Domain Wall Velocity Research Articles

Staggered field driven domain walls motion in antiferromagnetic heterojunctions

In this work, we study the antiferromagnetic (AFM) spin dynamics in heterostructures which consist of two coupled AFM layers, i.e., AFM1 layers (describing CuMnAs or Mn2Au) with field-like Néel spin-orbit torque (NSOT) and AFM2 layers with easy-axis anisotropy orthogonal to that in AFM1 layers. Our micromagnetic simulations demonstrate that through the interface coupling, the AFM2 domain wall (DW) can be effectively driven by the AFM1 DW which is driven by the electrical current induced NSOT [Gomonay et al., Phys. Rev. Lett. 117, 017202 (2016)]. Furthermore, the two DWs detach from each other when the torque increases above a critical value. The critical field and the highest possible velocity of the AFM2 DW depend on several factors, which are investigated and discussed in detail. Based on the calculated results, we propose a method of efficiently modulating the multi DWs in antiferromagnets, which definitely provides useful information for future AFM spintronics device design.

Wire edge dependent magnetic domain wall creep

While edge pinning is known to play an important role in sub-$\ensuremath{\mu}\mathrm{m}$ wires, we demonstrate that strong deviations from the universal creep law can occur in 1 to $20\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ wide wires. Magnetic imaging shows that edge pinning translates into a marked bending of domain walls at low drive and is found to depend on the wire fabrication process and aging. Edge pinning introduces a reduction of domain wall velocity with respect to full films which increasingly dominates the creep dynamics as the wire width decreases. We show that the deviations from the creep law can be described by a simple model including a counter magnetic field which links the width of the wire to the edge dependent pinning strength. This counter field defines a key nonuniversal contribution to creep motion in patterned structures.

Imaging in-plane 90° magnetization switching in a (Ga,Mn)As epitaxial layer

The dynamics associated with in-plane, 90° magnetization switching in a (Ga,Mn)As epitaxial layer is studied on the basis of images obtained using a home-made magneto-optical microscope. A small contrast between two different 90° domains caused by magnetic birefringence (MB) is enhanced by digital image processing. Two consecutive 90° switchings are captured clearly in temperature regimes below and above the half-value of the Curie temperature. The dynamics is not the same for the first and the second switching, presumably reflecting the influence of the ⟨110⟩ uniaxial anisotropy and spin-dependent pinning sites. In particular, in the low-temperature regime, the first switching that passes via the relatively easy uniaxial (REU) axis (the [1–10] axis) is dominated by smooth 90° domain wall (DW) motion, whereas the second switching that passes via the relatively hard uniaxial (RHU) axis (the [110] axis) occurs through nucleation and coalescence of 90° domains together with the DW motion. In the high-temperature regime, the first switching via the REU axis is initiated by nucleations and their rapid expansion, whereas the second switching via the RHU axis is dominated by relatively slow DW motion. DW velocity is extracted from MB images and analyzed on the basis of thermally activated depinning and flow models. The values of two key parameters, namely, the activation volume and DW mobility, are deduced and compared with values from the literature. They are (28 nm)3 and 0.35 nm s−1 Oe at 10 K, respectively.

Current-induced domain-wall motion in patterned nanowires with various Gd–Fe compositions for magneto-optical light modulator applications

We have fabricated nanowires with various compositions of Gdx–Fe1−x and evaluated current-induced domain-wall (DW) motion for magneto-optical light modulator application. Successful DW expansion and shrinkage according to the direction of current injection using two nanomagnets aligned in an anti-parallel configuration. The fastest DW velocity was obtained with Gd22.7Fe77.3, which is slightly Fe richer than the magnetization compensation composition. This composition that gave the highest DW velocity was attributed to the angular momentum compensation composition in Gd–Fe, which is slightly Fe richer than the compensation composition.

Pinning of domain walls in thin ferromagnetic films

We present a quantitative investigation of magnetic domain wall pinning in thin magnets with perpendicular anisotropy. A self-consistent description exploiting the universal features of the depinning and thermally activated sub-threshold creep regimes observed in the field driven domain wall velocity, is used to determine the effective pinning parameters controlling the domain wall dynamics: the effective height of pinning barriers, the depinning threshold, and the velocity at depinning. Within this framework, the analysis of results published in the literature allows for a quantitative comparison of pinning properties for a set of magnetic materials in a wide temperature range. On the basis of scaling arguments, the microscopic parameters controlling the pinning: the correlation length of pinning, the collectively pinned domain wall length (Larkin length) and the strength of pinning disorder, are estimated from the effective pinning and the micromagnetic parameters. The analysis of thermal effects reveals a crossover between different pinning length scales and strengths at low reduced temperature.

Domain wall energy and strain in Pt/Co/Ir thin films on piezoelectric transducers

We study the energy and creep velocity of magnetic domain walls in perpendicularly magnetised Pt/Co/Ir thin films under strain. We find that the enhancement of domain wall creep velocity under strain from piezoelectric transducers is largest in films with the thinnest Co layers (0.56 nm), in which the strain causes the smallest relative change in perpendicular magnetic anisotropy and the largest relative change in domain wall creep velocity. We show how domain wall energy is predictive of the sensitivity of domain wall creep velocity to changes in strain, and thus provide a route to designing magnetic thin film systems for optimum strain control.

Ferrimagnetic Domain Wall Motion Induced by Damping-like Spin-orbit Torque

We theoretically and numerically investigate ferrimagnetic domain wall motion driven by damping-like spinorbit torque. We find that the damping-like spin-orbit torque combined with the interfacial Dzyaloshinskii-Moriya interaction efficiently drives the ferrimagnetic domain wall especially at the angular momentum compensation point. We obtain the analytic expression of the domain wall velocity with respect to the current density and the net spin density, which is in agreement with numerical simulation. The analytic expression is applicable to arbitrary compensation conditions, ranging from the ferromagnetic limit to the antiferromagnetic limit, and is thus useful to design and interpret ferrimagnetic domain wall experiments at various temperatures or compositions.

Engineering of Magnetic Properties of Co- and Fe-Rich Microwires

We present our experimental results on optimization of the magnetic softness, domain wall (DW) dynamics, and giant magnetoimpedance (GMI) effect of Fe- and Co-rich microwires. It is found that the as-prepared Co-rich microwires possess much higher GMI effects and linear hysteresis loop. On the other hand, the magnetic softness and GMI effect of Fe-rich microwires can be improved by stress annealing. In addition, the DW velocity of the microwires can be considerably improved by annealing. The single DW propagation can also be observed in properly annealed Co-rich microwires. These observed dependencies can be attributed to the relaxation of internal stresses after annealing and the interplay of compressive stresses and axial internal stresses after stress annealing.

Magnon-induced non-Markovian friction of a domain wall in a ferromagnet

Motivated by the recent study on the quasiparticle-induced friction of solitons in superfluids, we theoretically study magnon-induced intrinsic friction of a domain wall in a one-dimensional ferromagnet. To this end, we start by obtaining the hitherto overlooked dissipative interaction of a domain wall and its quantum magnon bath to linear order in the domain-wall velocity and to quadratic order in magnon fields. An exact expression for the pertinent scattering matrix is obtained with the aid of supersymmetric quantum mechanics. We then derive the magnon-induced frictional force on a domain wall in two different frameworks: time-dependent perturbation theory in quantum mechanics and the Keldysh formalism, which yield identical results. The latter, in particular, allows us to verify the fluctuation-dissipation theorem explicitly by providing both the frictional force and the correlator of the associated stochastic Langevin force. The potential for magnons induced by a domain wall is reflectionless, and thus the resultant frictional force is non-Markovian similarly to the case of solitons in superfluids. They share an intriguing connection to the Abraham-Lorentz force that is well-known for its causality paradox. The dynamical responses of a domain wall are studied under a few simple circumstances, where the non-Markovian nature of the frictional force can be probed experimentally. Our work, in conjunction with the previous study on solitons in superfluids, shows that the macroscopic frictional force on solitons can serve as an effective probe of the microscopic degrees of freedom of the system.

Velocity Enhancement by Synchronization of Magnetic Domain Walls.

Magnetic domain walls are objects whose dynamics is inseparably connected to their structure. In this Letter, we investigate magnetic bilayers, which are engineered such that a coupled pair of domain walls, one in each layer, is stabilized by a cooperation of Dzyaloshinskii-Moriya interaction and flux-closing mechanism. The dipolar field mediating the interaction between the two domain walls links not only their position but also their structure. We show that this link has a direct impact on their magnetic-field-induced dynamics. We demonstrate that in such a system the coupling leads to an increased domain wall velocity with respect to single domain walls. Since the domain wall dynamics is observed in a precessional regime, the dynamics involves the synchronization between the two walls to preserve the flux closure during motion. Properties of these coupled oscillating walls can be tuned by an additional in-plane magnetic field enabling a rich variety of states, from perfect synchronization to complete detuning.

Micromagnetic evaluation of the dissipated heat in cylindrical magnetic nanowires

Magnetic nanowires (NWs) are promising candidates for heat generation under AC-field application due to their large shape anisotropy. They may be used for catalysis, hyperthermia, or water purification treatments. In the present work, we theoretically evaluate the heat dissipated by a single magnetic nanowire, originated from the domain wall (DW) dynamics under the action of an AC-field. We compare the Permalloy NWs (which demagnetize via the transverse wall propagation) with the Co fcc NWs whose reversal mode is via a vortex domain wall. The average hysteresis loop areas—which are proportional to the Specific Absorption Rate (SAR)—as a function of the field frequency have a pronounced maximum in the range 200 MHz–1 GHz. This maximum frequency is smaller in Permalloy than that in Co and depends on the nanowire length. A simple model related to the nucleation and propagation time and DW velocity (higher for the vortex than for the transverse domain wall) is proposed to explain the non-monotonic SAR dependence on the frequency.

Driving chiral domain walls in antiferromagnets using rotating magnetic fields

We show theoretically and numerically that an antiferromagnetic domain wall can be moved by a rotating magnetic field in the presence of Dzyaloshinskii-Moriya interaction (DMI). Two motion modes are found: rigid domain wall motion at low frequency (corresponding to the perfect frequency synchronization) and the oscillating motion at high frequency. In the full synchronized region, the steady velocity of the domain wall is universal, in the sense that it depends only on the frequency of the rotating field and the ratio between DMI strength and exchange constant. The domain wall velocity is independent of the Gilbert damping and the rotating field strength. Moreover, a rotating field in megahertz is sufficient to move the antiferromagnetic domain wall.

Ferroelectric negative capacitance domain dynamics

Transient negative capacitance effects in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 capacitors are investigated with a focus on the dynamical switching behavior governed by domain nucleation and growth. Voltage pulses are applied to a series connection of the ferroelectric capacitor and a resistor to directly measure the ferroelectric negative capacitance during switching. A time-dependent Ginzburg-Landau approach is used to investigate the underlying domain dynamics. The transient negative capacitance is shown to originate from reverse domain nucleation and unrestricted domain growth. However, with the onset of domain coalescence, the capacitance becomes positive again. The persistence of the negative capacitance state is therefore limited by the speed of domain wall motion. By changing the applied electric field, capacitor area or external resistance, this domain wall velocity can be varied predictably over several orders of magnitude. Additionally, detailed insights into the intrinsic material properties of the ferroelectric are obtainable through these measurements. A new method for reliable extraction of the average negative capacitance of the ferroelectric is presented. Furthermore, a simple analytical model is developed, which accurately describes the negative capacitance transient time as a function of the material properties and the experimental boundary conditions.

Effect of depinning field on determination of angular-momentum-compensation temperature of ferrimagnets

The domain-wall (DW) motion of ferrimagnets is investigated with respect to the angular-momentum-compensation temperature TA for a wide range of magnetic fields μ0Hz, ranging from the depinning to flow regimes. While the DW velocity v exhibits a maximum at TA in the flow regime regardless of μ0Hz, the temperature at which v is maximized depends on μ0Hz because of the temperature dependence of the depinning field μ0Hdep, causing difficulty in determining TA. To solve this problem, we propose a reduced coordinate μ0Hz − μ0Hdep, which reveals that v is maximized at TA even in the depinning regime. Our work suggests that μ0Hdep should be identified prior to determining TA.

Hydrogen-mediated magnetic domain formation and domain wall motion in Co30Pd70 alloy films

In this study, the microscopic origin of the hydrogen effect on magnetic materials was explored through the characterization of time-dependent magnetic domain evolution. We prepared 25-nm Co30Pd70 alloy films with canted magnetic moment on SiO2/Si(001) substrates. From macroscopic Kerr hysteresis loops, considerable hydrogen-induced reduction of magnetic coercivity by a factor of 1/5 in a longitudinal direction and enhancement of magnetic remanence to saturation ratio from 60% to 100% were observed. The magnetic reversal behavior of the Co30Pd70 alloy films gradually transformed from nucleation- to domain-wall-motion dominance when H2 pressure was increased from a vacuum of 1 × 10−5 mbar to 0.8 bar. Domain size also increased considerably with H2 pressure. When H2 pressure was above 0.4 bar, the domain wall (DW) motion was clear to observe and the DW velocity was approximately 10−6–10−5 m/s. Greater hydrogen content in the Co30Pd70 alloy films promoted DW motion that was closer to the behavior of a thermally activated model. The hydrogen effects on magnetism were observed to be reversible and could have valuable future application in spintronic devices for hydrogen sensing.

The influence of annealing on domain wall propagation in bistable amorphous microwire with unidirectional effect

The effect of gradual annealing on the domain wall mobility (velocity), nucleation, critical depinning and propagation fields in amorphous FeSiB microwires has been studied. A new experimental set-up, presented in this paper, allows measurement of average domain wall velocity for four different conditions and detection of the presence of unidirectional effect in wall propagation without manipulation of the microwire. The proposed interpretation is that a domain wall is considered as a relatively long object which can change its axial dimension due to inhomogeneity of damping forces acting on the wall during its propagation. It is demonstrated that unidirectional effect in domain wall propagation can be strongly reduced by annealing the wire at temperatures higher than 350 °C.

Field‐Polarity‐Dependent Domain Growth in Epitaxial BaTiO3 Films

The growth of circular tip‐induced domains has been studied in epitaxial BaTiO3 (BTO) films as a function of writing voltage and time using piezoresponse force microscopy (PFM). While abundant for Pb(Zr,Ti)O3 (PZT) films, such studies are rare for BTO. Strong relaxation of written domains is observed in the form of reduction of the PFM amplitude inside the area of written domains which occurs additionally to a decrease of the domain radius. The domain wall velocity observed for negative tip voltage is systematically smaller than that for positive tip voltage. Based on maps of the positive and negative switching fields, the effective driving field for both polarities has been estimated. The polarity‐dependent effective field cannot account for the different velocities, indicating a polarity‐dependent mobility of the domain walls.

Current induced domain wall motion and tilting in Pt/Co/Ta structures with perpendicular magnetic anisotropy in the presence of the Dyzaloshinskii–Moriya interaction

Current induced domain wall motion (CIDWM) was studied in Pt/Co/Ta structures with perpendicular magnetic anisotropy and the Dyzaloshinskii–Moriya interaction (DMI) by the spin-orbit torque (SOT). We measured the strength of DMI and SOT efficiency in Pt/Co/Ta with the variation of the thickness of Ta using a current induced hysteresis loop shift method. The results indicate that the DMI stabilizes a chiral Néel-type domain wall (DW), and the DW motion can be driven by the enhanced large SOT generated from Pt and Ta with opposite signs of spin Hall angle in Pt/Co/Ta stacks. The CIDWM velocity, which is 104 times larger than the field driven DW velocity, obeys a creep law, and reaches around tens of meters per second with current density of ~106 A cm−2. We also found that the Joule heating accompanied with current also accelerates the DW motion. Meanwhile, a domain wall tilting was observed, which increases with current density increasing. These results can be explained by the spin Hall effect generated from both heavy metals Pt and Ta, inherent DMI, and the current accompanying Joule heating effect. Our results could provide some new designing prospects to move multiple DWs by SOT for achieving racetrack memories.

Minor hysteresis patterns with a rounded/sharpened reversing behavior in ferromagnetic multilayer

Hysteresis of ferromagnetic system exhibits a fundamental stimulus-response behavior, thereby casting all the important macromagnetic system parameters such as coercivity, nucleation field, saturation magnetization, and hysteresis loss. Recently, increasing attention has been paid to exploration of relatively less understood minor loop behavior, since faster operation of magnetic devices is inevitably accompanied by minor hysteresis behavior from cycling among unsaturated ferromagnetic states. Here, we report our microscopic investigation of unusual minor hysteresis loop behavior, represented by rounded or sharpened response of minor hysteresis loop of (CoFeB/Pd)4 multilayer film. It is observed that rounded and sharpened response in the minor hysteresis response could be manifested under proper conditions. The minor loop behavior has been systematically investigated by direct microscopic magnetic domain observation using magneto-optical Kerr microscopy. The rounded response of magnetization at the reversing external field along the minor hysteresis curve, so far neglected or considered as one of ‘unusual’ behaviors, has been found to be elaborately controllable by tuning the reversing field strength and the field sweep rate for multilayers with low repeat numbers. Variable roundedness of the minor hysteresis loop is understandable based on the analysis of magnetic domain dynamics such as domain nucleation and the domain wall velocity.

Domain-wall motion at an ultrahigh speed driven by spin–orbit torque in synthetic antiferromagnets

In this article, we present our numerical investigation about the spin–orbit-torque induced domain-wall (DW) motion in a synthetic antiferromagnetic multilayer nanotrack. This nanotrack was composed by two ferromagnetic (FM) layers with a RKKY inter-layer antiferromagnetic (AFM) exchange coupling. The velocity of DW was well manipulated by varying parameters including inter-layer exchange constant, the Dzyaloshinskii–Moriya interaction (DMI) strength, the current density and the magnetic anisotropy. The DW velocity was found to be strictly related to the orientation of the moments in the two FM layers. When the interlayer exchange constant or the DMI constant were larger than a critical value, there was a large angle between the moments in one FM layer and that in the other one under the current, and the DW was driven to move at an ultrahigh speed (around 10 000 m s−1). However, when the DMI or the AFM exchange coupling was weaker than the critical value, the moments in one FM layer were parallel to that in the other one under the current, and the velocity was significantly reduced.