Electron Spin Dynamics Research Articles

Spin dynamics in helical molecules with nonlinear interactions

It is widely admitted that the helical conformation of certain chiral molecules may induce a sizable spin selectivity observed in experiments. Spin selectivity arises as a result of the interplay between a helicity-induced spin–orbit coupling (SOC) and electric dipole fields in the molecule. From the theoretical point of view, different phenomena might affect the spin dynamics in helical molecules, such as quantum dephasing, dissipation and the role of metallic contacts. With a few exceptions, previous studies usually neglect the local deformation of the molecule about the carrier, but this assumption seems unrealistic to describe charge transport in molecular systems. We introduce an effective model describing the electron spin dynamics in a deformable helical molecule with weak SOC. We find that the electron–lattice interaction allows the formation of stable solitons such as bright solitons with well defined spin projection onto the molecule axis. We present a thorough study of these bright solitons and analyze their possible impact on the spin dynamics in deformable helical molecules.

Chemical tunnel-splitting-engineering in a dysprosium-based molecular nanomagnet

Total control over the electronic spin relaxation in molecular nanomagnets is the ultimate goal in the design of new molecules with evermore realizable applications in spin-based devices. For single-ion lanthanide systems, with strong spin–orbit coupling, the potential applications are linked to the energetic structure of the crystal field levels and quantum tunneling within the ground state. Structural engineering of the timescale of these tunneling events via appropriate design of crystal fields represents a fundamental challenge for the synthetic chemist, since tunnel splittings are expected to be suppressed by crystal field environments with sufficiently high-order symmetry. Here, we report the long missing study of the effect of a non-linear (C4) to pseudo-linear (D4d) change in crystal field symmetry in an otherwise chemically unaltered dysprosium complex. From a purely experimental study of crystal field levels and electronic spin dynamics at milliKelvin temperatures, we demonstrate the ensuing threefold reduction of the tunnel splitting.

Field control of anisotropic spin transport and spin helix dynamics in a modulation-doped GaAs quantum well

Electron spin transport and dynamics are investigated in a single, high-mobility, modulation-doped, GaAs quantum well using ultrafast two-color Kerr-rotation micro-spectroscopy, supported by qualitative kinetic theory simulations of spin diffusion and transport. Evolution of the spins is governed by the Dresselhaus bulk and Rashba structural inversion asymmetries, which manifest as an effective magnetic field that can be extracted directly from the experimental coherent spin precession. A spin precession length L-SOI is defined as one complete precession in the effective magnetic field. It is observed that application of (a) an out-of-plane electric field changes the spin decay time and L-SOI through the Rashba component of the spin-orbit coupling, (b) an in-plane magnetic field allows for extraction of the Dresselhaus and Rashba parameters, and (c) an in-plane electric field markedly modifies both the L-SOI and diffusion coefficient. While simulations reproduce the main features of the experiments, the latter results exceed the corresponding simulations and extend previous studies of drift-current-dependent spin-orbit interactions.

Zero-field splitting in the isoelectronic aqueous Gd(III) and Eu(II) complexes from a first principles analysis

The zero-field splitting (ZFS) of the ground state octet in aqueous Eu(II) and Gd(III) solutions was investigated through multi- configurational quantum chemical calculations and ab initio molecular dynamics (AIMD) simulations. Investigation of the ZFS of the lanthanide ions is essential to understand the electron spin dynamics and nuclear spin relaxation around paramagnetic ions and consequently the mechanisms underlying applications like magnetic resonance imaging.We found by comparing clusters at identical geometries but different metallic centres that there is not a simple relationship for their ZFS, in spite of the complexes being isoelectronic - each containing 7 unpaired f electrons. Through sampling it was established that inclusion of the first hydration shell has a dominant (over 90 %) influence on the ZFS. Extended sampling of aqueous Gd(III) showed that the 2nd order spin Hamiltonian formalism is valid and that the rhombic ZFS component is decisive.

Solitons in a nonlinear model of spin transport in helical molecules.

We study an effective integrable nonlinear model describing an electron moving along the axis of a deformable helical molecule. The helical conformation of dipoles in the molecular backbone induces an unconventional Rashba-like interaction that couples the electron spin with its linear momentum. In addition, a focusing nonlinearity arises from the electron-lattice interaction, enabling the formation of a variety of stable solitons such as bright solitons, breathers, and rogue waves. A thorough study of the soliton solutions for both focusing and defocusing nonlinear interaction is presented and discussed.

Spin-Dependent Electronic Dynamics in a Hybrid Nonresonance III–V/II–VI Heterostructure

The processes of electron spin dynamics in a hybrid nonresonance structure, which includes a layer of a diluted magnetic II–Mn–VI semiconductor and an asymmetric quantum well (QW) of a nonmagnetic III–V semiconductor, are experimentally studied. The nonresonance of the structure is determined by the fact that the level of the ground state of the magnetic layer falls into the range of the excited states of the nonmagnetic QW. The electron polarization in the ground thermalized state of QW is found not to depend on the magnetic part of the structure. However, the magnetic part affects the electron polarization in the excited state via spin injection from the magnetic semiconductor and the mixing of the electronic states of the magnetic and nonmagnetic subsystems of the structure. The possibility of controlling the polarization of an electron spin by carrier excitation toward the region of mixed states along with the absence of depolarizing influence of the magnetic semiconductor on carriers in the thermalized state of QW can be applied to design new spintronic devices along with those that use spin injection, optical orientation, and depolarization.

Photocharging dynamics in colloidal CdS quantum dots visualized by electron spin coherence

AbstractWe 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.

Femtosecond Dynamics of Spin-Polarized Electrons in Topological Insulators

A fast control of spins is a major quest in spintronic systems. Ultrashort light pulses have been utilized to trigger and detect the spin dynamics of electrons in magnetic materials and multilayers. Recently, three-dimensional topological insulators have received attention due to the existence, within the insulating band gap of bulk states, of spin-polarized surface states that are protected from backscattering by time-reversal symmetry. We studied sub-picosecond dynamics in the spin-polarized unoccupied electronic structure of Bi2Te3, employing circular-polarized light in time- and angle-resolved photoemission spectroscopy. Noncollinear optical parametric amplification and several nonlinear optical processes result in tunable, ultrashort visible pump pulses with a duration of 30 fs and 1.8 eV energy and ultraviolet probe pulses with about 60 fs duraction and about 6 eV energy. The stable optical setup and the high repetition rate of an Yb-laser source gives a high signal-to-noise ratio in our photoemission process. The 65 fs time resolution, along with 30 meV energy resolution of the time-of-flight energy analyzer, provides the opportunity to explore the ultrafast electronic dynamics in the unoccupied band structures. Furthermore, circular dichroism allows access to the spin state of the photoemitted electrons. A signature of femtosecond unpolarized bulk bands dynamics appears in the presence of spin-polarized electrons of the surface states. This helps distinguish the bulk and surface contributions in the spin-electronic current.

Pump-orientation-probe technique and its applications

The pump-orientation-probe technique is a recently-developed novel transient measurement technique, which has unique advantages in probing the ultrafast dynamics of charge separation in colloidal nanostructures. In this technique, the linearly-polarized pump pulse is applied to generating electron-hole pairs, and the circularly-polarized spin-orientation pulse is used to establish the electron spin polarization, whose dynamics is detected by monitoring the polarization change of the linearly-polarized probe pulse. Initially, the wavefunctions of the electron-hole pairs are spatially overlapped, and the lifetime of the electron spin is short because of the strong electron-hole exchange interaction. If the electrons or the holes are trapped by the surfaces of the colloidal nanostructures, the spatial separations between the electrons and the holes weaken the exchange effect, and thus the lifetime of the electron spin is largely lengthened. The evolutions of electrons and holes from their spatial overlap to separation can be revealed by monitoring the change of the electron spin dynamics. Based on the introduction of the conventional two-beam carrier pump-probe and spin pump-probe techniques, the features and optical layout of three-beam pump-orientation-probe technique are described in depth. The application to probing negative or positive photocharging in CdS colloidal quantum dots is taken for example and discussed in depth. Compared with the conventional time-resolved absorption or time-resolved fluorescence spectroscopy, the pump-orientation-probe technique can detect the dynamics of trapping electrons or holes and distinguish the type of charging state easily and directly, which has particular advantages under the high-power excitation condition. Further outlook of the three-beam pump-orientation-probe technique is also presented finally.

Electron charge and spin delocalization revealed in the optically probed longitudinal and transverse spin dynamics in n -GaAs

The evolution of the electron spin dynamics as consequence of carrier delocalization in $n$-type GaAs is investigated by the recently developed extended pump-probe Kerr/Faraday rotation spectroscopy. We find that isolated electrons localized on donors demonstrate a prominent difference between the longitudinal and transverse spin relaxation rates in magnetic field, which is almost absent in the metallic phase. The inhomogeneous transverse dephasing time $T_2^*$ of the spin ensemble strongly increases upon electron delocalization as a result of motional narrowing that can be induced by increasing either the donor concentration or the temperature. An unexpected relation between $T_2^*$ and the longitudinal spin relaxation time $T_1$ is found, namely that their product is about constant, as explained by the magnetic field effect on the spin diffusion. We observe a two-stage longitudinal spin relaxation which suggests the establishment of spin temperature in the system of exchange-coupled donor-bound electrons.

Nuclear spin cooling by helicity-alternated optical pumping at weak magnetic fields in n -GaAs

The spin dynamics of localized donor-bound electrons interacting with the nuclear spin ensemble in $n$-doped GaAs epilayers is studied using nuclear spin polarization by light with modulated circular polarization. We show that the observed build-up of the nuclear spin polarization is a result of competition between nuclear spin cooling and nuclear spin warm-up in the oscillating Knight field. The developed model allows us to explain the dependence of nuclear spin polarization on the modulation frequency and to estimate the equilibration time of the nuclear spin system that appears to be shorter than the transverse relaxation time $T_2$ determined from nuclear magnetic resonance.

Long-time coherence in fourth-order spin correlation functions

We study the long-time decay of fourth-order electron spin correlation functions for an isolated singly charged semi-conductor quantum dot. The electron spin dynamics is governed by the applied external magnetic field as well as the hyperfine interaction. While the long-time coherent oscillations in the correlation functions can be understood within an semi-classical approach treating the Overhauser field as frozen, the field dependent decay of its amplitude reported in different experiments cannot be explained by the central-spin model indicating the insufficiency of such a description. By incorporating the nuclear Zeeman splitting and the strain induced nuclear-electric quadrupolar interaction, we find the correct crossover from a fast decay in small magnetic fields to a slow exponential asymptotic in large magnetic fields. It originates from a competition between the quadrupolar interaction inducing an enhanced spin decay and the nuclear Zeeman term that suppressed the spin-flip processes. We are able to explain the magnetic field dependency of the characteristic long-time decay time $T_2$ depending on the experimental setups. The calculated asymptotic values of $T_2 = 3 -4\,\mu$s agree qualitatively well with the experimental data.

Closing the gap between spatial and spin dynamics of electrons at the metal-to-insulator transition

We combine extensive precision measurements of the optically detected spin dynamics and magneto-transport measurements in a contiguous set of n-doped bulk GaAs structures in order to unambiguously unravel the intriguing but complex contributions to the spin relaxation at the metal-to-insulator transition (MIT). Just below the MIT, the interplay between hopping induced loss of spin coherence and hyperfine interaction yields a maximum spin lifetime exceeding 800~ns. At slightly higher doping concentrations, however, the spin relaxation deviates from the expected Dyakonov-Perel mechanism which is consistently explained by a reduction of the effective motional narrowing with increasing doping concentration. The reduction is attributed to the change of the dominant momentum scattering mechanism in the metallic impurity band where scattering by local conductivity domain boundaries due to the intrinsic random distribution of donors becomes significant. Here, we fully identify and model all intricate contributions of the relevant microscopic scattering mechanisms which allows the complete quantitative modeling of the electron spin relaxation in the entire regime from weakly interacting up to fully delocalized electrons.

Room-temperature electron spin dynamics of Ce3+ ions in a YAG crystal

Circularly polarized optical excitation generates electron spin polarization in the lowest 5d state of rare-earth Ce3+ ions in a YAG crystal. The 5d electron spin dynamics is investigated in transverse and longitudinal magnetic fields by time-resolved pump-probe Faraday rotation. Long lived electron spin coherence with a dephasing time of 2.5 ns is found at room temperature. In a transverse magnetic field of 1 T, the electron spin coherence shows a distinct beating-like amplitude modulation due to several slightly different Larmor frequencies corresponding to different electron g factors of magnetically inequivalent positions of the Ce3+ ions in the crystal lattice. Hyperfine coupling between the 5d electron of Ce3+ ions and environmental nuclear spins dominates the spin relaxation, which can be efficiently suppressed by a longitudinal magnetic field as small as 10 mT. The dependence of electron spin relaxation on both the transverse and longitudinal magnetic fields agrees well with the one predicted theoretically for the hyperfine coupling mechanism.

Nonexponential spin decay in a quantum kinetic description of the D'yakonov-Perel' mechanism mediated by impurity scattering

The electron spin dynamics in an optically excited narrow quantum well is studied, where the electron spins precess in a k-dependent magnetic field while the electrons scatter at localized impurities. For the resulting spin decay, which is commonly known as the D'yakonov-Perel' mechansim, analytical expressions in the strong- and weak-scattering limits are available. It is found by the numerical solution of quantum kinetic equations in a broad range of parameters that, in situations that are typically relevant for ultrafast optical experiments, the dynamics of the total spin polarization significantly deviates from the pertinent analytical results. This is attributed to the broad spectral width of the optically excited spin-polarized electron distribution, which gives rise to a spin dephasing due to inhomogeneous broadening. Furthermore, it is found that the decay of the spin polarization need not be exponential. The notion of a spin decay time becomes ambiguous and different definitions of spin decay times can lead to different outcomes. The long-term dynamics of the decay of the spin polarization is even dominated by an algebraically decaying component. These findings highlight the importance of the effects of the broad spectral distribution of optically excited carriers in ultrashort magneto-optical experiments.

Advances in Two‐Dimensional Layered Materials

Advances in Two‐Dimensional Layered Materials

Dynamic Evolution from Negative to Positive Photocharging in Colloidal CdS Quantum Dots.

The optical properties of colloidal semiconductor nanocrystals are largely influenced by the trapping of charge carriers on the nanocrystal surface. Different concentrations of electron and hole traps and different rates of their capture to the traps provide dynamical charging of otherwise neutral nanocrystals. We study the photocharging formation and evolution dynamics in CdS colloidal quantum dots with native oleic acid surface ligands. A time-resolved technique with three laser pulses (pump, orientation, and probe) is developed to monitor the photocharging dynamics with picosecond resolution on wide time scales ranging from picoseconds to milliseconds. The detection is based on measuring the coherent spin dynamics of electrons, allowing us to distinguish the type of carrier in the QD core (electron or hole). We find that although initially negative photocharging happens because of fast hole trapping, it eventually evolves to positive photocharging due to electron trapping and hole detrapping. The positive photocharging lasts up to hundreds of microseconds at room temperature. These findings give insight into the photocharging process and provide valuable information for understanding the mechanisms responsible for the emission blinking in colloidal nanostructures.

Magnetic behavior of the nanophase of YbNi2 alloys

Variations in magnetic properties of the heavy-fermion YbNi2 alloy when milled in a high energy ball milling system have been investigated. The ferromagnetic transition (T C = 10.4 K) in the initial sample almost vanishes after milling, which leads to the appearance of a magnetic transition at T* = 3.2 K in nanocrystallites. Before milling, processes of spin–lattice relaxation of the Orbach–Aminov type with the participation of the first excited Stark sublevel of the Yb3+ ion located at 75 K are dominating in the electron spin dynamics in the paramagnetic phase of the alloy. A comparative study of the temperature dependence of the magnetic properties and spectra of electron paramagnetic resonance in poly- and nanocrystalline samples indicates the existence of a magnetic inhomogeneity of the compound arising upon milling.

Magnetic order and spin dynamics across a ferromagnetic quantum critical point:μSRinvestigations ofYbNi4(P1−xAsx)2

In the quasi-1D heavy-fermion system YbNi$_4$(P$_{1-x}$As$_x$)$_2$ the presence of a ferromagnetic (FM) quantum critical point (QCP) at $x_c$ $\approx 0.1$ with unconventional quantum critical exponents in the thermodynamic properties has been recently reported. Here, we present muon-spin relaxation ($\mu$SR) experiments on polycrystals of this series to study the magnetic order and the low energy 4$f$-electronic spin dynamics across the FM QCP. The zero field $\mu$SR measurements on pure YbNi$_4$(P$_{2}$ proved static long range magnetic order and suggested a strongly reduced ordered Yb moment of about 0.04$\mu_B$. With increasing As substitution the ordered moment is reduced by half at $x = 0.04$ and to less than 0.005 $\mu_B$ at $x=0.08$. The dynamic behavior in the $\mu$SR response show that magnetism remains homogeneous upon As substitution, without evidence for disorder effect. In the paramagnetic state across the FM QCP the dynamic muon-spin relaxation rate follows 1/$T_{1}T\propto T^{-n}$ with $1.01 \pm 0.04 \leq n \leq 1.13 \pm 0.06$. The critical fluctuations are very slow and are even becoming slower when approaching the QCP.

Subpicosecond spin dynamics of excited states in the topological insulator Bi2Te3

Using time-, spin- and angle-resolved photoemission, we investigate the ultrafast spin dynamics of hot electrons on the surface of the topological insulator Bi$_2$Te$_3$ following optical excitation by fs-infrared pulses. We observe two surface-resonance states above the Fermi level coexisting with a transient population of Dirac fermions that relax in about $\sim$2 ps. One state is located below $\sim$0.4 eV just above the bulk continuum, the other one at $\sim$0.8 eV inside a projected bulk band gap. At the onset of the excitation, both states exhibit a reversed spin texture with respect to that of the transient Dirac bands, in agreement with our one-step photoemission calculations. Our data reveal that the high-energy state undergoes spin relaxation within $\sim$0.5 ps, a process that triggers the subsequent spin dynamics of both the Dirac cone and the low-energy state, which behave as two dynamically-locked electron populations. We discuss the origin of this behavior by comparing the relaxation times observed for electrons with opposite spins to the ones obtained from a microscopic Boltzmann model of ultrafast band cooling introduced into the photoemission calculations. Our results demonstrate that the nonequilibrium surface dynamics is governed by electron-electron rather than electron-phonon scattering, with a characteristic time scale unambiguously determined by the complex spin texture of excited states above the Fermi level. Our findings reveal the critical importance of detecting momentum and energy-resolved spin textures with fs resolution to fully understand the sub-ps dynamics of transient electrons on the surface of topological insulators.