Current-induced Domain Wall Dynamics Research Articles

On the current-induced domain-wall dynamics

On the current-induced domain-wall dynamics

Electric current and field control of vortex structures in cylindrical magnetic nanowires

Magnetization dynamics in a cylindrical Permalloy nanowire under simultaneously applied electric current and field is investigated by means of micromagnetic simulations. The reversal process starts with the creation of open vortex structures with different rotation senses at the nanowire ends. Our results conclude that the current alone enlarges or reduces the size of these vortex structures according to the rotational sense of the associated Oersted field. Large current intensity creates a vortex structure which covers the whole nanowire surface. At the same time the magnetization in the nanowire core remains the same, i.e., no complete magnetization reversal is possible in the absence of external field. The simultaneous action of the current and field allows for the complete control of the vortex structures in terms of setting the polarity and vorticity. The state diagram for the minimum field and current required for the vorticity and axial magnetization switching is presented. This control is essential for future information technologies based on three-dimensional vertical structures, and the presented state diagram will become very useful for future experiments on current-induced domain wall dynamics in cylindrical magnetic nanowires.

Current-Induced Domain Wall Motion in a Compensated Ferrimagnet.

Owing to the difficulty in detecting and manipulating the magnetic states of antiferromagnetic materials, studying their switching dynamics using electrical methods remains a challenging task. By employing heavy-metal-rare-earth-transition-metal alloy bilayers, we experimentally study current-induced domain wall dynamics in an antiferromagnetically coupled system. We show that the current-induced domain wall mobility reaches a maximum at the angular momentum compensation point. With experiment and modeling, we further reveal the internal structures of domain walls and the underlying mechanisms for their fast motion. We show that the chirality of the ferrimagnetic domain walls remains the same across the compensation points, suggesting that spin orientations of specific sublattices rather than net magnetization determine Dzyaloshinskii-Moriya interaction in heavy-metal-ferrimagnet bilayers. The high current-induced domain wall mobility and the robust domain wall chirality in compensated ferrimagnetic material opens new opportunities for high-speed spintronic devices.

Anomalous feedback and negative domain wall resistance

Magnetic induction can be regarded as a negative feedback effect, where the motive-force opposes the change of magnetic flux that generates the motive-force. In artificial electromagnetics emerging from spintronics, however, this is not necessarily the case. By studying the current-induced domain wall dynamics in a cylindrical nanowire, we show that the spin motive-force exerting on electrons can either oppose or support the applied current that drives the domain wall. The switching into the anomalous feedback regime occurs when the strength of the dissipative torque β is about twice the value of the Gilbert damping constant α. The anomalous feedback manifests as a negative domain wall resistance, which has an analogy with the water turbine.

Simultaneous resolution of the micromagnetic and spin transport equations applied to current-induced domain wall dynamics

In this paper, we use simulations to study current-induced domain wall dynamics by simultaneously resolving the spin transport and micromagnetic equations for a three-dimensional ferromagnetic strip. In contrast to local approaches, which neglect mutual interaction between spins and magnetic moments, our approach recalculates the spin distribution at each time step using the generalized drift diffusion model, which takes the transverse spin absorption phenomenon into account. We quantified the differences between a local approach and treatment based on a self-consistent method by plotting the domain wall velocity as a function of the domain wall width. We also characterized the domain wall velocity and the Walker breakdown condition as a function of the transverse spin absorption length ${l}_{\ensuremath{\perp}}$, which plays a crucial role in domain wall dynamics.

Domain wall dynamics along curved strips under current pulses: The influence of Joule heating

The current-induced domain wall dynamics along curved ferromagnetic strips is studied by coupling the magnetization dynamics to the heat transport. Permalloy strips with uniform and non-uniform cross section are evaluated, taking into account the influence of the electrical contacts used to inject the current pulses and the substrate on top of which the ferromagnetic strip is sited. Micromagnetic simulations indicate that the geometry and the non-ferromagnetic materials in the system play a significant role in the current-induced domain wall dynamics. Due to the natural pinning, domain walls are hardly affected by the spin-transfer torques when placed in uniform cross section strips under current pulses with reduced magnitude. On the contrary, the current-induced domain wall displacement is significantly different in strips with non-uniform cross section, where thermal gradients emerge as due to the Joule heating. It is found that these thermal gradients can assist or act against the pure spin-transfer torques, in agreement with the recent experimental observations.

Current induced domain wall dynamics in the presence of spin orbit torques

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 both torques.

Chirality-sensitive domain wall motion in spin-orbit coupled ferromagnets

Using the Lagrangian formalism, we solve analytically the equations of motion for current-induced domain-wall dynamics in a ferromagnet with Rashba spin-orbit coupling. An exact solution for the domain wall velocity is provided, including the effect of non-equilibrium conduction electron spin-density, Gilbert damping, and the Rashba interaction parameter. We demonstrate explicitly that the influence of spin-orbit interaction can be qualitatively different from the role of non-adiabatic spin-torque in the sense that the former is sensitive to the chirality of the domain wall whereas the latter is not: the domain wall velocity shows a reentrant behavior upon changing the chirality of the domain wall. This could be used to experimentally distinguish between the spin-orbit and non-adiabatic contribution to the wall speed. A quantitative estimate for the attainable domain wall velocity is given, based on an experimentally relevant set of parameters for the system.

Current induced domain wall dynamics in the presence of a transverse magnetic field in out-of-plane magnetized materials

An analytical model was developed to describe the current induced domain wall (DW) dynamics of a Bloch DW in the presence of an external transverse magnetic field. The model takes into account the DW deformation and the magnetization tilting in the domain. The model is compared to the results of micromagnetic simulation and an excellent agreement is obtained. In the steady state regime, the model shows that the domain tilting does not change the DW mobility. An external or current induced transverse magnetic field such as the Oersted or Rashba field can prevent the Walker breakdown leading to a higher domain wall velocity.

The influence of the Rashba field on the current-induced domain wall dynamics: A full micromagnetic analysis, including surface roughness and thermal effects

A micromagnetic study is carried out to analyze the influence of the spin-orbit Rashba field on the current-driven domain wall dynamics along a ferromagnetic strip with high perpendicular magnetocrystalline anisotropy, taking into account both surface roughness and thermal effects. Similarly to the creep and flow regimes seen in recent experiments, the domain wall velocity increases exponentially and linearly for low and high currents, respectively. The induced transverse Rashba field stabilizes the Bloch structure, extending the rigid mobility regime toward high currents and allowing higher velocities than in single-layer or symmetric stacks with negligible Rashba field.

Electrical signature of magnetic domain-wall dynamics

Current-induced domain-wall dynamics is studied in a thin ferromagnetic nanowire. The domain-wall dynamics is described by simple equations with four parameters. We propose a procedure to unambiguously determine these parameters by all-electric measurements of the time-dependent voltage induced by the domain-wall motion. We provide an analytical expression for the time variation of this voltage. Furthermore, we show that the measurement of the proposed effects is within reach of current experimental techniques.

Spin-wave contributions to current-induced domain wall dynamics

We examine theoretically the role of spin-waves on current-induced domain wall dynamics in a ferromagnetic wire. At room temperature, we find that an interaction between the domain wall and the spin waves appears when there is a finite difference between the domain wall velocity $\dot{x}_0$ and the spin current $u$. Three important consequences of this interaction are found. Firstly, spin-wave emission leads to a Landau-type damping of the current-induced domain wall motion towards restoring the solution $\dot{x}_0 = u$, where spin angular momentum is perfectly transfered from the conduction electrons to the domain wall. Secondly, the interaction leads to a modification of the domain wall width and mass, proportional to the kinetic energy of the domain wall. Thirdly, the coupling by the electrical current between the domain wall and the spin waves leads to temperature-dependent effective wall mass.

Numerical Study of Current-Induced Domain-Wall Dynamics: Crossover from Spin Transfer to Momentum Transfer

We study current-induced dynamics of a magnetic domain wall by solving a time-dependent Schr\{o}dinger equation combined with Landau-Lifshitz-Gilbert equation in a one-dimensional electron system coupled to localized spins. Two types of domain-wall motions are observed depending on the hard-axis anisotropy, $K_{\perp}$, of the localized spin system. For small values of $K_{\perp}$, the magnetic domain wall shows a streaming motion driven by spin transfer. In contrast, for large values of $K_{\perp}$, a stick-slip motion driven by momentum transfer is obtained. We clarify the origin of these characters of domain-wall motions in terms of the dynamics of one-particle energy levels and distribution functions.

Time-resolved imaging of current-induced domain-wall oscillations

Current-induced domain-wall dynamics is investigated via high-resolution soft x-ray transmission microscopy by a stroboscopic pump-and-probe measurement scheme at a temporal resolution of 200 ps. A $180\ifmmode^\circ\else\textdegree\fi{}$ domain wall in a restoring potential of a permalloy microstructure is displaced from its equilibrium position by nanosecond current pulses leading to oscillations with velocities up to 325 m/s. The motion of the wall is described with an analytical model of a rigid domain wall in a nonharmonic potential allowing one to determine the mass of the domain wall. We show that Oersted fields dominate the domain-wall dynamics in our geometry.