Spin Relaxation Of Conduction Electrons Research Articles

Spin relaxation of conduction electrons in coupled quantum wells

Spin relaxation of conduction electrons in coupled quantum wells

Electrical magnetochiral effect and kinetic magnetoelectric effect induced by chiral exchange field in helical magnetics

The features of spin and charge transport in conductive helimagnets, which are due to the action of an inhomogeneous exchange magnetic field on the spin of conduction electrons, are theoretically studied. The interaction between the spin of moving particles and an inhomogeneous external magnetic field was first recorded in the famous Stern-Gerlach experiment that investigated the quantum nature of spin. In the present paper, we have demonstrated that two physical effects---the electrical magnetochiral effect (EMChE) and the kinetic magnetoelectric effect (KMEE)---can be explained through the interaction of the spins of itinerant electrons in chiral helimagnets with spatially inhomogeneous effective magnetic field of exchange origin. All parameters of the EMChE and KMEE are presented in terms of both the characteristic frequencies of spin relaxation of conduction electrons in a helimagnet and the frequencies of their Larmor precession in external and internal exchange fields. It has been shown that the effective frequency of conduction-electron spin relaxation in a helimagnet contains three components: (i) the rate of spin-lattice relaxation caused by spin-orbit scattering of conduction electrons by defects of the crystal lattice, (ii) the rate of change in the average spin of electrons due to their ``diffusion'' escape from a region with a given direction of the average spin to a region with a different direction of spin density, and (iii) the contribution of the Larmor precession of the spins of electrons moving in the helimagnet's exchange field that assigns the precession axis altering its direction in space. The peculiarities of the EMChE and KMEE that substantially depend on the ratio of the above-listed spin relaxation rates and the angular frequencies of electron precession are described. The numerical estimates performed show that the mechanism of generating EMChE provides the effect magnitude sufficient to be experimentally detected in metallic helimagnets. The frequency regions of spin relaxation and spin precession are determined to observe a giant electrical magnetochiral effect and resonant behavior of the chiral magnetoresistance. We have called the appropriate effect ``magnetochiral kinetic resonance'' (MChKR). The physical nature of MChKR is elucidated. The latter arises due to the coincidence of the Larmor precession frequency of an electron in the effective field and the phase change frequency of the helicoidal exchange field acting on the electron moving along the helicoid's axis with a speed equal to that of the electron flow. We have demonstrated how the experimental studies of the KMEE can be used to directly determine the chirality of helimagnets.

Extrinsic spin-orbit coupling and spin relaxation in phosphorene

An effective Hamiltonian is derived to describe the conduction band of monolayer black phosphorus (phosphorene) in the presence of spin-orbit coupling and external electric field. Envelope function approximation along with symmetry arguments and Lowdin partitioning are utilized to derive extrinsic spin-orbit coupling. The resulting spin splitting appears in fourth order perturbation terms and is shown to be linear in both the magnitude of the external electric field and the strength of the atomic spin-orbit coupling, similar to the Bychkov-Rashba expression but with an in-plane anisotropy. The anisotropy depends on the coupling between conduction band and other bands both close and distant in energy. The spin relaxation of conduction electrons is then calculated within the Dyakonov-Perel mechanism where momentum scattering randomizes the polarization of a spin ensemble. We show how the anisotropic Fermi contour and the anisotropic extrinsic spin splitting contribute to the anisotropy of spin-relaxation time. Scattering centers in the substrate are considered to be charged impurities with screened Coulomb potential.

Current-Induced Modulation of Coercive Field in the Ferromagnetic Oxide SrRuO3

We investigated the coercive field $H_{\text {c}}$ for domain wall (DW) motion as a function of the current ${I}$ in the ferromagnetic oxide SrRuO3, a model system with narrow DWs for fabricating high-density spintronics devices. The DW is moved by ${I}$ in the direction of the current, and $H_{\text {c}}$ is modulated linearly in ${I}$ . This linear relationship is consistent with an effective magnetic field $H_{\text {eff}}$ driving the DW. The direction of DW motion and the magnitude of $H_{\text {eff}}$ are well described by a model based on the field-like torque arising from the spin relaxation of conduction electrons in the DW.

Strained germanium for applications in spintronics (Phys. Status Solidi A 11∕2016)

Germanium (Ge) is another group–IV semiconductor material which recently started attracting tremendous attention in spintronics following the success of silicon (Si). The crystal inversion symmetry of Si and Ge precludes the spin relaxation of conduction electrons by the Dyakonov–Perel mechanism, resulting in a long spin relaxation time. Since the proposal of the spin FET in 1990 by Datta and Das, semiconductor materials have been studied for their spin–orbit (S–O) interactions, particularly those that can be modified by an applied electric field, such as the Rashba S–O interaction, in order to create devices that utilise spin modulation and control to perform logic operations. Since then new proposals have appeared. Nowadays they include spin transistors with several different operating principles, spin–based diodes, spin–based field programmable gate arrays, dynamic spin–logic circuits, spinonly logic, spin communication and others. In the review by Morrison and Myronov (pp. 2809–2819), the focus is made on presenting progress in Ge spintronics including recent key advances.

Strained germanium for applications in spintronics

Germanium (Ge) is another group‐IV semiconductor material, which recently started attracting tremendous attention in spintronics following success of silicon (Si). The crystal inversion symmetry of Si and Ge precludes the spin relaxation of conduction electrons by the Dyakonov–Perel mechanism, resulting in a long spin relaxation time. Since the proposal of the spin FET in 1990 by Datta and Das, semiconductor materials have been studied for their spin–orbit (S–O) interactions, particularly those that can be modified by an applied electric field, such as the Rashba S–O interaction, in order to create devices that utilise spin modulation and control to perform logic operations. Since then new proposals have appeared. Nowadays they include spin transistors with several different operating principles, spin‐based diodes, spin‐based field programmable gate arrays, dynamic spin‐logic circuits, spin‐only logic, spin communication and others. In this review, the focus will be made on presenting recent progress in Ge spintronics including the key advances made. The absence of Dresselhaus S–O coupling in Ge enables a longer spin diffusion length when compared to III–V semiconductor materials. Evidence of a strong Rashba S–O interaction in strained Ge quantum wells has begun to emerge. Also, the first experimental demonstration of room‐temperature spin transport in Ge has recently been reported.

The Impurity Spin-Dependent Scattering Effects in the Transport and Spin Resonance of Conduction Electrons in Bismuth Doped Silicon

Transport and spin relaxation characteristics of the conduction electrons in silicon samples doped with bismuth in the 1.1·1013 - 7.7·1015 cm-3 concentration range were studied by the Hall and electron spin resonance spectroscopy. Hall effect measurements in the temperature range 10-80 K showed a deviation from the linear dependence of the Hall resistance in the magnetic field, which is a manifestation of the anomalous Hall effect. The magnetoresistance investigation shows that with current increasing magnetoresistance may change its sign from positive to negative, which is most clearly seen when the bismuth concentration goes up to 7.7·1015 cm-3. The conduction electron spin relaxation rate dramatically increases in silicon samples with sufficiently low concentration of bismuth ~ 2·1014 cm-3. All these results can be explained in terms of the concept of spin-dependent and spin flip scattering induced by heavy bismuth impurity centers.

Monte Carlo simulation of spin relaxation of conduction electrons in silicon

Recently, electrical injection of spin polarization in n-type and p-type silicon up to room-temperature has been experimentally carried out. Despite of these promising experimental results, a comprehensive theoretical framework concerning the influence of transport conditions on the spin depolarization process in silicon structures, in a wide range of values of temperature, doping concentration and amplitude of external fields, is still in a developing stage. In this contribution we use a semiclassical multiparticle Monte Carlo approach to simulate the electron transport and spin dynamics in lightly doped n-type Si crystals and numerically calculate the spin lifetimes of drifting electrons. Spin flipping is taken into account through the Elliot-Yafet mechanism, which is dominant in group IV materials. We discuss the influence of different intravalley and intervalley phonon interactions in the spin relaxation process during the spin transport. Our findings are in good agreement with those obtained by using different theoretical approaches. Moreover, our Monte Carlo predictions, in ranges of temperature and field amplitude yet unexplored, can guide future experimental studies towards a more effective design of room-temperature silicon based spintronic-devices.

Monte Carlo simulation of spin relaxation of conduction electrons in silicon

Recently, electrical injection of spin polarization in n-type and p-type silicon up to room-temperature has been experimentally carried out. Despite of these promising experimental results, a comprehensive theoretical framework concerning the influence of transport conditions on the spin depolarization process in silicon structures, in a wide range of values of temperature, doping concentration and amplitude of external fields, is still in a developing stage. In this contribution we use a semiclassical multiparticle Monte Carlo approach to simulate the electron transport and spin dynamics in lightly doped n-type Si crystals and numerically calculate the spin lifetimes of drifting electrons. Spin flipping is taken into account through the Elliot-Yafet mechanism, which is dominant in group IV materials. We discuss the influence of different intravalley and intervalley phonon interactions in the spin relaxation process during the spin transport. Our findings are in good agreement with those obtained by using different theoretical approaches. Moreover, our Monte Carlo predictions, in ranges of temperature and field amplitude yet unexplored, can guide future experimental studies towards a more effective design of room-temperature silicon based spintronic-devices.

Electric field dependence of the spin relaxation anisotropy in (111) GaAs/AlGaAs quantum wells

Time-resolved optical spectroscopy experiments in (111)-oriented GaAs/AlGaAs quantum wells (QWs) show a strong electric field dependence of the conduction electron spin relaxation anisotropy. This results from the interplay between the Dresselhaus and Rashba spin splitting in this system with C3v symmetry. By varying the electric field applied perpendicular to the QW plane from 20 to 50 kV cm−1 the anisotropy of the spin relaxation time parallel (τs∥) and perpendicular (τs⊥) to the growth axis can be first canceled and eventually inversed with respect to the one usually observed in III–V zinc-blende QW (τs⊥ = 2τs∥). This dependence stems from the nonlinear contributions of the k-dependent conduction band spin splitting terms which begin to play the dominant spin relaxing role while the linear Dresselhaus terms are compensated by the Rashba ones through the applied bias. A spin density matrix model for the conduction band spin splitting including both linear and cubic terms of the Dresselhaus Hamiltonian is used which allows a quantitative description of the measured electric field dependence of the spin relaxation anisotropy. The existence of an isotropic point where the spin relaxation tensor reduces to a scalar is predicted and confirmed experimentally. The spin splitting compensation electric field and collision processes type in the QW can be likewise directly extracted from the model without complementary measurements.

Analysis of phonon-induced spin relaxation processes in silicon

We study all of the leading-order contributions to spin relaxation of conduction electrons in silicon due to the electron-phonon interaction. Using group theory, the $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ perturbation method, and the rigid-ion model, we derive an extensive set of matrix element expressions for all of the important spin-flip transitions in the multivalley conduction band. The scattering angle has an explicit dependence on the electron wave vectors, phonon polarization, valley position, and spin orientation of the electron. Comparison of the derived analytical expressions with results of empirical pseudopotential and adiabatic band charge models shows excellent agreement.

Intrinsic spin lifetime of conduction electrons in germanium

We investigate the intrinsic spin relaxation of conduction electrons in germanium due to electron-phonon scattering. We derive intravalley and intervalley spin-flip matrix elements for a general spin orientation and quantify the resulting anisotropy in spin relaxation. The form of the intravalley spin-flip matrix element is derived from the eigenstates of a compact spin-dependent $\mathbf{k}$$\cdot$$\mathbf{p}$ Hamiltonian in the vicinity of the $L$ point (where thermal electrons are populated in Ge). Spin lifetimes from analytical integrations of the intravalley and intervalley matrix elements show excellent agreement with independent results from elaborate numerical methods.

Efficient room-temperature spin detector based on GaNAs

Efficient and highly spin-dependent recombination processes are shown to not only turn GaNAs into an efficient spin filter but also to make it an excellent spin detector functional at room temperature (RT). By taking advantage of the defect-engineered spin-filtering effect, the spin detection efficiency is no longer limited by the fast spin relaxation of conduction electrons. This leads to a significant enhancement in the optical polarization of the spin detector, making it possible to reliably detect even very weak electron spin polarization at RT, as demonstrated by a study of spin loss during optical spin injection across a GaAs/GaNAs interface.

Spin and charge transport induced by gauge fields in a ferromagnet

We present a microscopic theory of spin-dependent motive force (``spin motive force'') induced by magnetization dynamics in a conducting ferromagnet, by taking account of spin relaxation of conduction electrons. The theory is developed by calculating spin and charge transport driven by two kinds of gauge fields; one is the ordinary electromagnetic field ${A}_{\ensuremath{\mu}}^{\mathrm{em}}$, and the other is the effective gauge field ${A}_{\ensuremath{\mu}}^{z}$ induced by dynamical magnetic texture. The latter acts in the spin channel and gives rise to a spin motive force. It is found that the current induced as a linear response to ${A}_{\ensuremath{\mu}}^{z}$ is not gauge invariant in the presence of spin-flip processes. This fact is intimately related to the nonconservation of spin via Onsager reciprocity, so is robust, but indicates a theoretical inconsistency. This problem is resolved by considering the time dependence of spin-relaxation source terms in the ``rotated frame,'' as in the previous study on Gilbert damping [H. Kohno and J. Shibata, J. Phys. Soc. Jpn. 76, 063710 (2007)]. This effect restores the gauge invariance while keeping spin nonconservation. It also gives a dissipative spin motive force expected as a reciprocal to the dissipative spin torque (``$\ensuremath{\beta}$ term'').

Effect of spin diffusion on current generated by spin motive force

Spin motive force is a spin-dependent force on conduction electrons induced by magnetization dynamics. To examine its effects on magnetization dynamics, it is indispensable to take into account spin accumulation, spin diffusion, and spin-flip scattering since the spin motive force is, in general, nonuniform. We examine the effects of all these on the way the spin motive force generates the charge and spin currents in conventional situations, where the conduction electron spin relaxation dynamics is much faster than the magnetization dynamics. When the spin-dependent electric field is spatially localized, which is common in experimental situations, we find that the conservative part of the spin motive force is unable to generate the charge current due to the cancellation effect by the diffusion current. We also find that the spin current is a nonlocal function of the spin motive force and can be effectively expressed in terms of nonlocal Gilbert damping tensor. It turns out that any spin-independent potential such as Coulomb potential does not affect our principal results. At the last part of this paper, we apply our theory to current-induced domain wall motion.

Theory of the Spin Relaxation of Conduction Electrons in Silicon

A realistic pseudopotential model is introduced to investigate the phonon-induced spin relaxation of conduction electrons in bulk silicon. We find a surprisingly subtle interference of the Elliott and Yafet processes affecting the spin relaxation over a wide temperature range, suppressing the significance of the intravalley spin-flip scattering, previously considered dominant, above roughly 120 K. The calculated spin relaxation times T1 agree with the spin resonance and spin injection data, following a T(-3) temperature dependence. The valley anisotropy of T1 and the spin relaxation rates for hot electrons are predicted.

Spin relaxation of conduction electrons in (110)-grown quantum wells: A microscopic theory

The theory of spin relaxation of conduction electrons is developed for zinc-blende-type quantum wells grown on (110)-oriented substrate. It is shown that, in asymmetric structures, the relaxation of electron spin initially oriented along the growth direction is characterized by two different lifetimes and leads to the appearance of an in-plane spin component. The magnitude and sign of the in-plane component are determined by the structure inversion asymmetry of the quantum well and can be tuned by the gate voltage. In an external magnetic field, the interplay of cyclotron motion of carriers and the Larmor precession of electron spin can result in a nonmonotonic dependence of the spin density on the magnetic field.

Quantum simulations of spin-relaxation and transport in copper

A quantum equation of motion method is applied to simulate conduction electron spin-relaxation and transport in the presence of the spin-orbit interaction and disorder. A spin-relaxation time of 25ps is calculated for Cu with a realistic low temperature resistivity of 3.2 μΩ cm – corresponding to a spin-diffusion length of about 0.4 μm. Spin-relaxation in a finite nanocrystallite of Cu is also simulated and a short spin-relaxation time (0.47 ps) is calculated for a crystallite with 7% surface atoms. The spin-relaxation calculated for bulk Cu is in good agreement with experimental evidence, and the dramatic nanocrystallite effect observed has important implications for nano-spintronic devices.

Influence of current leads on critical current for spin precession in magnetic multilayers

In magnetic multilayers, a dc current induces a spin precession above a certain critical current. Drive torques responsible for this can be calculated from the spin accumulation Δμ . Existing calculations of Δμ assume a uniform cross-section of conductors. But most multilayer samples are pillars with current leads flaring out immediately to a much wider cross-section area than that of the pillar itself. We write spin-diffusion equations of a form valid for variable cross-section, and solve the case of flat electrodes with radial current distribution perpendicular to the axis of the pillar. Because of the increased volume available for conduction–electron-spin relaxation in such leads, Δμ is reduced in the pillar by at least a factor of 2 below its value for uniform cross-section, for given current density in the pillar. Also, Δμ and the critical current density for spin precession become nearly independent of the thickness of the pinned magnetic layer, and more dependent on the thickness of the spacer, in better agreement with measurements by Albert et al. (Phys. Rev. Lett. 89 (2002) 226802).

Suppression of spin relaxation of conduction electrons by cyclotron motion

We investigate the spin relaxation of two-dimensional (2D) electrons in a Si/SiGe quantum well by means of electron spin resonance. Simultaneous observation of cyclotron resonance allows us to evaluate the influence of momentum scattering on spin relaxation. We identify thus a dominant contribution due to the D'yakonov-Perel mechanism which is expected to be more efficient for slow momentum-relaxation. The observed relaxation times of microseconds can be explained, however, only by an additional motional narrowing due to modulation of the spin-orbit coupling caused by the cyclotron motion. The latter is evidenced by the observed dependence of spin relaxation on the direction of applied magnetic field which changes the cyclotron frequency of the 2D electrons.