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

Position error-free control of magnetic domain-wall devices via spin-orbit torque modulation

Magnetic domain-wall devices such as racetrack memory and domain-wall shift registers facilitate massive data storage as hard disk drives with low power portability as flash memory devices. The key issue to be addressed is how perfectly the domain-wall motion can be controlled without deformation, as it can replace the mechanical motion of hard disk drives. However, such domain-wall motion in real media is subject to the stochasticity of thermal agitation with quenched disorders, resulting in severe deformations with pinning and tilting. To sort out the problem, we propose and demonstrate a new concept of domain-wall control with a position error-free scheme. The primary idea involves spatial modulation of the spin-orbit torque along nanotrack devices, where the boundary of modulation possesses broken inversion symmetry. In this work, by showing the unidirectional motion of domain wall with position-error free manner, we provide an important missing piece in magnetic domain-wall device development.

Domain wall motion driven by a wide range of current in coupled soft/hard ferromagnetic nanowires

Racetrack memory with the advantages of small size and high reading speed is proposed based on current-induced domain wall (DW) motion in a ferromagnetic (FM) nanowire. Walker breakdown that restricts the enhancement of DW velocity in a single FM nanowire can be depressed by inter-wire magnetostatic coupling in a double FM nanowire system. However, this magnetostatic coupling also limits the working current density in a small range. In the present work, based on micromagnetic calculation, we have found that when there is a moderate difference of magnetic anisotropy constant between two FM nanowires, the critical current density for triggering the DW motion can be reduced while that for breaking the inter-wire coupling can be enhanced significantly to a magnitude of 10¹³ A m^-2, which is far above the working current density in current electronic devices. The manipulation of working current density is relevant to the modification of DW structure and inter-wire magnetostatic coupling due to the difference of the anisotropy constants between the two nanowires and paves a way to develop racetrack memory that can work in a wide range of current.

Magnetism and magnetoresistance in the critical region of a dilute ferromagnet

We present detailed experimental measurements and simulations of the field-dependent magnetization and magnetoresistance in the vicinity of the Curie temperature in the highly disordered dilute ferromagnetic semiconductor (Ga,Mn)As. The observed dependence of the magnetization on external magnetic field and temperature is consistent with three-dimensional Heisenberg equation of state calculations including a narrow distribution of critical temperatures. The magnetoresistance shows a peak at the Curie temperature due to the suppression of magnetic scattering in an applied magnetic field, which is well-described by considering changes in the square of the magnetization induced by the magnetic field.

Current-Induced Domain Wall Motion and Tilting in Perpendicularly Magnetized Racetracks

The influence of C insertion on Dzyaloshinskii-Moriya interaction (DMI) as well as current-induced domain wall (DW) motion (CIDWM) and tilting in Pt/Co/Ta racetracks is investigated via a magneto-optical Kerr microscope. The similar DMI strength for Pt/Co/Ta and Pt/Co/C/Ta samples reveals that DMI mainly comes from the Pt/Co interface. Fast DW velocity around tens of m/s with current density around several MA/cm² is observed in Pt/Co/Ta. However, it needs double times larger current density to reach the same magnitude in Pt/Co/C/Ta, indicating DW velocity is related to the spin-orbit torque efficiency and pinning potential barrier. Moreover, in CIDWM, DW velocity is around 10³ times larger than that in field-induced DW motion (FIDWM) with current-generated effective field keeping the same magnitude as applied magnetic field, revealing that the current-generated Joule heating has an influence on DW motion. Interestingly, current-induced DW tilting phenomenon is observed, while this phenomenon is absent in FIDWM, demonstrating that the current-generated Oersted field may also play an essential role in DW tilting. These findings could provide some designing prospects to drive DW motion in SOT-based racetrack memories.

Interaction of two domain walls during spin-torque-induced coherent motion

We show that the application of a spin-polarized current to a double p domain wall system with a variable distance between the walls results in an interaction between the two domain walls. The transmission spectrum changes from that of a spin-dependent resonant double barrier to one like a [Formula: see text] wall. In addition, the spin torque on each individual wall creates coupled motion in the domain walls. The walls move independently with a fast speed at large separations, but slow considerably at small separations.

Deterministic Spin-Orbit Torque Induced Magnetization Reversal In Pt/[Co/Ni] n /Co/Ta Multilayer Hall Bars

Spin-orbit torque (SOT) induced by electric current has attracted extensive attention as an efficient method of controlling the magnetization in nanomagnetic structures. SOT-induced magnetization reversal is usually achieved with the aid of an in-plane bias magnetic field. In this paper, we show that by selecting a film stack with weak out-of-plane magnetic anisotropy, field-free SOT-induced switching can be achieved in micron sized multilayers. Using direct current, deterministic bipolar magnetization reversal is obtained in Pt/[Co/Ni]₂/Co/Ta structures. Kerr imaging reveals that the SOT-induced magnetization switching process is completed via the nucleation of reverse domain and propagation of domain wall in the system.

Spatiotemporal Patterns in Ultraslow Domain Wall Creep Dynamics

In the presence of impurities, ferromagnetic and ferroelectric domain walls slide only above a finite external field. Close to this depinning threshold, they proceed by large and abrupt jumps called avalanches, while, at much smaller fields, these interfaces creep by thermal activation. In this Letter, we develop a novel numerical technique that captures the ultraslow creep regime over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatiotemporal patterns that resemble the complex sequence of aftershocks observed after a large earthquake. Remarkably, we show that events assemble in independent clusters that display at large scales the same statistics as critical depinning avalanches. We foresee these correlated dynamics being experimentally accessible by magnetooptical imaging of ferromagnetic films.

Picosecond Dynamics of Excitonic Magnetic Polarons in Colloidal Diffusion-Doped Cd(1-x)Mn(x)Se Quantum Dots

Spontaneous magnetization is observed at zero magnetic field in photoexcited colloidal Cd(1-x)Mn(x)Se (x = 0.13) quantum dots (QDs) prepared by diffusion doping, reflecting strong Mn(2+)-exciton exchange coupling. The picosecond dynamics of this phenomenon, known as an excitonic magnetic polaron (EMP), are examined using a combination of time-resolved photoluminescence, magneto-photoluminescence, and Faraday rotation (TRFR) spectroscopies, in conjunction with continuous-wave absorption, magnetic circular dichroism (MCD), and magnetic circularly polarized photoluminescence (MCPL) spectroscopies. The data indicate that EMPs form with random magnetization orientations at zero external field, but their formation can be directed by an external magnetic field. After formation, however, external magnetic fields are unable to reorient the EMPs within the luminescence lifetime, implicating anisotropy in the EMP potential-energy surfaces. TRFR measurements in a transverse magnetic field reveal rapid (<5 ps) spin transfer from excitons to Mn(2+) followed by coherent EMP precession at the Mn(2+) Larmor frequency for over a nanosecond. A dynamical TRFR phase inversion is observed during EMP formation attributed to the large shifts in excitonic absorption energies during spontaneous magnetization. Partial optical orientation of the EMPs by resonant circularly polarized photoexcitation is also demonstrated. Collectively, these results highlight the extraordinary physical properties of colloidal diffusion-doped Cd(1-x)Mn(x)Se QDs that result from their unique combination of strong quantum confinement, large Mn(2+) concentrations, and relatively narrow size distributions. The insights gained from these measurements advance our understanding of spin dynamics and magnetic exchange in colloidal doped semiconductor nanostructures, with potential ramifications for future spin-based information technologies.

Domain wall tilting in the presence of the Dzyaloshinskii-Moriya interaction in out-of-plane magnetized magnetic nanotracks

We show that the Dzyaloshinskii-Moriya interaction (DMI) can lead to a tilting of the domain wall (DW) surface in perpendicularly magnetized magnetic nanotracks when DW dynamics are driven by an easy axis magnetic field or a spin polarized current. The DW tilting affects the DW dynamics for large DMI, and the tilting relaxation time can be very large as it scales with the square of the track width. The results are well explained by an extended collective coordinate model where DMI and DW tilting are included. We propose a simple way to estimate the DMI in magnetic multilayers by measuring the dependence of the DW tilt angle on a transverse static magnetic field. These results shed light on the current induced DW tilting observed recently in Co/Ni multilayers with structural inversion asymmetry.

Piezoelectric control of the mobility of a domain wall driven by adiabatic and non-adiabatic torques

The rich internal degrees of freedom of magnetic domain walls make them an attractive complement to electron charge for exploring new concepts of storage, transport and processing of information. Here we use the tunable internal structure of a domain wall in a perpendicularly magnetized GaMnAsP/GaAs ferromagnetic semiconductor and demonstrate devices in which piezoelectrically controlled magnetic anisotropy yields up to 500% mobility variations for an electrical-current-driven domain wall. We observe current-induced domain wall motion over a wide range of current-pulse amplitudes and report a direct observation and the piezoelectric control of the Walker breakdown separating two regimes with different mobilities. Our work demonstrates that in spin-orbit-coupled ferromagnets with weak extrinsic domain wall pinning, the piezoelectric control allows one to experimentally assess the upper and lower boundaries of the characteristic ratio of adiabatic and non-adiabatic spin-transfer torques in the current-driven domain wall motion.

Current-induced magnetic domain wall motion below intrinsic threshold triggered by Walker breakdown

Controlling the position of a magnetic domain wall with electric current may allow for new types of non-volatile memory and logic devices. To be practical, however, the threshold current density necessary for domain wall motion must be reduced below present values. Intrinsic pinning due to magnetic anisotropy, as recently observed in perpendicularly magnetized Co/Ni nanowires, has been shown to give rise to an intrinsic current threshold J(th)(0). Here, we show that domain wall motion can be induced at current densities 40% below J(th)(0) when an external magnetic field of the order of the domain wall pinning field is applied. We observe that the velocity of the domain wall motion is the vector sum of current- and field-induced velocities, and that the domain wall can be driven against the direction of a magnetic field as large as 2,000 Oe, even at currents below J(th)(0). We show that this counterintuitive phenomenon is triggered by Walker breakdown, and that the additive velocities provide a unique way of simultaneously determining the spin polarization of current and the Gilbert damping constant.

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.

Spin drift velocity, polarization, and current-driven domain-wall motion in (Ga,Mn)(As,P)

Current-driven domain-wall motion is studied in (Ga,Mn)(As,P) ferromagnetic semiconducting tracks with perpendicular anisotropy. A linear steady state flow regime is observed over a large temperature range of the ferromagnetic phase (0.1T(c)<T<T(c)). Close to 0 K, the domain-wall velocity is found to coincide with the spin drift velocity. This result is obtained below the intrinsic threshold for domain-wall motion which implies a nonadiabatic contribution to the spin transfer torque. The current spin polarization is deduced close to 0 K and to T(c). It suggests that the temperature dependence of the spin polarization can be inferred from the domain-wall dynamics.

Thermal rounding exponent of the depinning transition of an elastic string in a random medium

We study numerically thermal effects at the depinning transition of an elastic string driven in a two-dimensional uncorrelated disorder potential. The velocity of the string exactly at the sample critical force is shown to behave as V~T(ψ), with ψ the thermal rounding exponent. We show that the computed value of the thermal rounding exponent, ψ=0.15, is robust and accounts for the different scaling properties of several observables both in the steady state and in the transient relaxation to the steady state. In particular, we show the compatibility of the thermal rounding exponent with the scaling properties of the steady-state structure factor, the universal short-time dynamics of the transient velocity at the sample critical force, and the velocity scaling function describing the joint dependence of the steady-state velocity on the external drive and temperature.

The stochastic nature of the domain wall motion along high perpendicular anisotropy strips with surface roughness

The domain wall dynamics along thin ferromagnetic strips with high perpendicular magnetocrystalline anisotropy driven by either magnetic fields or spin-polarized currents is theoretically analyzed by means of full micromagnetic simulations and a one-dimensional model, including both surface roughness and thermal effects. At finite temperature, the results show a field dependence of the domain wall velocity in good qualitative agreement with available experimental measurements, indicating a low field, low velocity creep regime, and a high field, linear regime separated by a smeared depinning region. Similar behaviors were also observed under applied currents. In the low current creep regime the velocity-current characteristic does not depend significantly on the non-adiabaticity. At high currents, where the domain wall velocity becomes insensitive to surface pinning, the domain wall shows a precessional behavior even when the non-adiabatic parameter is equal to the Gilbert damping. These analyses confirm the relevance of both thermal fluctuations and surface roughness for the domain wall dynamics, and that complete micromagnetic modeling and one-dimensional studies taking into account these effects are required to interpret the experimental measurements in order to get a better understanding of the origin, the role and the magnitude of the non-adiabaticity.

Current-induced domain wall motion and magnetization dynamics in CoFeB/Cu/Co nanostripes

Current-induced domain wall motion and magnetization dynamics in the CoFeB layer of CoFeB/Cu/Co nanostripes were studied using photoemission electron microscopy combined with x-ray magnetic circular dichroism (XMCD-PEEM). Quasi-static measurements show that current-induced domain wall motion in the CoFeB layer is similar to the one observed in the NiFe layer of NiFe/Cu/Co trilayers, although the threshold current densities for domain wall depinning are lower. Time-resolved XMCD-PEEM measurements are used as an efficient probe of domain wall depinning statistics. They also reveal that, during the application of current pulses, the CoFeB magnetization rotates in the direction transverse to the nanostripe. The corresponding tilt angles have been quantified and compared to analytical and micromagnetic calculations, highlighting the influence of magnetostatic interactions between the two magnetic layers on the magnetization rotation.

Temperature estimation in a ferromagnetic Fe-Ni nanowire involving a current-driven domain wall motion

We observed a magnetic domain wall (DW) motion induced by the spin-polarized pulsed current in a nanoscale Fe(19)Ni(81) wire using a magnetic force microscope. High current density, which is of the order of 10(11) A m(-2), was required for the DW motion. A simple method to estimate the temperature of the wire was developed by comparing the wire resistance measured during the DW motion with the temperature dependence of the wire resistance. Using this method, we found the temperature of the wire was proportional to the square of the current density and became just beneath at the threshold Curie temperature. Our experimental data qualitatively support this analytical model that the temperature is proportional to the resistivity, thickness, width of the wire and the square of the current density, and also inversely proportional to the thermal conductivity.

Current induced domain wall motion in GaMnAs close to the Curie temperature

Domain wall dynamics produced by spin transfer torques is investigated in (Ga, Mn)As ferromagnetic semiconducting tracks with perpendicular anisotropy, close to the Curie temperature. The domain wall velocities are found to follow a linear flow regime which only slightly varies with temperature. Using the Döring inequality, boundaries of the spin polarization of the current are deduced. A comparison with the predictions of the mean field k·p theory leads to an estimation of the carrier density whose value is compatible with results published in the literature. The spin polarization of the current and the magnetization of the magnetic atoms present similar temperature variations. This leads to a weak temperature dependence of the spin drift velocity and thus of the domain wall velocity. A combined study of field- and current-driven motion and deformation of magnetic domains reveals a motion of domain walls in the steady state regime without transition to the precessional regime. The ratio between the non-adiabatic torque β and the Gilbert damping factor α is shown to remain close to unity.

Maximum relative height of elastic interfaces in random media

The distribution of the maximal relative height (MRH) of self-affine one-dimensional elastic interfaces in a random potential is studied. We analyze the ground-state configuration at zero driving force, and the critical configuration exactly at the depinning threshold, both for the random-manifold and random-periodic universality classes. These configurations are sampled by exact numerical methods, and their MRH distributions are compared with those with the same roughness exponent and boundary conditions, but produced by independent Fourier modes with normally distributed amplitudes. Using Pickands' theorem we derive an exact analytical description for the right tail of the latter. After properly rescaling the MRH distributions we find that corrections from the Gaussian independent modes approximation are, in general, small, as previously found for the average width distribution of depinning configurations. In the large size limit all corrections are finite except for the ground state in the random-periodic class whose MRH distribution becomes, for periodic boundary conditions, indistinguishable from the Airy distribution. We find that the MRH distributions are, in general, sensitive to changes of boundary conditions.

Universality classes of magnetic domain wall motion

We examine magnetic domain wall motion in metallic nanowires Pt-Co-Pt. Regardless of whether the motion is driven by either magnetic fields or current, all experimental data fall onto a single universal curve in the creep regime, implying that both the motions belong to the same universality class. This result is in contrast to the report on magnetic semiconductor (Ga,Mn)As exhibiting two different universality classes. Our finding signals the possible existence of yet other universality classes which go beyond the present understanding of the statistical mechanics of driven interfaces.

Tuning magnetotransport through a magnetic kink crystal in a chiral helimagnet

We consider magnetotransport properties in a conducting chiral helimagnet, where the magnetic kink crystal (MKC) is formed under weak magnetic field applied perpendicular to the helical axis. The MKC behaves as a magnetic superlattice potential and results in Bragg scattering of conduction electrons. Tuning of the weak magnetic field enables us to control the size of the superlattice Brillouin zone and gives rise to a series of divergent resistivity anomalies originating from resonant Bragg scatterings. We discuss as well a nontrivial magnetic structure in the resonant states realized in the subsystem of the itinerant electrons.

Observation of the intrinsic pinning of a magnetic domain wall in a ferromagnetic nanowire

The spin transfer torque is essential for electrical magnetization switching. When a magnetic domain wall is driven by an electric current through an adiabatic spin torque, the theory predicts a threshold current even for a perfect wire without any extrinsic pinning. The experimental confirmation of this 'intrinsic pinning', however, has long been missing. Here, we give evidence that this intrinsic pinning determines the threshold, and thus that the adiabatic spin torque dominates the domain wall motion in a perpendicularly magnetized Co/Ni nanowire. The intrinsic nature manifests itself both in the field-independent threshold current and in the presence of its minimum on tuning the wire width. The demonstrated domain wall motion purely due to the adiabatic spin torque will serve to achieve robust operation and low energy consumption in spintronic devices.

Dynamical pinning of a domain wall in a magnetic nanowire induced by Walker breakdown

Transmission probability of a domain wall through a magnetic nanowire is investigated as a function of the external magnetic field. A very intriguing phenomenon is found that the transmission probability shows a significant drop after exceeding the threshold driving field, which contradicts our intuition that a domain wall is more mobile in the higher magnetic field. The micromagnetics simulation reveals that the domain wall motion in the wire with finite roughness causes the dynamical pinning due to the Walker breakdown, which semiquantitatively explains our experimental results.

The emergence of spin electronics in data storage

Electrons have a charge and a spin, but until recently these were considered separately. In classical electronics, charges are moved by electric fields to transmit information and are stored in a capacitor to save it. In magnetic recording, magnetic fields have been used to read or write the information stored on the magnetization, which 'measures' the local orientation of spins in ferromagnets. The picture started to change in 1988, when the discovery of giant magnetoresistance opened the way to efficient control of charge transport through magnetization. The recent expansion of hard-disk recording owes much to this development. We are starting to see a new paradigm where magnetization dynamics and charge currents act on each other in nanostructured artificial materials. Ultimately, 'spin currents' could even replace charge currents for the transfer and treatment of information, allowing faster, low-energy operations: spin electronics is on its way.

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.

Giant current-driven domain wall mobility in (Ga,Mn)As

We study theoretically hole current-driven domain wall dynamics in (Ga,Mn)As. We show that the spin-orbit coupling causes significant hole reflection at the domain wall, even in the adiabatic limit when the wall is much thicker than the Fermi wavelength, resulting in spin accumulation and mistracking between current-carrying spins and the domain wall magnetization. This increases the out-of-plane nonadiabatic spin-transfer torque and consequently the current-driven domain wall mobility by 3 to 4 orders of magnitude. Trends and magnitude of the calculated domain wall current mobilities agree with experimental findings.

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.

Stable multidomain structures formed in the process of magnetization reversal in GaMnAs ferromagnetic semiconductor thin films

The process of magnetization reversal in ferromagnetic Ga(1-x)Mn(x)As epilayers has been systematically investigated using the planar Hall effect (PHE). Interestingly, we have observed a pronounced asymmetry in the PHE hysteresis when the range of the field scan is restricted to fields below the final magnetization transition. The observed behavior indicates that (a) multidomain structures are formed as M undergoes a reorientation, (b) the domain landscape formed in this way remains stable even after the magnetic field is switched off, and (c) the reorientation of magnetization directions corresponding to the transition points in PHE takes place separately within each domain.

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.

Domain-wall resistance in ferromagnetic (Ga,Mn)As

A series of microstructures designed to pin domain walls (DWs) in (Ga,Mn)As with perpendicular magnetic anisotropy has been employed to determine extrinsic and intrinsic contributions to DW resistance. The former is explained quantitatively as resulting from a polarity change in the Hall electric field at DW. The latter is 1 order of magnitude greater than a term brought about by anisotropic magnetoresistance and is shown to be consistent with disorder-induced mistracking of the carrier spins subject to spatially varying magnetization.