Spin Diffusion Equation Research Articles

Diffusive Spin Dynamics in Ferromagnetic Thin Films with a Rashba Interaction

In a ferromagnetic metal layer, the coupled charge and spin diffusion equations are obtained in the presence of both Rashba spin-orbit interaction and magnetism. The misalignment between the magnetization and the nonequilibrium spin density induced by the Rashba field gives rise to Rashba spin torque acting on the ferromagnetic order parameter. In a general form, we find that the Rashba torque consists of both in-plane and out-of-plane components, i.e., T=T(perpendicular)y^×m^+T(parallel)m^×(y^×m^). Numerical simulations on a two-dimensional nanowire consider the impact of diffusion on the Rashba torque and reveal a large enhancement to the ratio T(parallel)/T(perpendicular) for thin wires. Our theory provides an explanation for the mechanism driving the magnetization switching in a single ferromagnet as observed in the recent experiments.

Spin transport in Au films: An investigation by spin pumping

The thickness and temperature dependence of spin transport in Au has been investigated in multilayer films via the spin pumping effect. To study spin transport in Au, single layer GaAs/16Fe/(d)Au(001) and double layer GaAs/16Fe/(d)Au/12Fe/20Au(001) were investigated using ferromagnetic resonance (FMR), where d = 20, 300, and the numerals preceding Fe and Au indicate the layer thickness in atomic layers (AL). FMR measurements were performed at frequencies ranging from 27.3 to 40.6 GHz and at temperatures ranging from 88 to 295 K. By measuring the total Gilbert damping in the 16Fe layer as a function of d and temperature for both single and double magnetic layer structures and by utilizing the spin diffusion equation, one is able to determine the spin mixing conductance, g↑↓, at the Fe/Au interface, and the spin flip relaxation time, τsf, in Au as a function of temperature. The temperature dependence of the momentum relaxation time, τm, in Au was measured independently by means of electron transport measurements in a van der Pauw configuration. It has been found that the spin flip relaxation time, τsf, in Au is dominated by phonon interactions.

Spin Pumping in a Ferromagnetic/Nonmagnetic/Spin-Sink Trilayer Film: Spin Current Termination

A Spin Current Generated by Spin Pumping in a Ferromagnetic/Nonmagnetic/Spin-Sink Trilayer Film Is Calculated Based on the Spin Pumping Theory and the Standard Spin Diffusion Equation. By Attaching the Spin-Sink Layer, the Injected Spin Current Is Drastically Enhanced when the Interlayer Thickness Is Shorter than the Spin Diffusion Length of the Interlayer. We Also Provided the Formula of the Charge Current which Is Induced from the Pumped Spin Current via the Inverse Spin-Hall Effect.

Imaging spin properties using spatially varying magnetic fields

We propose a novel method to image spin properties of spintronic systems using the spatially confined field of a scanned micromagnetic probe in conjunction with existing electrical or optical global spin detection schemes. It is thus applicable to all material systems susceptible to either of those approaches. The proposed technique relies on numerical solutions of the spin diffusion equation in the presence of spatially varying fields to obtain the local spin response to a micromagnetic probe field.

Relaxation mechanisms of the persistent spin helix

We study the lifetime of the persistent spin helix in semiconductor quantum wells with equal Rashba and linear Dresselhaus spin-orbit coupling strengths. In order to address the temperature dependence of the relevant spin relaxation mechanisms we derive and solve a semiclassical spin diffusion equation taking into account the effects of spin-dependent impurity scattering, cubic Dresselhaus spin-orbit coupling and electron-electron interactions. For the experimentally relevant regime we find that the lifetime of the persistent spin helix is mainly determined by the interplay of cubic Dresselhaus spin-orbit interaction and electron-electron interactions. We propose that even longer lifetimes can be achieved by generating a spatially damped spin profile instead of the persistent spin helix state.

Spin-current vortices in current-perpendicular-to-plane nanoconstricted spin valves

The charge and spin diffusion equations, taking into account spin-flip and spin-transfer torque, were numerically solved using a finite element method in complex noncollinear geometry with strongly inhomogeneous current flow. As an illustration, spin-dependent transport through a nonmagnetic nanoconstriction, separating two magnetic layers was investigated. Unexpected results such as vortices of spin-currents in the vicinity of the nanoconstriction were obtained. The angular variations of magnetoresistance and spin-transfer torque are strongly influenced by the structure geometry.

Spin current generation due to mechanical rotation in the presence of impurity scattering

We investigate theoretically the generation of a spin current from a uniformly rotating body with impurity scattering based on the spin-dependent transport equation. If the cyclotron frequency is lower than the inverse of the relaxation time, the spin current is then created mainly in the radial direction when a weak magnetic field is applied parallel to the rotation axis. Spin accumulation is estimated by solving the spin diffusion equation. We show that the inverse spin Hall effect can be used to detect the spin current induced by rotation.

Time evolution of spin accumulation induced from electric field in ferromagnet

The spin transport induced from an electric field in the ferromagnet with a uniform magnetization is studied microscopically. Taking into account the time dependence of the electric field and the spin relaxation due to a spin-orbit interaction at impurity, we derive the spin diffusion equation including the time evolution. We also discuss a relationship between a frequency dependence of the spin accumulation and the spin diffusion length.

Magnetoresistance of lateral semiconductor spin valves

The magnetoresistance of two terminal lateral semiconductor spin valves with respect to varying mesa size is studied. It is shown theoretically that extended regions outside the spin-current path can act as an additional source of spin-relaxation, decreasing the magnetoresistance response. From a simplified expression of magnetoresistance derived from spin-diffusion equations, we show that it is important to etch away these extended regions for devices with channel lengths much smaller than the spin-diffusion length in order to achieve maximum magnetoresistance. Preliminary experimental data on a two terminal local spin valve are in good agreement with the theory established in this article.

Spin and charge transport induced by magnetization dynamics in diffusive ferromagnetic metals

In ferromagnetic metals, the temporal and spatial dependence of the magnetization vector generates spin-dependent electric and magnetic fields. We study spin and charge transport by using the linearalized Boltzmann equation in response to these fields. A generalized spin-diffusion equation is derived and then exactly solved for a nanowire where the spatial dependence of the magnetization is one dimensional. It is found that the relative length scales between the domain-wall width and the spin-diffusion length are important in determining the local electromotive force and the enhanced damping induced by magnetization dynamics.

Out-of-Plane Torque Influence on Magnetization Switching and Susceptibility in Magnetic Multilayers

Based on both the spin diffusion equation and the Landau–Lifshitz–Gilbert (LLG) equation, we demonstrate the influence of out-of-plane spin torque on magnetization switching and susceptibility in a magnetic multilayer system. The variation of spin accumulation and local magnetization with respect to time are studied in the magnetization reversal induced by spin torque. We also research the susceptibility subject to a microwave magnetic field, which is compared with the results obtained without out-of-plane torque.

Local spin injectors using GaAs tips under light excitation

Local spin injectors using GaAs tips at the end of transparent cantilevers have been fabricated using a combination of epitaxial growth, etching processes and photolithographic techniques. The tip luminescence polarization is found to be small because of total internal light reflections of the luminescence inside the tip. However, measurements on planar films of similar doping along with a numerical solution of the spin and charge diffusion equations indicate that the injected spin polarization can be as high as 40% with corresponding electronic concentrations at the tip apex of the order of 1014 cm−3.

Bulk manifestation of the spin Hall effect

We show that a two-dimensional spin-orbit-coupled system in the presence of a charge/spin-density wave with a wave-vector perpendicular to an applied electric field supports bulk manifestations of the direct/inverse spin-Hall effect. We develop a theory of this phenomenon in the framework of the spin diffusion equation formalism and show that, due to the inhomogeneity created by a spin-grating, an anomalous bulk charge-density wave is induced away from sample boundaries. The optimal conditions for the observation of the effect are determined. The main experimental manifestation of the bulk spin-Hall effect, the induced charge/spin-density-wave, is characterized by a pi/2-phase shift relative to the initial non-homogeneous spin/charge-polarization profile and has a non-monotonic time-varying amplitude.

Finite Element Modeling of Charge- and Spin-Currents in Magnetoresistive Pillars With Current Crowding Effects

The charge and spin diffusion equations taking into account spin-flip and spin-transfer torque were numerically solved using a finite element method in complex non-collinear geometry. This approach was used to study the spin-dependent transport in giant magnetoresistance metallic pillars sandwiched between extended electrodes as in magnetoresistive heads for hard disk drives. The charge current crowding around the boundaries between the electrodes and the pillar has a quite significant influence on the spin current.

The origin of dispersion of magnetoresistance of a domain wall spin valve

We theoretically study the current-perpendicular-to-plane magnetoresistance of a domain wall confined in a nanocontact which is experimentally fabricated as current-confined-path (CCP) structure in a nano-oxide-layer (NOL). We solve the non-collinear spin diffusion equation by using the finite element method and calculate the MR ratio by evaluating the additional voltage drop due to the spin accumulation. We investigate the origin of dispersion of magnetoresistance by considering the effect of randomness of the size and distribution of the nanocontacts in the NOL. It is observed that the effect of randomness of the contact size is much larger than that of the contact distribution. Our results suggest that the origin of dispersion of magnetoresistance observed in the experiments is the randomness of the size of the nanocontacts in the NOL.

Signatures of dynamically polarized nuclear spins in all-electrical lateral spin transport devices

The effect of nuclear spins in Fe/GaAs all-electrical spin-injection devices is investigated. At temperatures below 50 K, strong modifications of the non-local spin signal are found that are characteristic for hyperfine coupling between conduction electrons and dynamically polarized nuclear spins. The perpendicular component of the nuclear Overhauser field depolarizes electron spins near zero in-plane external magnetic field, and can suppress such dephasing when antialigned with the external field, leading to satellite peaks in a Hanle measurement. The features observed agree well with a Monte Carlo simulation of the spin diffusion equation including hyperfine interaction, and are used to study the nuclear spin dynamics and relate it to the spin polarization of injected electrons.

Morphology and side-chain dynamics in hydrated hard α-keratin fibres by 1H solid-state NMR

The effect of hydration on phase composition, aminoacids side-chain dynamics, and domain thickness of hard α-keratin was investigated by 1H solid-state NMR. Decomposition of wide-line 1H NMR spectra was used to determine the phase composition and to obtain information on molecular motion. Proton spin-diffusion NMR experiments using a double-quantum dipolar filter were used to estimate the rigid domain sizes for the hydrated Caucasian hair fibres. The relative domain sizes were obtained from the solution of spin-diffusion equation for cylindrical morphologies in the initial-rate approximation by a novel approach. A qualitative model describing the morphological and molecular dynamics changes induced by hydration was developed.

Detecting and switching magnetization of Stoner nanograin in nonlocal spin valve

The magnetization detection and switching of an ultrasmall Stoner nanograin in a nonlocal spin valve (NLSV) device is studied theoretically. With the help of the rate equations, a unified description can be presented on the same footing for the NLSV signal that reads out the magnetization, and for the switching process. The setup can be viewed as that the grain is connected to two nonmagnetic leads via sequential tunneling. In one lead, the chemical potentials for spin-up and -down electrons are split due to the spin injection in the NLSV. This splitting (or the spin bias) is crucial to the NLSV signal and the critical condition to the magnetization switching. By using the standard spin diffusion equation and parameters from recent NLSV device, the magnitude of the spin bias is estimated and found large enough to drive the magnetization switching of the cobalt nanograin reported in earlier experiments. A microscopic interpretation of NLSV signal in the sequential tunneling regime is thereby raised, which show properties due to the ultrasmall size of the grain. The dynamics at the reversal point shows that there may be a spin-polarized current instead of the anticipated pure spin current flowing during the reversal due to the electron accumulation in the floating lead used for the readout of NLSV signal.

Magnetization dynamics in the presence of pure spin currents in magnetic single and double layers in spin ballistic and diffusive regimes

In this paper we study the spin transport by using the spin-pumping effect in epitaxial magnetic single and double layer film structures. For the magnetic single layer sample we show the spin-pumping-induced interface damping increases and saturates with the Au capping layer thickness. In addition magnetic double layer structures allowed us to investigate both the spin-pump and spin-sink effects. Coupling of pure spin currents to the magnetization via spin-sink effect is studied using time-resolved magneto-optical Kerr effect. These measurements were used to study the propagation of pure spin currents across a Au spacer layer between the two ferromagnets. The propagation of spin momentum density through the Au spacer layer was well described by spin-diffusion equation, which takes into account electron momentum and spin-flip scattering. The spin-diffusion theory was integrated into modified Landau-Lifshitz equations accounting in self-consistent manner for spin-pump/sink mechanism and spin momentum density propagation. Good agreement between theory and experimental data was found.

Effect of Co permeation on spin polarized transport in a Co/organic semiconductor (OSC) structure

Co atoms will permeate into the soft organic material to form a magnetic permeated sublayer (MPS) during the fabrication of an organic spin device, such as Co/OSC/LSMO. We considered the OSC as a two-sublayer structure of MPS and pristine OSC, and then established a dynamic spin-diffusion equation to study the effect of MPS on the spin current polarization and the magnetoresistance of the device. It was found that the MPS will change the spin transport due to its different spin-flip time and mobility from that in the pristine OSC. The splitting of spin-flip times will be favorable to the spin polarization transport. Mobility of spin polarons in the MPS will be reduced due to the scattering of the Co atoms, which will weaken the spin polarization. For a given device, effect of the thickness of the MPS on the spin polarization is discussed. Finally, we calculated the magnetoresistance of a Co/OSC/LSMO device. A theoretical result which is consistent with the experimental data was obtained.