with the applied field, but shows a step-like behavior with pronounced plateaus, given by multiples of the laser repetition rate. This discretization occurs by a feedback mechanism in which the electron spins polarize the nuclear spins, which in turn generate a local Overhauser field adjusting the total magnetic field accordingly. Varying the optical excitation power, we can control the plateaus, in agreement with our theoretical model. From this model, we trace the observed discretization to the optically induced Stark field, which causes the dynamic nuclear polarization.

Polaron freezing and the quantum liquid-crystal phase in the ferromagnetic metallic La0.67Ca0.33MnO3

The remarkable electronic properties of colossal magnetoresistive manganites are widely believed to be caused by the competition between a ferromagnetic metallic state and an antiferromagnetic insulating state with complex spin, charge, and orbital ordering. However, the physics underlying their magnetotransport properties is still not clear, especially the role of correlated Jahn–Teller polarons, which depending on temperature and doping, might form a liquid, glass or stripe polaron state. This question touches one of the most fundamental problems in the physics of doped Mott insulators, i.e. understanding the mechanism that chemical doping makes an insulator becoming superconductive as in the case of cuprates, or exhibiting the colossal magnetoresistance effect, as in the case of manganites. Here, by using 139La NMR and high resolution transmission electron microscopy in the temperature range 3.2–1000 K, we have monitored the formation and evolution of CE-type polarons in optimally doped La0.67Ca0.33MnO3. While NMR experiments show that correlated polarons dominate electron spin dynamics in the ferromagnetic phase, at very low temperatures they appear to form a quantum liquid-crystal like ferromagnetic phase, embedded into a ferromagnetic matrix with 3D polaron correlations. This is evidence that similarly to high Tc cuprates, quantum soft phases underlie the exotic physical properties of colossal magnetoresistive manganites.

Anomalous quantum critical spin dynamics in YFe2Al10

We report results of a muon spin relaxation ($\mu$SR) study of YFe$_2$Al$_{10}$, a quasi-2D nearly-ferromagnetic metal in which unconventional quantum critical behavior is observed. No static Fe$^{2+}$ magnetism, with or without long-range order, is found down to 19~mK\@. The dynamic muon spin relaxation rate~$\lambda$ exhibits power-law divergences in temperature and magnetic field, the latter for fields that are too weak to affect the electronic spin dynamics directly. We attribute this to the proportionality of $\lambda(\omega_\mu,T)$ to the dynamic structure factor~$S(\omega_\mu,T)$, where $\omega_\mu \approx 10^5$--$10^7~\mathrm{s}^{-1}$ is the muon Zeeman frequency. These results suggest critical divergences of $S(\omega_\mu,T)$ in both temperature and frequency. Power-law scaling and a 2D dissipative quantum XY (2D-DQXY) model both yield forms for $S(\omega,T)$ that agree with neutron scattering data ($\omega \approx 10^{12}~\mathrm{s}^{-1}$). Extrapolation to $\mu$SR frequencies agrees semi-quantitatively with the observed temperature dependence of $\lambda(\omega_\mu,T)$, but predicts frequency independence for $\omega_\mu \ll T$ in extreme disagreement with experiment. We conclude that the quantum critical spin dynamics of YFe$_2$Al$_{10}$ are not well understood at low frequencies.

Electrically tunable dynamic nuclear spin polarization in GaAs quantum dots at zero magnetic field

In III–V semiconductor nano-structures, the electron and nuclear spin dynamics are strongly coupled. Both spin systems can be controlled optically. The nuclear spin dynamics are widely studied, but little is known about the initialization mechanisms. Here, we investigate optical pumping of carrier and nuclear spins in charge tunable GaAs dots grown on 111A substrates. We demonstrate dynamic nuclear polarization (DNP) at zero magnetic field in a single quantum dot for the positively charged exciton X+ state transition. We tune the DNP in both amplitude and sign by variation of an applied bias voltage Vg. Variation of ΔVg on the order of 100 mV changes the Overhauser splitting (nuclear spin polarization) from −30 μeV (−22%) to +10 μeV (+7%) although the X+ photoluminescence polarization does not change sign over this voltage range. This indicates that absorption in the structure and energy relaxation towards the X+ ground state might provide favourable scenarios for efficient electron-nuclear spin flip-flops, generating DNP during the first tens of ps of the X+ lifetime which is on the order of hundreds of ps. Voltage control of DNP is further confirmed in Hanle experiments.

Photocharging Dynamics in Colloidal CdS Quantum Dots Visualized by Electron Spin Coherence

We use a time-resolved technique with three laser pulses (pump, orientation and probe) to study the photocharging dynamics with picosecond resolution on a long timescale ranging from ps to ms in CdS colloidal quantum dots. The detection is based on measuring the coherent spin dynamics of electrons, allowing us to distinguish the type of carrier in the dot core (electron or hole). We find that although initially negative photocharging happens because of fast hole trapping on surface states, eventually it evolves to positive photocharging due to electron trapping and hole detrapping. The positive photocharging lasts up to hundreds of microseconds at room temperature.