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

Self-assembly of Co/Pt stripes with current-induced domain wall motion towards 3D racetrack devices

Modification of the magnetic properties under the induced strain and curvature is a promising avenue to build three-dimensional magnetic devices, based on the domain wall motion. So far, most of the studies with 3D magnetic structures were performed in the helixes and nanowires, mainly with stationary domain walls. In this study, we demonstrate the impact of 3D geometry, strain and curvature on the current-induced domain wall motion and spin-orbital torque efficiency in the heterostructure, realized via a self-assembly rolling technique on a polymeric platform. We introduce a complete 3D memory unit with write, read and store functionality, all based on the field-free domain wall motion. Additionally, we conducted a comparative analysis between 2D and 3D structures, particularly addressing the influence of heat during the electric current pulse sequences. Finally, we demonstrated a remarkable increase of 30% in spin-torque efficiency in 3D configuration.

Universal Hopping Motion Protected by Structural Topology

A scaling law elucidates the universality in nature, presiding over many physical phenomena which seem unrelated. Thus, exploring the universality class of scaling law in a particular system enlightens its physical nature in relevance to other systems and sometimes unearths an unprecedented new dynamic phase. Here, the dynamics of weakly driven magnetic skyrmions are investigated, and its scaling law is compared with the motion of a magnetic domain wall (DW) creep. This study finds that the skyrmion does not follow the scaling law of the DW creep in 2D space but instead shows a hopping behavior similar to that of the particle-like DW in 1D confinement. In addition, the hopping law satisfies even when a topological charge of the skyrmion is removed. Therefore, the distinct scaling behavior between the magnetic skyrmion and the DW stems from a general principle beyond the topological charge. This study demonstrates that the hopping behavior of skyrmions originates from the bottleneck process induced by DW segments with diverging collective lengths, which is inevitable in any closed-shape spin structure in 2D. This work reveals that the structural topology of magnetic texture determines the universality class of its weakly driven motion, which is distinguished from the universality class of magnetic DW creep.

Critical behavior of nonequilibrium depinning transitions for vortices driven by current and vortex density

We study the critical dynamics of vortices associated with dynamic disordering near the depinning transitions driven by dc force (dc current I) and vortex density (magnetic field B). Independent of the driving parameters, I and B, we observe the critical behavior of the depinning transitions, not only on the moving side, but also on the pinned side of the transition, which is the first convincing verification of the theoretical prediction. Relaxation times, [Formula: see text] and [Formula: see text], to reach either the moving or pinned state, plotted against I and B, respectively, exhibit a power-law divergence at the depinning thresholds. The critical exponents of both transitions are, within errors, identical to each other, which are in agreement with the values expected for an absorbing phase transition in the two-dimensional directed-percolation universality class. With an increase in B under constant I, the depinning transition at low B is replaced by the repinning transition at high B in the peak-effect regime. We find a trend that the critical exponents in the peak-effect regime are slightly smaller than those in the low-B regime and the theoretical one, which is attributed to the slight difference in the depinning mechanism in the peak-effect regime.

Critical behavior of density-driven and shear-driven reversible-irreversible transitions in cyclically sheared vortices

Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. Here, we measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. At the critical point of each RIT, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_{\mathrm {c}}$$\end{document}Bc and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{\mathrm {c}}$$\end{document}dc, the relaxation time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}τ to reach the steady state shows a power-law divergence. The critical exponent for B-driven RIT is in agreement with that for d-driven RIT and both types of RIT fall into the same universality class as the absorbing transition in the two-dimensional directed-percolation universality class. As d is decreased to the average intervortex spacing in the reversible regime, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (d)$$\end{document}τ(d) shows a significant drop, indicating a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state. In either regime, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (d)$$\end{document}τ(d) exhibits a power-law divergence at the same \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{\mathrm {c}}$$\end{document}dc with nearly the same exponent.

Universality classes of the domain-wall creep motion driven by spin-transfer torques

With the stochastic Landau-Lifshitz-Gilbert equation, we numerically simulate the creep motion of a magnetic domain wall driven by the adiabatic and nonadiabatic spin-transfer torques induced by the electric current. The creep exponent μ and the roughness exponent ζ are accurately determined from the scaling behaviors. The creep motions driven by the adiabatic and nonadiabatic spin-transfer torques belong to different universality classes. The scaling relation between μ and ζ based on certain simplified assumptions is valid for the nonadiabatic spin-transfer torque, while invalid for the adiabatic one. Our results are compatible with the experimental ones, but go beyond the existing theoretical prediction. Our investigation reveals that the disorder-induced pinning effect on the domain-wall rotation alters the universality class of the creep motion.

Spin-reorientation critical dynamics in the two-dimensional XY model with a domain wall

In recent years, static and dynamic properties of non-180^{∘} domain walls in magnetic materials have attracted a great deal of interest. In this paper, spin-reorientation critical dynamics in the two-dimensional XY model is investigated with Monte Carlo simulations and theoretical analyses based on the Langevin equation. At the Kosterlitz-Thouless phase transition, the dynamic scaling behaviors of the magnetization and the two-time correlation function are carefully analyzed, and critical exponents are accurately determined. When the initial value of the angle between adjacent domains is slightly lower than π, a critical exponent is introduced to characterize the abnormal power-law increase of the magnetization in the horizontal direction inside the domain interface, which is measured to be ψ=0.0568(8). In addition, the relation ψ=η/2z is analytically deduced from the Langevin dynamics in the long-wavelength approximation, well consistent with numerical results.

Free-Standing GaMnAs Nanomachined Sheets for van der Pauw Magnetotransport Measurements

We report on the realization of free-standing GaMnAs epilayer sheets using nanomachining techniques. By optimizing the growth conditions of the sacrificial Al_0.75Ga_0.25As layer, free-standing metallic GaMnAs (with ~6% Mn) microsheets (with T_C ~85 K) with integrated electrical probes are realized for magnetotransport measurements in the van der Pauw geometry. GaMnAs epilayer needs to be physically isolated to avoid buckling effects stemming from the release of lattice mismatch strain during the removal of the AlGaAs sacrificial layer. From finite element analysis, symmetrically placed and serpentine-shaped electrical leads induce minimal thermal stress at low temperatures. From magnetotransport measurements, changes in magnetic anisotropy are readily observed.

Universal Pinning Energy Barrier for Driven Domain Walls in Thin Ferromagnetic Films

We report a comparative study of magnetic field driven domain wall motion in thin films made of different magnetic materials for a wide range of field and temperature. The full thermally activated creep motion, observed below the depinning threshold, is shown to be described by a unique universal energy barrier function. Our findings should be relevant for other systems whose dynamics can be modeled by elastic interfaces moving on disordered energy landscapes.

Creep turns linear in narrow ferromagnetic nanostrips

The motion of domain walls in magnetic materials is a typical example of a creep process, usually characterised by a stretched exponential velocity-force relation. By performing large-scale micromagnetic simulations, and analyzing an extended 1D model which takes the effects of finite temperatures and material defects into account, we show that this creep scaling law breaks down in sufficiently narrow ferromagnetic strips. Our analysis of current-driven transverse domain wall motion in disordered Permalloy nanostrips reveals instead a creep regime with a linear dependence of the domain wall velocity on the applied field or current density. This originates from the essentially point-like nature of domain walls moving in narrow, line- like disordered nanostrips. An analogous linear relation is found also by analyzing existing experimental data on field-driven domain wall motion in perpendicularly magnetised media.

Magnetic domains in H-mediated Zn0.9Co0.1O microdisk arrays

We have fabricated and studied magnetic domains in the periodic ZnCoO microdisk structures at room temperature with MFM technique. The z-component of the remanent magnetic moment is uniform even though the value is much smaller than the saturation magnetic moment.

Visualization of superparamagnetic dynamics in magnetic topological insulators

Quantized Hall conductance is a generic feature of two-dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is believed to be broken by long-range ferromagnetic order, with quantized resistance observed even at zero external magnetic field. We use scanning nanoSQUID (nano-superconducting quantum interference device) magnetic imaging to provide a direct visualization of the dynamics of the quantum phase transition between the two anomalous Hall plateaus in a Cr-doped (Bi,Sb)2Te3 thin film. Contrary to naive expectations based on macroscopic magnetometry, our measurements reveal a superparamagnetic state formed by weakly interacting magnetic domains with a characteristic size of a few tens of nanometers. The magnetic phase transition occurs through random reversals of these local moments, which drive the electronic Hall plateau transition. Surprisingly, we find that the electronic system can, in turn, drive the dynamics of the magnetic system, revealing a subtle interplay between the two coupled quantum phase transitions.

Finite-temperature crossovers in periodic disordered systems

We consider the static properties of periodic structures in weak random disorder. We apply a functional renormalization group approach (FRG) and a Gaussian variational method (GVM) to study their displacement correlations. We focus in particular on the effects of temperature and we compute explicitly the crossover length scales separating different regimes in the displacement correlation function. We compare the FRG and GVM results and find excellent agreement. We show that the FRG predicts, in addition, the existence of a third length scale associated with the screening of the disorder by thermal fluctuations and discuss a protocol to observe it.

Nonsteady dynamic properties of a domain wall for the creep state under an alternating driving field

With Monte Carlo simulations, the nonsteady dynamic properties of a domain wall have been systematically investigated for the thermally activated creep state under an alternating driving field. Taking the driven random-field Ising model in two dimensions as an example, two distinct growth stages of the domain interface are identified with both the correlation length and roughness function. One stage belongs to the universality class of the random depositions, and the other to that of the quenched Edwards-Wilkinson equation. In the latter case, due to the dynamic effect of overhangs, the domain interface may exhibit an intrinsic anomalous scaling behavior, different from that of the quenched Edwards-Wilkinson equation.

Distinct universality classes of domain wall roughness in two-dimensional Pt/Co/Pt films

We demonstrate here that the current-driven domain wall (DW) in two dimensions forms a "facet" roughness, distinctive to the conventional self-affine roughness induced by a magnetic field. Despite the different universality classes of these roughnesses, both the current- and field-driven DW speed follow the same creep law only with opposite angular dependences. Such angular dependences result in a stable facet angle, from which a single DW image can unambiguously quantify the spin-transfer torque efficiency, an essential parameter in DW-mediated nanodevices.

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.

Nanowire spintronics for storage class memories and logic

Patterned magnetic nanowires are extremely well suited for data storage and logic devices. They offer non-volatile storage, fast switching times, efficient operation and a bistable magnetic configuration that are convenient for representing digital information. Key to this is the high level of control that is possible over the position and behaviour of domain walls (DWs) in magnetic nanowires. Magnetic random access memory based on the propagation of DWs in nanowires has been released commercially, while more dynamic shift register memory and logic circuits have been demonstrated. Here, we discuss the present standing of this technology as well as reviewing some of the basic DW effects that have been observed and the underlying physics of DW motion. We also discuss the future direction of magnetic nanowire technology to look at possible developments, hurdles to overcome and what nanowire devices may appear in the future, both in classical information technology and beyond into quantum computation and biology.

Measurements of nanoscale domain wall flexing in a ferromagnetic thin film

We use the high spatial sensitivity of the anomalous Hall effect in the ferromagnetic semiconductor Ga(1-x)Mn(x)As, combined with the magneto-optical Kerr effect, to probe the nanoscale elastic flexing behavior of a single magnetic domain wall in a ferromagnetic thin film. Our technique allows position sensitive characterization of the pinning site density, which we estimate to be ∼10(14) cm(-3). Analysis of single site depinning events and their temperature dependence yields estimates of pinning site forces (10 pN range) as well as the thermal deactivation energy. Our data provide evidence for a much higher intrinsic domain wall mobility for flexing than previously observed in optically probed μm scale measurements.

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.

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.

Universal hysteresis scaling for incommensurate magnetic order in dysprosium

We study the scaling properties of magnetic minor hysteresis loops in a polycrystalline dysprosium metal, varying temperature and magnetic-field amplitudes. We observe irreversibility-related hysteresis loss in the helical antiferromagnetic phase, which is related with remanent flux density as a power law with the same scaling exponent of 1.25±0.05 as that in ferromagnetic materials. In contrast to hysteresis scalings in ferromagnets associated with 180° Bloch walls, the observed law is governed by spiral walls which separate helical domains with oppositely rotating spins.

Photoinduced Barkhausen effect in the ferromagnetic semiconductor (Ga,Mn)As

Magnetization of ferromagnetic materials commonly occurs via random jumps of domain walls between pinning sites, a phenomenon known as the Barkhausen effect. Using strongly focused light pulses of appropriate power and duration we demonstrate the ability to selectively activate single jumps in the domain wall propagation in (Ga,Mn)As, manifesting itself as a discrete photoinduced domain wall creep as a function of illumination time. The propagation velocity can be increased over 7 orders of magnitude varying the illumination power density and the magnetic field.

Dynamic effect of overhangs and islands at the depinning transition in two-dimensional magnets

With the Monte Carlo methods, we systematically investigate the short-time dynamics of domain-wall motion in the two-dimensional random-field Ising model with a driving field (DRFIM). We accurately determine the depinning transition field and critical exponents. Through two different definitions of the domain interface, we examine the dynamics of overhangs and islands. At the depinning transition, the dynamic effect of overhangs and islands reaches maximum. We argue that this should be an important mechanism leading the DRFIM model to a different universality class from the Edwards-Wilkinson equation with quenched disorder.

Spin-transfer-torque-assisted domain-wall creep in a Co/Pt multilayer wire

We have studied field- and current-driven domain-wall (DW) creep motion in a perpendicularly magnetized Co/Pt multilayer wire by real-time Kerr microscopy. The application of a dc current of density of approximately < 10(7) A/cm2 assisted only the DW creeping under field in the same direction as the electron flow, a signature of spin-transfer torque effects. We develop a model dealing with both bidirectional spin-transfer effects and Joule heating, with the same dynamical exponent mu=1/4 for both field- and current-driven creep, and use it to quantify the spin-transfer efficiency as 3.6+/-0.6 Oe cm2/MA in our wires, confirming the significant nonadiabatic contribution to the spin torque.

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.