In this report we demonstrate a simple model for the motion of a vortex domain wall in a ferromagnetic strip of submicron width under the influence of an external magnetic field. The model exhibits three distinct dynamical regimes. In a viscous regime at low fields the wall moves rigidly with a velocity proportional to the field. Above a critical field the motion becomes underdamped as the vortex moves periodically across the strip; these oscillations are accompanied by a slow drift with a decreasing velocity. At still higher fields the drift velocity starts rising linearly with the field again but with a much lower mobility dv/dH than in the low-field regime. We calculate the relevant quantities and compare them to experimentally observed values.
Using magnetic force microscopy and micromagnetic simulations, we studied the effect of Oersted magnetic fields on the chirality of transverse magnetic domain walls in Fe$_{20}$Ni$_{80}$/Ir bilayer nanostrips. Applying nanosecond current pulses with a current density of around $2\times10^{12}$ A/m$^2$, the chirality of a transverse domain wall could be switched reversibly and reproducibly. These current densities are similar to the ones used for current-induced domain wall motion, indicating that the Oersted field may stabilize the transverse wall chirality during current pulses and prevent do…
We report on the criterion for the dynamic transformation of the internal structure of moving domain walls (DWs) in soft magnetic thin-film nanostripes above the Walker threshold field, Hw. In order for the process of transformation from transverse wall (TW) to vortex wall (VW) or antivortex wall (AVW) occurs, the edge-soliton core of the TW-type DW should grow sufficiently to the full width at half maximum of the out-of-plane magnetizations of the core area of the stabilized vortex (or antivortex) by moving inward along the transverse (width) direction. Upon completion of the nucleation of th…
Domain wall motion induced by nanosecond current pulses in nanostripes with perpendicular magnetic anisotropy (Pt/Co/AlO$_x$) is shown to exhibit negligible inertia. Time-resolved magnetic microscopy during current pulses reveals that the domain walls start moving, with a constant speed, as soon as the current reaches a constant amplitude, and no or little motion takes place after the end of the pulse. The very low 'mass' of these domain walls is attributed to the combination of their narrow width and high damping parameter $α$. Such a small inertia should allow accurate control of domain wall…
Controlling domain wall motion is important due to the impact on the viability of proposed nanowire devices. One hurdle is slow domain wall speed when driven by fields greater than the Walker field, due to nucleation of vortices in the wall. We present simulation results detailing the dynamics of these vortices; including the nucleation and subsequent fast ejection of the vortex core leading to fast domain wall speeds. The ejection is due to the reversal of the core moments by an out-of-plane field. The technique can be used to produce domain walls of known orientation independent of the initi…
We express dynamics of domain walls in ferromagnetic nanowires in terms of collective coordinates generalizing Thiele's steady-state results. For weak external perturbations the dynamics is dominated by a few soft modes. The general approach is illustrated on the example of a vortex wall relevant to recent experiments with flat nanowires. A two-mode approximation gives a quantitatively accurate description of both the steady viscous motion of the wall in weak magnetic fields and its oscillatory behavior in moderately high fields above the Walker breakdown.
Current-induced magnetic domain wall motion at zero magnetic field is observed in the permalloy layer of a spin-valve-based nanostripe using photoemission electron microscopy. The domain wall movement is hampered by pinning sites, but in between them high domain wall velocities (exceeding 150 m/s) are obtained for current densities well below $10^{12} \unit{A/m^2}$, suggesting that these trilayer systems are promising for applications in domain wall devices in case of well controlled pinning positions. Vertical spin currents in these structures provide a potential explanation for the increase …
In a thin magnetic nanostripe, an anti-vortex nucleates inside a moving domain wall when driven by an in-plane magnetic field greater than the so-called Walker field. The nucleated anti-vortex must cross the width of the nanostripe before the domain wall can propagate again, leading to low average domain wall speeds. A large out-of-plane magnetic field, applied perpendicularly to the plane of the nanostripe, inhibits the nucleation of the anti-vortex leading to fast domain wall speeds for all in-plane driving fields. We present micromagnetic simulation results relating the anti-vortex dynamics…
We use spin-torque resonance to probe simultaneously and separately the dynamics of a magnetic domain wall and of magnetic domains in a nanostripe magnetic tunnel junction. Thanks to the large associated resistance variations we are able to analyze quantitatively the resonant properties of these single nanoscale magnetic objects. In particular, we find that the magnetic damping of both domains and domain walls is doubled compared to the damping value of their host magnetic layer. We estimate the contributions to damping arising from dipolar couplings between the different layers in the junctio…
It is known that oscillatory domain-wall (DW) motions in soft magnetic thin-film nanostripes above the Walker critical field lead to a remarkable reduction in the average DW velocities. In a much-higher-field region beyond the velocity-breakdown regime, however, the DW velocities have been found to increase in response to a further increase of the applied field. We report on the physical origin and detailed mechanism of this unexpected behavior. We associate the mechanism with the serial dynamic processes of the nucleation of vortex-antivortex (V-AV) pairs inside the stripe or at its edges, th…
Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research, and became in the past years the subject of intense works, mainly focused on controlling, manipulating, and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The as…
We present an analytical theory of domain wall tilt due to a transverse in-plane magnetic field in a ferromagnetic nanostrip with out-of-plane anisotropy and Dzyaloshinskii-Moriya interaction (DMI). The theory treats the domain walls as one-dimensional objects with orientation-dependent energy, which interact with the sample edges. We show that under an applied field the domain wall remains straight, but tilts at an angle to the direction of the magnetic field that is proportional to the field strength for moderate fields and sufficiently strong DMI. Furthermore, we obtain a nonlinear dependen…
We investigated head-to-head domain walls in nanostrips of epitaxial $\mathrm{Fe}_4\mathrm{N}(001)$ thin films, displaying a fourfold magnetic anisotropy. Magnetic force microscopy and micromagnetic simulations show that the domain walls have specific properties, compared to soft magnetic materials. In particular, strips aligned along a hard axis of magnetization are wrapped by partial flux-closure concertina domains below a critical width, while progressively transforming to zigzag walls for wider strips. Transverse walls are favored upon initial application of a magnetic field transverse to …
The motion of a vortex domain wall in a ferromagnetic strip of submicron width under the influence of an external magnetic field exhibits three distinct dynamical regimes. In a viscous regime at low fields the wall moves rigidly with a velocity proportional to the field. Above a critical field the viscous motion breaks down giving way to oscillations accompanied by a slow drift of the wall. At still higher fields the drift velocity starts rising with the field again but with a much lower mobility dv/dH than in the viscous regime. To describe the dynamics of the wall we use the method of collec…
We study the effect of disorder on the dynamics of a transverse domain wall in ferromagnetic nanostrips, driven either by magnetic fields or spin-polarized currents, by performing a large ensemble of GPU-accelerated micromagnetic simulations. Disorder is modeled by including small, randomly distributed non-magnetic voids in the system. Studying the domain wall velocity as a function of the applied field and current density reveals fundamental differences in the domain wall dynamics induced by these two modes of driving: For the field-driven case, we identify two different domain wall pinning m…
Antivortex birth, growth and death due to the propagation of a transverse domain wall (DW) in magnetic nanostrips are observed and analyzed. Antivortex formation is an intrinsic process of a strawberry-like transverse DW originated from magnetostatic interaction. Under an external magnetic field, DW in a wider width region tends to move faster than that of a narrower part. This speed mismatch tilts and elongates DW centre line. An antivortex is periodically born near the tail of the DW centre line. The antivortex either moves along the centre line and dies on the other side of the strip, or gr…
We have used time-resolved x-ray photoemission electron microscopy to investigate the magnetization dynamics induced by nanosecond current pulses in NiFe/Cu/Co nanostripes. A large tilt of the NiFe magnetization in the direction transverse to the stripe is observed during the pulses. We show that this effect cannot be quantitatively understood from the amplitude of the Oersted field and the shape anisotropy. High frequency oscillations observed at the onset of the pulses are attributed to precessional motion of the NiFe magnetization about the effective field. We discuss the possible origins o…
We found by micromagnetic simulations that the motion of a transverse wall (TW) type domain wall in magnetic thin-film nanostripes can be manipulated via interaction with spin waves (SWs) propagating through the TW. The velocity of the TW motion can be controlled by changes of the frequency and amplitude of the propagating SWs. Moreover, the TW motion is efficiently driven by specific SW frequencies that coincide with the resonant frequencies of the local modes existing inside the TW structure. The use of propagating SWs, whose frequencies are tuned to those of the intrinsic TW modes, is an al…
A concept of magnetic vortex guide is proposed and numerically studied. Similar to the waveguides of electromagnetic waves, a magnetic vortex guide allows a vortex domain wall to move along a nanostrip without annihilation at the strip edges. It is shown by micromagnetic simulations that a magnetic nanostrip of a properly designed superlattice structure or bilayered structure can serve as vortex guides.
We investigate electron-phonon couplings, scattering rates, and mean free paths in zigzag-edge graphene strips with widths of the order of 10 nm. Our calculations for these graphene nanostrips show both the expected similarity with single-wall carbon nanotubes (SWNTs) and the suppression of the electron-phonon scattering due to a Dirichlet boundary condition that prohibits one major backscattering channel present in SWNTs. Low-energy acoustic phonon scattering is exponentially small at room temperature due to the large phonon wave vector required for backscattering. We find within our model th…
Propagation of easy-plane magnetic precession can enable more efficient spin transport than conventional spin waves. Such easy-plane spin transport is typically understood in terms of a hydrodynamic model, partially analogous to superfluids. Here, using micromagnetic simulations, we examine easy-plane spin transport in magnetic strips as the motion of a train of domain walls rather than as hydrodynamic flow. We observe that the motion transitions from diffusive to fluid-like as the density of domain walls is increased. This transition is most evident in notched nanostrips, where the the domain…
Current induced domain wall (DW) motion in perpendicularly magnetized nanostripes in the presence of spin orbit torques is studied. We show using micromagnetic simulations that the direction of the current induced DW motion and the associated DW velocity depend on the relative values of the field like torque (FLT) and the Slonczewski like torques (SLT). The results are well explained by a collective coordinate model which is used to draw a phase diagram of the DW dynamics as a function of the FLT and the SLT. We show that a large increase in the DW velocity can be reached by a proper tuning of…
Magnetic domain wall (DW) motion induced by a localized Gaussian temperature profile is studied in a Permalloy nanostrip within the framework of the stochastic Landau-Lifshitz-Bloch equation. The different contributions to thermally induced DW motion, entropic torque and magnonic spin transfer torque, are isolated and compared. The analysis of magnonic spin transfer torque includes a description of thermally excited magnons in the sample. A third driving force due to a thermally induced dipolar field is found and described. Finally, thermally induced DW motion is studied under realistic condit…
The dynamics of transverse Neel domain wall in a ferromagnetic nanostrip in the presence of driving field, current and transverse magnetic field is investigated by the Landau-Lifshitz-Gilbert(LLG) equation with the adiabatic and non-adiabatic spin-transfer torques both analytically and numerically. The analytical expressions for the velocity, width, excitation angle and displacement for the domain wall are obtained by using small angle approximation along with Walkers trial function. The results show that the initial velocity of the domain wall can be controlled by the adiabatic spin-transfer …
The dynamics of a 90$^{\circ }$ domain wall in an antiferromagnetic nanostrip driven by the current-induced spin-orbital torque are theoretically examined in the presence of random thermal fluctuations. A soliton-type equation of motion is developed on the basis of energy balance between the driving forces and dissipative processes in terms of the domain wall velocity. Comparison with micromagnetic simulations in the deterministic conditions shows good agreement in both the transient and steady-state transport. When the effects of random thermal fluctuations are included via a stochastic treat…
The domain wall depinning from a notch in a Permalloy nanostrip on top of a ${\rm SiO_2/Si}$ substrate is studied theoretically under application of static magnetic fields and the injection of short current pulses. The influence of Joule heating on current-induced domain wall depinning is explored self-consistently by coupling the magnetization dynamics in the ferromagnetic strip to the heat transport throughout the system. Our results indicate that Joule heating plays a remarkable role in these processes, resulting in a reduction in the critical depinning field and/or in a temporary destructi…
Current-driven domain wall (DW) motion is investigated in Pt/Co/GdOx nanostrips with perpendicular magnetic anisotropy. Measurements of the propagation field and the energy barrier for thermally activated DW motion reveal a large current-induced torque equivalent to an out-of-plane magnetic field of ~60 Oe per 10^11 A/m^2. This same field-to-current scaling is shown to hold in both the slow thermally activated and fast near-flow regimes of DW motion. The current-induced torque decreases with 4 Å of Pt decorating the Co/GdOx interface and vanishes entirely with Pt replacing GdOx, suggesting tha…
We theoretically and experimentally analyze the pinning of a magnetic domain wall (DW) at engineered anisotropy variations in Pt/Co/Pt strips with perpendicular magnetic anisotropy. An analytical model is derived showing that a step in the anisotropy acts as an energy barrier for the DW. Quantitative measurements are performed showing that the anisotropy can be controlled by focused ion beam irradiation with Ga ions. This tool is used to experimentally study the field-induced switching of nanostrips which are locally irradiated. The boundary of the irradiated area indeed acts as a pinning barr…
