Current-spin coupling for ferromagnetic domain walls in fine wires

Current-driven fast magnetic octupole domain-wall motion in noncollinear antiferromagnets

Antiferromagnets (AFMs) have the natural advantages of terahertz spin dynamics and negligible stray fields, thus appealing for use in domain-wall applications. However, their insensitive magneto-electric responses make controlling them in domain-wall devices challenging. Recent research on noncollinear chiral AFMs Mn3X (X = Sn, Ge) enabled us to detect and manipulate their magnetic octupole domain states. Here, we demonstrate a current-driven fast magnetic octupole domain-wall (MODW) motion in Mn3X. The magneto-optical Kerr observation reveals the Néel-like MODW of Mn3Ge can be accelerated up to 750 m s-1 with a current density of only 7.56 × 1010 A m-2 without external magnetic fields. The MODWs show extremely high mobility with a small critical current density. We theoretically extend the spin-torque phenomenology for domain-wall dynamics from collinear to noncollinear magnetic systems. Our study opens a new route for antiferromagnetic domain-wall-based applications.

The origin of spin wave pulse-induced domain wall inertia

The fundamental problem of domain wall (DW) inertia-the property that gives to inertial behaviors remains unclear in the physics of magnetic solitons. To understand its nature as well as to achieve accurate DW positioning and efficient manipulation of domain wall motion (DWM), spin wave (SW) pulse-induced DW transient effect is studied both numerically and theoretically in a magnetic nanostrip. It is shown for the first time that there occurs inevitable deceleration/automotion after SW pulse, which indicates nonzero DW inertia. The induced DWM is revealed to relate to two factors: energy storing within DW and out-of-plane tilting of DW. To explain the DWM dynamics, a one-dimensional collective model is developed to account for the excitation of spin wave pulse. The model successfully bridges DW energy, DW tilting and DW displacement and provides descriptions in accordance with numerical findings. It is made clear that the DW automotion hence DW inertia originate from the process of DW relaxation toward equilibrium. The DW inertia is expressed in terms of effective mass and turns out to be a time-dependent function with damping constantαas the governing parameter, which opposes the nature of intrinsic mass. For case containing multiple DWs, the total effective mass is shown to concern the reached velocity and stored energy of DWs instead of the number of DWs, which is against common intuition.

Emergent gauge field and the Lifshitz transition of spin-orbit coupled bosons in one dimension

In the presence of strong spin-independent interactions and spin-orbit coupling, we show that the spinor Bose liquid confined to one spatial dimension undergoes an interaction- or density-tuned quantum phase transition similar to one theoretically proposed for itinerant magnetic solid-state systems. The order parameter describes broken Z₂ inversion symmetry, with the ordered phase accompanied by non-vanishing momentum which is generated by fluctuations of an emergent dynamical gauge field at the phase transition. This quantum phase transition has dynamical critical exponent z ≃ 2, typical of a Lifshitz transition, but is described by a nontrivial interacting fixed point. From direct numerical simulation of the microscopic model, we extract previously unknown critical exponents for this fixed point. Our model describes a realistic situation of 1D ultracold atoms with Raman-induced spin-orbit coupling, establishing this system as a platform for studying exotic critical behavior of the Hertz-Millis type.

Nanometric alternating magnetic field generator

In this work we introduce an alternating magnetic field generator in a cylindrical nanostructure. This field appears due to the rotation of a magnetic domain wall located at some position, generating a magnetic region that varies its direction of magnetization alternately, thus inducing an alternating magnetic flux in its vicinity. This phenomenon occurs due to the competition between a spin-polarized current and a magnetic field, which allows to control both the angular velocity and the pinning position of the domain wall. As proof of concept, we study the particular case of a diameter-modulated nanowire with a spin-polarized current along its axis and the demagnetizing field produced by its modulation. This inhomogeneous field allows one to control the angular velocity of the domain wall as a function of its position along the nanowire allowing frequencies in the GHz range to be achieved. This generator could be used in telecommunications for devices in the range of radiofrequencies or, following Faraday's induction law, could also induce an electromotive force and be used as a movable alternate voltage source in future nanodevices.

Skyrmion-Anti-Skyrmion Pair Creation by in-Plane Currents

Magnetic Skyrmions can be considered as localized vortexlike spin textures which are topologically protected in continuous systems. Because of their stability, their small size, and the possibility to move them by low electric currents, they are promising candidates for spintronic devices. Without changing the topological charge, it is possible to create Skyrmion-anti-Skyrmion pairs. We derive a Skyrmion equation of motion which reveals how spin-polarized charge currents create Skyrmion-anti-Skyrmion pairs. It allows us to identify general prerequisites for the pair creation process. We corroborate these general principles by numerical simulations. On a lattice, where the concept of topological protection has to be replaced by that of a finite energy barrier, the anti-Skyrmion partner of the pairs is annihilated and only the Skyrmion survives. This eventually changes the total Skyrmion number and yields a new way of creating and controlling Skyrmions.

Magnonic Black Holes

We show that the interaction between the spin-polarized current and the magnetization dynamics can be used to implement black-hole and white-hole horizons for magnons-the quanta of oscillations in the magnetization direction in magnets. We consider three different systems: easy-plane ferromagnetic metals, isotropic antiferromagnetic metals, and easy-plane magnetic insulators. Based on available experimental data, we estimate that the Hawking temperature can be as large as 1 K. We comment on the implications of magnonic horizons for spin-wave scattering and transport experiments, and for magnon entanglement.

The magnetic monopole and the separation between fast and slow magnetic degrees of freedom

The Landau-Lifshitz-Gilbert (LLG) equation that describes the dynamics of a macroscopic magnetic moment finds its limit of validity at very short times. The reason for this limit is well understood in terms of separation of the characteristic time scales between slow degrees of freedom (the magnetization) and fast degrees of freedom. The fast degrees of freedom are introduced as the variation of the angular momentum responsible for the inertia. In order to study the effect of the fast degrees of freedom on the precession, we calculate the geometric phase of the magnetization (i.e. the Hannay angle) and the corresponding magnetic monopole. In the case of the pure precession (the slow manifold), a simple expression of the magnetic monopole is given as a function of the slowness parameter, i.e. as a function of the ratio of the slow over the fast characteristic times.

Intrinsic spin torque without spin-orbit coupling

We derive an intrinsic contribution to the non-adiabatic spin torque for non-uniform magnetic textures. It differs from previously considered contributions in several ways and can be the dominant contribution in some models. It does not depend on the change in occupation of the electron states due to the current flow but rather is due to the perturbation of the electronic states when an electric field is applied. Therefore it should be viewed as electric-field-induced rather than current-induced. Unlike previously reported non-adiabatic spin torques, it does not originate from extrinsic relaxation mechanisms nor spin-orbit coupling. This intrinsic non-adiabatic spin torque is related by a chiral connection to the intrinsic spin-orbit torque that has been calculated from the Berry phase for Rashba systems.

Model of spin accumulation and spin torque in spatially varying magnetisation structures: limitations of the micromagnetic approach

We study the spin-transfer torque acting on the magnetisation when injecting polarised conduction electrons into a magnetic system. The spin accumulation is calculated self-consistently and naturally includes the adiabatic and non-adiabatic contributions which depend on the rate of change of magnetisation in relation to the spin diffusion length. As an example we consider a system where a spin-polarised current is injected into a structure containing a domain wall. We calculate the spin torque and related parameters corresponding to the adiabatic and non-adiabatic terms directly from the spin accumulation, and find that the dynamic micromagnetic approach based on adiabatic and non-adiabatic terms with constant coefficients is valid only for systems with slowly spatially varying magnetisation.

Theory of the spin Seebeck effect

The spin Seebeck effect refers to the generation of a spin voltage caused by a temperature gradient in a ferromagnet, which enables the thermal injection of spin currents from the ferromagnet into an attached nonmagnetic metal over a macroscopic scale of several millimeters. The inverse spin Hall effect converts the injected spin current into a transverse charge voltage, thereby producing electromotive force as in the conventional charge Seebeck device. Recent theoretical and experimental efforts have shown that the magnon and phonon degrees of freedom play crucial roles in the spin Seebeck effect. In this paper, we present the theoretical basis for understanding the spin Seebeck effect and briefly discuss other thermal spin effects.

A mechanism to pin skyrmions in chiral magnets

We propose a mechanism to pin skyrmions in chiral magnetic thin films by introducing local maxima of magnetic exchange strength as pinning centers. The local maxima can be realized by engineering the local density of itinerant electrons. The stationary properties and the dynamical pinning and depinning processes of an isolated skyrmion around a pinning center are studied. We carry out numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equation and find a way to control the position of an isolated skyrmion in a pinning center lattice using electric current pulses. The results are verified by a Thiele equation analysis. We also find that the critical current to depin a skyrmion, which is estimated to have order of magnitude 10(7)-10(8) A m(-2), has linear dependence on the pinning strength.

Domain-wall dynamics in translationally nonivariant nanowires: theory and applications

We generalize domain-wall dynamics to the case of translationally noninvariant ferromagnetic nanowires. The obtained equations of motion make the description of the domain-wall propagation more realistic by accounting for the variations along the wire, such as disorder or change in the wire shape. We show that the effective equations of motion are very general and do not depend on the model details. As an example of their use, we consider an hourglass-shaped nanostrip in detail. A transverse domain wall is trapped in the middle and has two stable magnetization directions. We study the switching between the two directions by short current pulses. We obtain the exact time dependence of the current pulses required to switch the magnetization with the minimal Ohmic losses per switching. Furthermore, we find how the Ohmic losses per switching depend on the switching time for the optimal current pulse. As a result, we show that as a magnetic memory device this nanodevice may be 10(5) times more energy efficient than the best modern devices.

Current-induced torques in magnetic materials

The magnetization of a magnetic material can be reversed by using electric currents that transport spin angular momentum. In the reciprocal process a changing magnetization orientation produces currents that transport spin angular momentum. Understanding how these processes occur reveals the intricate connection between magnetization and spin transport, and can transform technologies that generate, store or process information via the magnetization direction. Here we explain how currents can generate torques that affect the magnetic orientation and the reciprocal effect in a wide variety of magnetic materials and structures. We also discuss recent state-of-the-art demonstrations of current-induced torque devices that show great promise for enhancing the functionality of semiconductor devices.

Influence of a transport current on a domain wall in an antiferromagnetic metal

We consider the influence of an electric current on the position of a domain wall in an antiferromagnetic metal. We first microscopically derive an equation of motion for the Néel vector in the presence of current by performing, in the transport steady state, a linear-response calculation in the deviation from collinearity of the antiferromagnet. This equation of motion is then solved variationally for an antiferromagnetic domain wall. We find that, in the absence of dissipative or non-adiabatic coupling between magnetization and current, the current displaces the domain wall by a finite amount and that the domain wall is then intrinsically pinned by the exchange interactions. In the presence of dissipative or non-adiabatic current-to-domain-wall coupling, the domain wall velocity is proportional to the current and is no longer pinned.

Spin control by application of electric current and voltage in FeCo-MgO junctions

Efficient control and detection of spins are the most important tasks in spintronics. The current and voltage applied to a magnetic tunnel junction may exert a torque on the magnetic thin layer in the junction and cause its reversal or continuous precession. The discovery of the giant tunnelling magnetoresistance effect in ferromagnetic tunnelling junctions using an MgO barrier enabled us to obtain a large signal output from the magnetization reversal and precession. Also, the interplay of large spin configuration-electric conduction coupling provides highly nonlinear effects like the spin-torque diode effect. The negative resistance effect and amplification using it are predicted. A new discovery about a voltage-induced magnetic anisotropy change in Fe ultrathin films is also discussed.

Dynamics of Skyrmion crystals in metallic thin films

We study the collective dynamics of the Skyrmion crystal in thin films of ferromagnetic metals resulting from the nontrivial Skyrmion topology. It is shown that the current-driven motion of the crystal reduces the topological Hall effect and the Skyrmion trajectories bend away from the direction of the electric current (the Skyrmion Hall effect). We find a new dissipation mechanism in noncollinear spin textures that can lead to a much faster spin relaxation than Gilbert damping, calculate the dispersion of phonons in the Skyrmion crystal, and discuss the effects of impurity pinning of Skyrmions.

Dynamics of magnetic domain walls under their own inertia

The motion of magnetic domain walls induced by spin-polarized current has considerable potential for use in magnetic memory and logic devices. Key to the success of these devices is the precise positioning of individual domain walls along magnetic nanowires, using current pulses. We show that domain walls move surprisingly long distances of several micrometers and relax over several tens of nanoseconds, under their own inertia, when the current stimulus is removed. We also show that the net distance traveled by the domain wall is exactly proportional to the current pulse length because of the lag derived from its acceleration at the onset of the pulse. Thus, independent of its inertia, a domain wall can be accurately positioned using properly timed current pulses.

Discrete domain wall positioning due to pinning in current driven motion along nanowires

Racetrack memory is a novel storage-class memory device in which a series of domain walls (DWs), representing zeros and ones, are shifted to and fro by current pulses along magnetic nanowires. Here we show, by precise measurements of the DW's position using spin-valve nanowires, that these positions take up discrete values. This results from DW relaxation after the end of the current pulse into local energy minima, likely derived from imperfections in the nanowire.

Minimization of Ohmic losses for domain wall motion in a ferromagnetic nanowire

We study current-induced domain-wall motion in a narrow ferromagnetic wire. We propose a way to move domain walls with a resonant time-dependent current which dramatically decreases the Ohmic losses in the wire and allows driving of the domain wall with higher speed without burning the wire. For any domain-wall velocity we find the time dependence of the current needed to minimize the Ohmic losses. Below a critical domain-wall velocity specified by the parameters of the wire the minimal Ohmic losses are achieved by dc current. Furthermore, we identify the wire parameters for which the losses reduction from its dc value is the most dramatic.

Direct determination of large spin-torque nonadiabaticity in vortex core dynamics

We use a pump-probe photoemission electron microscopy technique to image the displacement of vortex cores in Permalloy discs due to the spin-torque effect during current pulse injection. Exploiting the distinctly different symmetries of the spin torques and the Oersted-field torque with respect to the vortex spin structure we determine the torques unambiguously, and we quantify the amplitude of the strongly debated nonadiabatic spin torque. The nonadiabaticity parameter is found to be β=0.15±0.07, which is more than an order of magnitude larger than the damping constant α, pointing to strong nonadiabatic transport across the high magnetization gradient vortex spin structures.

Width dependence of the nonadiabatic spin-transfer torque in narrow domain walls

We analytically determine the spatially varying spin-transfer torque within a domain wall. In the case of ballistic spin and diffusive charge transport, the spin-transfer torque as well as the local degree of nonadiabaticity oscillate within a domain wall. In narrow domain walls, the degree of nonadiabaticity ceases to be a constant material parameter but depends on the domain-wall width including a possible sign change, which is crucial for experiments and the technological utilization in spin-transfer-torque-based storage devices.

Current driven magnetization dynamics in ferromagnetic nanowires with a Dzyaloshinskii-Moriya interaction

We study current-induced magnetization dynamics in a long thin ferromagnetic wire with a Dzyaloshinskii-Moriya interaction (DMI). We find a spiral domain wall configuration of the magnetization and obtain an analytical expression for the width of the domain wall as a function of the interaction strengths. Our findings show that above a certain value of DMI a domain wall configuration cannot exist in the wire. Below this value we determine the domain wall dynamics for small currents, and calculate the drift velocity of the domain wall along the wire. We show that the DMI suppresses the minimum value of current required to move the domain wall. Depending on its sign, the DMI increases or decreases the domain wall drift velocity.

Nonadiabatic spin torque investigated using thermally activated magnetic domain wall dynamics

Using transmission electron microscopy, we investigate the thermally activated motion of domain walls (DWs) between two positions in Permalloy (Ni80Fe20) nanowires at room temperature. We show that this purely thermal motion is well described by an Arrhenius law, allowing for a description of the DW as a quasiparticle in a one-dimensional potential landscape. By injecting small currents, the potential is modified, allowing for the determination of the nonadiabatic spin torque: βt=0.010±0.004 for a transverse DW and βv=0.073±0.026 for a vortex DW. The larger value is attributed to the higher magnetization gradients present.

Magnetic domain wall pumping by spin transfer torque

We show that spin transfer torque from a direct spin-polarized current applied parallel to a magnetic domain wall (DW) induces DW motion in a direction independent of the current polarity. This unidirectional response of the DW to spin torque enables DW pumping--long-range DW displacement driven by an alternating current. Our numerical simulations reveal that DW pumping can be resonantly amplified through excitation of internal degrees of freedom of the DW by the current.

Beating the walker limit with massless domain walls in cylindrical nanowires

We present a micromagnetic study on the current-induced domain-wall motion in cylindrical Permalloy nanowires with diameters below 50 nm. The transverse domain walls forming in such thin, round wires are found to differ significantly from those known from flat nanostrips. In particular, we show that these domain walls are zero-mass micromagnetic objects. As a consequence, they display outstanding dynamic properties, most importantly the absence of a breakdown velocity generally known as the Walker limit. Our simulation data are confirmed by an analytic model which provides a detailed physical understanding. We further predict that a particular effect of the current-induced dynamics of these domain walls could be exploited to measure the nonadiabatic spin-transfer torque coefficient.

Intrinsic coupling between current and domain wall motion in (Ga,Mn)As

We consider current-induced domain wall motion and, the reciprocal process, moving domain wall-induced current. The associated Onsager coefficients are expressed in terms of scattering matrices. Uncommonly, in (Ga,Mn)As, the effective Gilbert damping coefficient alphaw and the effective out-of-plane spin-transfer torque parameter betaw are dominated by spin-orbit interaction in combination with scattering off the domain wall, and not scattering off extrinsic impurities. Numerical calculations give alphaw approximately 0.01 and betaw approximately 1 in dirty (Ga,Mn)As. The extraordinarily large betaw parameter allows experimental detection of current or voltage induced by domain wall motion in (Ga,Mn)As.

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.

The quantum-mechanical basis of an extended Landau-Lifshitz-Gilbert equation for a current-carrying ferromagnetic wire

An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for a simple model which includes impurity scattering. This is done by comparing the energies and lifetimes of a spin wave calculated from the LLG equation and from the explicit model. Two terms are of particular importance since they describe non-adiabatic spin-transfer torque and damping processes which do not rely on spin-orbit coupling. It is shown that these terms may have a significant influence on the velocity of a current-driven domain wall and they become dominant in the case of a narrow wall.

Dependence of domain-wall depinning threshold current on pinning profile

We have investigated the threshold current density required for depinning a domain wall from constrictions in NiFe nanowires, which give rise to pinning potentials of fixed amplitude but variable profile. We observed it to vary linearly with the angle of the triangular constriction. These results are reproduced using micromagnetic simulations including the adiabatic and nonadiabatic spin-torque terms. By curve-fitting the calculated variations to the experimental results, we obtain the nonadiabaticity parameter beta=0.04(+/-0.005) and current spin polarization P=0.51(+/-0.02).

Relationship between nonadiabaticity and damping in permalloy studied by current induced spin structure transformations

By direct imaging we determine spin structure changes in Permalloy wires and disks due to spin transfer torque as well as the critical current densities for different domain wall types. Periodic domain wall transformations from transverse to vortex walls and vice versa are observed, and the transformation mechanism occurs by vortex core displacement perpendicular to the wire. The results imply that the nonadiabaticity parameter beta does not equal the damping alpha, in agreement with recent theoretical predictions. The vortex core motion perpendicular to the current is further studied in disks revealing that the displacement in opposite directions can be attributed to different polarities of the vortex core.

Domain walls in the (Ga,Mn)as diluted magnetic semiconductor

We report experimental and theoretical studies of magnetic domain walls in an in-plane magnetized (Ga,Mn)As dilute moment ferromagnetic semiconductor. Our high-resolution electron holography technique provides direct images of domain wall magnetization profiles. The experiments are interpreted based on microscopic calculations of the micromagnetic parameters and Landau-Lifshitz-Gilbert simulations. We find that the competition of uniaxial and biaxial magnetocrystalline anisotropies in the film is directly reflected in orientation dependent wall widths, ranging from approximately 40 to 120 nm. The domain walls are of the Néel type and evolve from near-90 degrees walls at low temperatures to large angle [11[over ]0]-oriented walls and small angle [110]-oriented walls at higher temperatures.

Universality Classes for Domain Wall Motion in the Ferromagnetic Semiconductor (Ga,Mn)As

Magnetic domain wall motion induced by magnetic fields and spin-polarized electrical currents is experimentally well established. A full understanding of the underlying mechanisms, however, remains elusive. For the ferromagnetic semiconductor (Ga,Mn)As, we have measured and compared such motions in the thermally activated subthreshold, or "creep," regime, where the velocity obeys an Arrhenius scaling law. Within this law, the clearly different exponents of the current and field reflect different universality classes, showing that the drive mechanisms are fundamentally different.

Generalization of Faraday's Law to include nonconservative spin forces

The usual Faraday's Law E=-dPhi/dt determines an electromotive force E which accounts only for forces resulting from the charge of electrons. In ferromagnetic materials, in general, there exist nonconservative spin forces which also contribute to E. These might be included in Faraday's Law if the magnetic flux Phi is replaced by [Planck's constant/(-e)]gamma, where gamma is a Berry phase suitably averaged over the electron spin direction. These contributions to E represent the requirements of energy conservation in itinerant ferromagnets with time dependent order parameters.

Resonant Amplification of Magnetic Domain-Wall Motion by a Train of Current Pulses

The current-induced motion of magnetic domain walls confined to nanostructures is of interest for applications in magnetoelectronic devices in which the domain wall serves as the logic gate or memory element. The injection of spin-polarized current below a threshold value through a domain wall confined to a pinning potential results in its precessional motion within the potential well. We show that by using a short train of current pulses, whose length and spacing are tuned to this precession frequency, the domain wall's oscillations can be resonantly amplified. This makes possible the motion of domain walls with much reduced currents, more than five times smaller than in the absence of resonant amplification.

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.

Current driven domain wall velocities exceeding the spin angular momentum transfer rate in permalloy nanowires

The velocity of domain walls driven by current in zero magnetic field is measured in permalloy nanowires using real-time resistance measurements. The domain wall velocity increases with increasing current density, reaching a maximum velocity of approximately 110 m/s when the current density in the nanowire reaches approximately 1.5 x 10(8) A/cm(2). Such high current driven domain wall velocities exceed the estimated rate at which spin angular momentum is transferred to the domain wall from the flow of spin polarized conduction electrons, suggesting that other driving mechanisms, such as linear momentum transfer, need to be taken into account.

Dependence of current and field driven depinning of domain walls on their structure and chirality in permalloy nanowires

A magnetic domain wall (DW) injected and pinned at a notch in a permalloy nanowire is shown to exhibit four well-defined magnetic states, vortex and transverse, each with two chiralities. These states, imaged using magnetic force microscopy, are readily detected from their different resistance values arising from the anisotropic magnetoresistance effect. Whereas distinct depinning fields and critical depinning currents in the presence of magnetic fields are found, the critical depinning currents are surprisingly similar for all four DW states in low magnetic fields. We observe current-induced transformations between these DW states below the critical depinning current which may account for the similar depinning currents.

Oscillatory dependence of current-driven magnetic domain wall motion on current pulse length

Magnetic domain walls, in which the magnetization direction varies continuously from one direction to another, have long been objects of considerable interest. New concepts for devices based on such domain walls are made possible by the direct manipulation of the walls using spin-polarized electrical current through the phenomenon of spin momentum transfer. Most experiments to date have considered the current-driven motion of domain walls under quasi-static conditions, whereas for technological applications, the walls must be moved on much shorter timescales. Here we show that the motion of domain walls under nanosecond-long current pulses is surprisingly sensitive to the pulse length. In particular, we find that the probability of dislodging a domain wall, confined to a pinning site in a permalloy nanowire, oscillates with the length of the current pulse, with a period of just a few nanoseconds. Using an analytical model and micromagnetic simulations, we show that this behaviour is connected to a current-induced oscillatory motion of the domain wall. The period is determined by the wall's mass and the slope of the confining potential. When the current is turned off during phases of the domain wall motion when it has enough momentum, the domain wall is driven out of the confining potential in the opposite direction to the flow of spin angular momentum. This dynamic amplification effect could be exploited in magnetic nanodevices based on domain wall motion.

Influence of current on field-driven domain wall motion in permalloy nanowires from time resolved measurements of anisotropic magnetoresistance

The motion of magnetic domain walls in permalloy nanowires is investigated by real-time resistance measurements. The domain wall velocity is measured as a function of the magnetic field in the presence of a current flowing through the nanowire. We show that the current can significantly increase or decrease the domain wall velocity, depending on its direction. These results are understood within a one-dimensional model of the domain wall dynamics which includes the spin transfer torque.

Velocity of domain-wall motion induced by electrical current in the ferromagnetic semiconductor (Ga,Mn)As

Current-induced domain-wall motion with velocity spanning over 5 orders of magnitude up to 22 m/s has been observed by the magneto-optical Kerr effect in (Ga,Mn)As with perpendicular magnetic anisotropy. The data are employed to verify theories of spin transfer by the Slonczewski-like mechanism as well as by the torque resulting from spin-flip transitions in the domain-wall region. Evidence for domain-wall creep at low currents is found.

Dynamics of localized spins coupled to the conduction electrons with charge and spin currents

The dynamics of the localized spins coupled to the conduction electrons is studied theoretically in the wide range of magnitudes of the charge and spin currents including the regime which has never been explored but is now possible in terms of the pure spin-current injection methods, e.g., the spin Hall effect and spin battery. The equations of motion for the two-spin system are investigated in detail, and its phase diagram of the dynamics is presented. It is found that the dynamics depends sensitively upon the relative magnitudes of the charge and spin currents; i.e., it shows steady state, periodic motion, and even chaotic behavior. The extension to the multispin system and its implications including a possible "spin-current detector" are also discussed.