Nonadiabatic Spin Torque Research Articles

Nonadiabatic spin-torque and damping effects on vortex core switching triggered by a single current pulse

Switching the orientation of a vortex core by spin-polarised pulse current introduces a promising concept for the reliable addressing of a single nanodisc element inside dense arrays. In this paper, micromagnetic simulations are employed to study the vortex core switching behaviour excited by a short in-plane Gaussian current pulse. We find that both the switching mechanism and the switching time are not sensitive to changes in the phenomenological parameters of spin-torque nonadiabaticity and Gilbert damping. The switching time, however, strongly depends on the current strength. In addition, we have theoretically predicted the parameter range of current pulses to achieve a single switching event.

Proposal of a Robust Measurement Scheme for the Nonadiabatic Spin Torque Using the Displacement of Magnetic Vortices

A spin-polarized current traversing a ferromagnet with continuously varying magnetization exerts a torque on the magnetization. The nonadiabatic contribution to this spin-transfer torque is currently under strong debate, as its value differs by orders of magnitude in theoretical predictions and in measurements. Here, a measurement scheme is presented that allows us to determine the strength of the nonadiabatic spin torque accurately and directly. Analytical and numerical calculations show that the scheme is robust against the uncertainties of the exact current direction and Oersted fields.

Current-Driven Multi-wall Motion in a Nanowire with Perpendicular Magnetic Anisotropy

The current-driven domain motion of a multi-wall in a magnetic nanowire with perpendicular magnetic anisotropy was analyzed in this study by using micromagnetic simulation. As a result, we found that there were two modes in the multi-wall motion, and the motion was determined by the applied current density and non-adiabatic spin torque parameters; this was similar to single-wall motion. The x-component of magnetization in the domain wall exhibited different behavior according to the current density. The bit length was extended for a low current density and the bit length was varied for a high current density due to interaction between the magnetic domain walls.

Micromagnetic analysis of current-driven domain wall motion of multi-bit in a nanowire with perpendicular magnetic anisotropy

The current-driven domain wall motion of a multi-bit in a magnetic nanowire with perpendicular magnetic anisotropy has been analyzed by performing a micromagnetic simulation. The multi-bit motion is determined by the applied current density and the non-adiabatic spin torque parameters, which is similar to the current-driven domain wall motion of the single wall. Consequently, it was found that are two modes in the multi-bit motion: (a) the bit length remains constant and (b) the bit length varies or the bit vanishes in the nanowire. It was found that these modes of the multi-bit motion can be classified by the critical current density or Walker breakdown for the single wall motion in a magnetic nanowire with perpendicular magnetic anisotropy.

Influence of magnetic viscosity on domain wall dynamics under spin-polarized currents

We present a theoretical study of the influence of magnetic viscosity on current-driven domain wall dynamics. In particular we examine how domain wall depinning transitions, driven by thermal activation, are influenced by the adiabatic and nonadiabatic spin-torques. We find the Arrhenius law that describes the transition rate for activation over a single energy barrier remains applicable under currents but with a current-dependent barrier height. We show that the effective energy barrier is dominated by a linear current dependence under usual experimental conditions, with a variation that depends only on the nonadiabatic spin torque coefficient beta.

Temperature dependence of the current-induced domain wall motion from a modified Landau-Lifshitz-Bloch equation

We employ the Landau-Lifshitz-Bloch (LLB) equation to investigate current-induced domain wall motion at finite temperatures by numerical micromagnetic simulations. We extend the LLB equation with spin torque terms that account for the effect of spin-polarized currents and we find that the velocities depend strongly on the interplay between adiabatic and nonadiabatic spin torque terms. As a function of temperature, we find nonmonotonous behavior, which might be useful to determine the relative strengths of the spin torque terms experimentally.

Non-adiabatic spin-torques in narrow magnetic domain walls

There is considerable debate over the size and direction of the non-adiabatic component of the spin-torque generated when a current flows across a domain wall in a ferromagnet. Measurements of this property in a wall just 1–10 nm wide suggest its value is small, arising from purely magnetic dissipation mechanisms. Torques appear between charge carrier spins and local moments in regions of ferromagnetic media where spatial magnetization gradients occur, such as a domain wall, owing to an exchange interaction. This phenomenon has been predicted by different theories1,2,3,4,5,6,7 and confirmed in a number of experiments on metallic and semiconductor ferromagnets8,9,10,11,12,13,14,15,16,17,18,19. Understanding the magnitude and orientation of such spin-torques is an important problem for spin-dependent transport and current-driven magnetization dynamics, as domain-wall motion underlies a number of emerging spintronic technologies20,21. One outstanding issue concerns the non-adiabatic spin-torque component β, which has an important role in wall dynamics, but no clear consensus has yet emerged over its origin or magnitude. Here, we report an experimental measurement of β in perpendicularly magnetized films with narrow domain walls (1–10 nm). By studying thermally activated wall depinning, we deduce β from the variation of the Arrhenius transition rate with applied currents. Surprisingly, we find β to be small and relatively insensitive to the wall width, which stands in contrast to predictions from transport theories2,5,6,7. In addition, we find β to be close to the Gilbert damping constant α, which, in light of similar results on planar anisotropy systems15, suggests a universal origin for the non-adiabatic torque.

Scaling of spin relaxation and angular momentum dissipation in permalloy nanowires

We study the relationship between the damping $(\ensuremath{\alpha})$ and the nonadiabaticity of the spin transport $(\ensuremath{\beta})$ in permalloy nanowires. $\ensuremath{\alpha}$ is engineered by Ho doping, and from the characteristics of the current-induced domain-wall velocity, determined by high-resolution x-ray magnetic circular-dichroism photoemission electron microscopy, $\ensuremath{\beta}$ due to spin relaxation is measured. We find that $\ensuremath{\beta}$ scales with $\ensuremath{\alpha}$ and conclude that the spin relaxation that leads to nonadiabatic spin torque originates from the same underlying mechanism as the angular momentum dissipation that causes viscous damping.

Effect of Non-Adiabatic Spin Torque Parameter on Domain Wall Motion Driven by Pulse Current in a Magnetic Nanowire

The effect of the non-adiabatic spin torque parameter on domain wall depinning driven by pulse current has been investigated using micromagnetic simulation. The results showed that domain wall depinning is sensitive to both pulse current frequency and the value of the non-adiabatic spin torque parameter. The transverse wall was found to be more easily depinned for larger values of the non-adiabatic constant. The largest improvement in the critical current density for a pulse current was found for a non-adiabatic spin torque parameter of 0.03.

Current-Induced Control of Spin-Wave Attenuation

The current-induced modification of the attenuation of a propagating spin wave in a magnetic nanowire is studied theoretically and numerically. The attenuation length of spin wave can increase when the spin waves and electrons move in the same direction. It is directly affected by the nonadiabaticity of the spin-transfer torque and thus can be used to estimate the nonadiabaticity. When the nonadiabatic spin torque is sufficiently large, the attenuation length becomes negative, resulting in the amplification of spin waves.

Current-induced resonant motion of a magnetic vortex core: Effect of nonadiabatic spin torque

The current-induced resonant excitation of a magnetic vortex core is investigated by means of analytical and micromagnetic calculations. We find that the radius and phase shift of the resonant motion are not correctly described by the analytical equations because of the dynamic distortion of a vortex core. In contrast, the initial tilting angle of a vortex core is free from the distortion and determined by the nonadiabaticity of the spin torque. It is insensitive to experimentally uncontrollable current-induced in-plane Oersted field and thus allows a direct comparison with experimental results. We propose that a time-resolved imaging of the very initial trajectory of a core is a plausible way to experimentally estimate the nonadiabaticity.

Current-induced multiple spin structures in 100 nm ring magnetic tunnel junctions

Nanoring magnetic tunnel junctions (NR-MTJs) with outer diameters as small as 100 nm and a thin wall width of 25 nm have been fabricated. NR-MTJs acquire different resistance states when they are switched by electrical currents compared with when they are switched by external magnetic fields. This can be explained by combining the effects of spin-transfer torque and circulatory Oersted field during current-induced switching. We provide a model for computing the equivalent circulatory magnetic field due to the nonadiabatic spin torque of the spin-polarized current through the MTJ. The multiple spin states in nanoring MTJs provide prospects for magnetic memory devices.

Current-induced motion of narrow domain walls and dissipation in ferromagnetic metals

Spin transport equations in a nonhomogeneous ferromagnet are derived in the limit where the sd exchange coupling between the electrons in the conduction band and those in the d band is dominant. It is shown that spin diffusion in ferromagnets assumes a tensor form. The diagonal terms are renormalized with respect to that in normal metals and enhance the dissipation in the magnetic system while the off-diagonal terms renormalize the precessional frequency of the conduction electrons and enhance the nonadiabatic spin torque. To demonstrate what additional physics is included in the theory, we show that self-consistent solutions of the spin diffusion equations and the Landau-Lifshitz equations in the presence of a current lead to an increase in the terminal velocity of a domain wall which becomes strongly dependent on its width. We also provide a simplified equation that predicts damping due to the conduction electrons.

Spin pumping of current in non-uniform conducting magnets

Using irreversible thermodynamics, we show that current-induced spin transfer torque within a magnetic domain implies spin pumping of current within that domain. This has experimental implications for samples both with conducting leads and that are electrically isolated. These results are obtained by deriving the dynamical equations for two models of non-uniform conducting magnets: (1) a generic conducting magnet, with net conduction electron density $n$ and net magnetization $\stackrel{P\vec}{M}$, and (2) a two-band magnet, with up and down spins each providing conduction and magnetism. For both models, in regions where the equilibrium magnetization is non-uniform, voltage gradients can drive adiabatic and nonadiabatic bulk spin torques. Onsager relations then ensure that magnetic torques likewise drive adiabatic and nonadiabatic currents\char22{}what we call bulk spin pumping. For a given amount of adiabatic and nonadiabatic spin torques, the two models yield similar but distinct results for the bulk spin pumping, thus distinguishing the two models. As for recent spin-Berry phase work, we find that within a domain wall, the ratio of the effective electromotive force to the magnetic field is approximately given by $P(2{\ensuremath{\mu}}_{B}∕e)$, where $P$ is the spin polarization. The adiabatic spin torque and spin-pumping terms are shown to be dissipative.

Effect of shape anisotropy on threshold current density for current-induced domain wall motion

Using micromagnetic simulations, the authors investigate the effects of the shape anisotropy of nanowires on the threshold current density (JC) in the adiabatic limit. It is observed that the type of domain wall significantly affects the dependence of JC on the shape anisotropy. For a transverse wall, JC is proportional to the shape anisotropy, but slightly deviates from the theoretical prediction [G. Tatara and H. Kohno, Phys. Rev. Lett. 92, 086601 (2004)] possibly due to antivortex formation. For a vortex wall, JC is almost independent of the shape anisotropy, as experimentally observed [A. Yamaguchi et al., Jpn. J. Appl. Phys. Part 1 45, 3850 (2006)]. Interestingly, JC and the velocity of the vortex wall at finite temperatures are in good agreement with the experimental values even when the nonadiabatic spin torque is not considered.

Effect of ac on current-induced domain wall motion

Saitoh et al. [Nature (London) 432, 203 (2004)] have reported the experimental result showing the interplay of a transverse domain wall with an electrical ac of megahertz-range frequencies. They observed a single peak of resistance in the frequency range and interpreted it with a nonadiabatic spin torque. It was argued that an ac current can induce a micrometer-range displacement of domain wall. We reconstructed the experiment in micromagnetic simulations considering the local nonzero nonadiabatic spin torque. We could not observe either an explicit single peak in the frequency-dependent resistance or an eventual displacement of domain wall by use of an ac. It indicates the local nonadiabatic torque is inappropriate to explain the experimental results of ac-induced domain wall motion. Other approaches such as the nonlocal nonadiabatic spin torque may be needed.

Numerical investigation of spin-torque using the Heisenberg model

We present numerical calculations of the spin transfer torque resulting in current-induced domain wall motion. Rather than the conventional micromagnetic finite difference or finite element method, we use an atomistic/classical Heisenberg spin model approach, which is well suited to study geometrically confined domain walls. We compute the behaviour of domain walls in a one dimensional chain when currents are injected using adiabatic and non-adiabatic spin torque terms. Our results are compared to analytical calculations and are found to agree very well for small current densities. At larger current densities deviations are observed, which can be attributed to the approximations used in the analytical calculations.

Thermally Assisted Current-Driven Domain-Wall Motion

Starting from the stochastic Landau-Lifschitz-Gilbert equation, we derive Langevin equations that describe the nonzero-temperature dynamics of a rigid domain wall. We derive an expression for the average drift velocity of the domain wall r(dw) as a function of the applied current, and find qualitative agreement with recent magnetic semiconductor experiments. Our model implies that at any nonzero-temperature r(dw) initially varies linearly with current, even in the absence of nonadiabatic spin torques.

Field- and current-driven domain wall dynamics: An experimental picture

Field- and current-driven domain wall velocities are measured and discussed in terms of existing spin-torque models. A reversal in the roles of adiabatic and non-adiabatic spin-torque is shown to arise in those models below and above Walker breakdown. The measured dependence of velocity on current is the same in both regimes, indicating both spin-torque components have similar magnitude. However, the models on which these conclusions are based have serious quantitative shortcomings in describing the observed field-driven wall dynamics, for which they were originally developed. Hence, the applicability of simple one-dimensional models to most experimental conditions may be limited.

Domain-wall resonance induced by spin-polarized current in metal thin films with stripe structures

The dynamics of a domain wall induced by spin-polarized current is studied in ferromagnetic metallic thin films with stripe structures. The solution of the generalized Landau-Lifshitz-Gilbert equation including adiabatic and nonadiabatic spin torque is used to describe motion and distortion of the domain wall. We show that ac currents facilitate the manipulation of the domain wall since domain wall resonance decreases the critical current density for depinning. In contrast with dc current, both the two spin torques induced by ac currents can produce wall motion and distortion.