Current-induced domain wall motion with adiabatic and nonadiabatic spin torques in magnetic nanowires

We investigate current-driven domain wall (DW) propagation in magnetic nanowires in the framework of the modified Landau-Lifshitz-Gilbert equation with both adiabatic and nonadiabatic spin torque (AST and NAST) terms. By employing a simple analytical model, we can demonstrate the essential physics that any small current density can drive the DW motion along a uniaxial anisotropy nanowire even in absence of NAST, while a critical current density threshold is required due to intrinsic anisotropy pinning in a biaxial nanowire without NAST. The DW motion along the uniaxial wire corresponds to the asymptotical DW oscillation solution under high field/current in the biaxial wire case. The current-driven DW velocity weakly depends on the NAST parameter β in a uniaxial wire and it is similar to the β = α case (α: damping) in the biaxial wire. Apart from that, we discuss the rigid DW motion from both the energy and angular momentum viewpoints and point out some physical relations in between. We also propose an experimental scheme to measure the spin current polarization by combining both field- and current-driven DW motion in a usual flat (biaxial) nanowire.     

Real-space observation of current-driven domain wall motion in submicron magnetic wires

We report direct observation of current-driven magnetic domain wall (DW) displacement by using a well-defined single DW in a microfabricated magnetic wire with submicron width. Magnetic force microscopy visualizes that a single DW introduced in a wire is displaced back and forth by positive and negative pulsed current, respectively. The direct observation gives quantitative information on the DW displacement as a function of the intensity and the duration of the pulsed current. The result is discussed in terms of the spin-transfer mechanism.     

In-plane current-induced magnetization reversal of Pd/CoZr/MgO magnetic multilayers

High critical current density ($> 10^{6}$ A/cm$^{2})$ is one of major obstacles to realize practical applications of the current-driven magnetization reversal devices. In this work, we successfully prepared Pd/CoZr(3.5 nm)/MgO thin films with large perpendicular magnetic anisotropy and demonstrated a way of reducing the critical current density with a low out-of-plane magnetic field in the Pd/CoZr/MgO stack. Under the assistance of an out-of-plane magnetic field, the magnetization can be fully reversed with a current density of about 10$^{4}$ A/cm$^{2}$. The magnetization reversal is attributed to the combined effect of the out-of-plane magnetic field and the current-induced spin-orbital torque. It is found that the current-driven magnetization reversal is highly relevant to the temperature owing to the varied spin-orbital torque, and the current-driven magnetization reversal will be more efficient in low-temperature range, while the magnetic field is helpful for the magnetization reversal in high-temperature range.     

Dynamics of Skyrmion crystals in metallic thin films

We study the collective dynamics of the Skyrmion crystal in thin films of ferromagnetic metals resulting from the nontrivial Skyrmion topology. It is shown that the current-driven motion of the crystal reduces the topological Hall effect and the Skyrmion trajectories bend away from the direction of the electric current (the Skyrmion Hall effect). We find a new dissipation mechanism in noncollinear spin textures that can lead to a much faster spin relaxation than Gilbert damping, calculate the dispersion of phonons in the Skyrmion crystal, and discuss the effects of impurity pinning of Skyrmions.     

Current-driven magnetization switching and domain wall motion in nanostructures—Survey of recent experiments

An overview of recent experimental studies and new routes in the field of current-driven magnetization dynamics in nanostructured materials is given. The review introduces the basic concepts (Landau–Lifshitz phenomenology, critical current, spin currents in relation to spin accumulation, adiabatic/non-adiabatic spin-torque) and describes the main results of recent experiments on current-driven magnetization reversal within vertical pillar-like nanostructures and current-driven domain wall motion within laterally confined specimens. While for the pillar systems a discussion is provided of how the introduction of layers with perpendicular magnetic anisotropy, tunnel barriers and exchange bias and(or) oxide layers can be used to reduce the critical current densities for current-induced switching, the role of perpendicular anisotropy, use of spin valve structures, diluted magnetic semiconductors and epitaxial materials to increase the domain wall velocities are reviewed in the case of current-driven domain wall movement within lateral systems.     

Magneto-optical and micromagnetic simulation study of the current-driven domain wall motion in ferromagnetic (Ga,Mn)As

We have studied current-driven domain wall motion in modified Ga_0.95Mn_0.05As Hall bar structures with perpendicular anisotropy by using spatially resolved polar magneto-optical Kerr effect microscopy and micromagnetic simulation. Regardless of the initial magnetic configuration, the domain wall propagates in the opposite direction to the current with critical current of 1-2×10⁵ A/cm². Considering the spin-transfer torque term as well as various effective magnetic field terms, the micromagnetic simulation results are consistent with the experimental results. Our simulated and experimental results suggest that the spin-torque rather than Oersted field is the reason for current-driven domain wall motion in this material.     

Roles of the magnetic field and electric current in thermally activated domain wall motion in a submicrometer magnetic strip with perpendicular magnetic anisotropy

We have experimentally studied micrometer-scale domain wall (DW) motion driven by a magnetic field and an electric current in a Co/Pt multilayer strip with perpendicular magnetic anisotropy. The thermal activation energy for DW motion, along with its scaling with the driving field and current, has been extracted directly from the temperature dependence of the DW velocity. The injection of DC current resulted in an enhancement of the DW velocity independent of the current polarity, but produced no measurable change in the activation energy barrier. Through this analysis, the observed current-induced DW velocity enhancement can be entirely and unambiguously attributed to Joule heating.     

Surface morphological response of crystalline solids to mechanical stresses and electric fields

Surface morphological evolution under the action of external fields is a fascinating topic that has attracted considerable attention within the surface science community over the past two decades. In addition to the interest in a fundamental understanding of field-induced nonlinear response and stability of surface morphology, the problem has been technologically significant in various engineering applications such as microelectronics and nanofabrication. In this report, we review theoretical progress in modeling the surface morphological response of stressed elastic solids under conditions that promote surface diffusion and of electrically conducting solids under surface electromigration conditions. A self-consistent model of surface transport and morphological evolution is presented that has provided the basis for the theoretical and computational work that is reviewed. According to this model, the surface morphological response of electrically conducting elastic solids to the simultaneous action of mechanical stresses and electric fields is analyzed. Emphasis is placed on metallic surfaces, including surfaces of voids in metallic thin films.Surfaces of stressed elastic solids are known to undergo morphological instabilities, such as the Asaro–Tiller or Grinfeld (ATG) instability that leads to emanation of crack-like features from the surface and their fast propagation into the bulk of the solid material. This instability is analyzed theoretically, simulated numerically, and compared with experimental measurements. The surface morphological evolution of electrically conducting, single-crystalline, stressed elastic solids under surface electromigration conditions is also examined. We demonstrate that, through surface electromigration, a properly applied and sufficiently strong electric field can stabilize the surface morphology of the stressed solid against both crack-like ATG instabilities and newly discovered secondary rippling instabilities; the effects of important parameters, such as surface crystallographic orientation, on the surface morphological response to the simultaneous action of an electric field and mechanical stress also are reviewed. In addition, electromigration-driven surface morphological response is analyzed systematically, focusing on the current-driven surface morphological evolution of voids in metallic thin films; this analysis has been motivated largely by the crucial role of void dynamics in determining the reliability of metallic interconnects in integrated circuits and has led to the interpretation of a large body of experimental observations and measurements. The electromigration-driven translational motion of morphologically stable voids, effects of current-driven void dynamics on the evolution of the electrical resistance of metallic thin films, and current-driven void–void interactions also are reviewed. Furthermore, theoretical studies are reviewed that demonstrated very interesting current-driven nonlinear void dynamics in stressed metallic thin films, including the inhibition of electromigration-induced instabilities due to the action of biaxial tensile stress, and stress effects on the electromigration-driven translational motion of morphologically stable voids.Complex, oscillatory surface states under surface electromigration conditions have been observed in numerical studies. In this report, emphasis is placed on void surfaces in metallic thin films, for which stable time-periodic states have been demonstrated. It is shown that increasing parameters such as the electric-field strength or the void size past certain critical values leads to morphological transitions from steady to time-periodic states; the latter states are characterized by wave propagation on the surface of a void that migrates along the metallic film at constant speed. The transition onset corresponds to a Hopf bifurcation that may be either supercritical or subcritical, depending on the symmetry of the surface diffusional anisotropy as determined by the crystallographic orientation of the film plane. It is also shown that, in the case where the Hopf bifurcation is subcritical, the simultaneous action of mechanical stress leads the current-driven void morphological response to the stabilization of chaotic attractors; in such cases, as the applied stress level increases, the void dynamics is set on a route to chaos through a sequence of period-doubling bifurcations. The observation of current-driven chaotic dynamics in homoepitaxial islands also is discussed.     

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.     

Control of Hall angle of Skyrmion driven by electric current

Skyrmions are very promising for applications in spintronics and magnetic memory.It is desired to manipulate and operate a single skyrmion.Here we report on the thermal effect on the motion of current-driven magnetic Skyrmions in magnetic metal.The results show that the magnon current induced by the thermal gradient acts on Skyrmions via magnonic spin-transfer torque,an effect of the transverse and longitudinal Skyrmions drift velocities,thus leading to the effective manipulation of the Hall angle through the ratio of thermal gradient to electric current density,which can be used as a Skyrmion valve.     

Modes of periodic domain wall motion in ultrathin ferromagnetic layers

Magnetization reversal in a periodic magnetic field is studied on an ultrathin, ultrasoft ferromagnetic Pt/Co(0.5 nm)/Pt trilayer exhibiting weak random domain wall (DW) pinning. The DW motion is imaged by polar magneto-optic Kerr effect microscopy and monitored by superconducting quantum interference device susceptometry. In close agreement with model predictions, the complex linear ac susceptibility corroborates the dynamic DW modes segmental relaxation, creep, slide, and switching.     

Current-driven electron drift solitons

The soliton formation by the current-driven drift-like wave is investigated for heavier ion (such as barium) plasma experiments planned to be performed in future. It is pointed out that the sheared flow of electrons can give rise to short scale solitary structures in the presence of stationary heavier ions. The nonlinearity appears due to convective term in the parallel equation of motion and not because of temperature gradient unlike the case of low frequency usual drift wave soliton. This higher frequency drift-like wave requires sheared flow of electrons and not the density gradient to exist.     

Nonmonotonic effects of perpendicular magnetic anisotropy on current-driven vortex wall motions in magnetic nanostripes

In a magnetic nanostripe, the effects of perpendicular magnetic anisotropy(PMA) on the current-driven horizontal motion of vortex wall along the stripe and the vertical motion of the vortex core are studied by micromagnetic simulations.The results show that the horizontal and vertical motion can generally be monotonously enhanced by PMA. However, when the current is small, a nonmonotonic phenomenon for the horizontal motion is found. Namely, the velocity of the horizontal motion firstly decreases and then increases with the increase of the PMA. We find that the reason for this is that the PMA can firstly increase and then decrease the confining force induced by the confining potential energy. In addition, the PMA always enhances the driving force induced by the current.     

Domain wall creation in nanostructures driven by a spin-polarized current

We report on current-driven magnetization reversal in nanopillars with elements having perpendicular magnetic anisotropy. Whereas only the two uniform magnetization states are available under the action of a magnetic field, we observed current-induced Bloch domain walls in pillars as small as 50 x 100 nm(2). This domain wall state can be further controlled by current to restore the uniform states. The ability to nucleate and manipulate domain walls by a current gives insight into the reversal mechanisms of small nanoelements and provides new prospects for ultrahigh density spintronic devices.     

Current induced domain wall motion in nanostripes with perpendicular magnetic anisotropy

We report micromagnetic modeling results of current induced domain wall (DW) motion in magnetic devices with perpendicular magnetic anisotropy by solving the Landau-Lifschitz-Gilbert equation including adiabatic and non-adiabatic terms. A nanostripe model system with dimensions of 500 nm (L)×25 nm (W)×5 nm (H) was selected for calculating the DW motion and its width, as a function of various parameters such as non-adiabatic contribution, anisotropy constant (K_u), saturation magnetization (M_s), and temperature (T). The DW velocity was found to increase when the values of K_u and T were increased and the M_s value decreased. In addition, a reduction of the domain wall width could be achieved by increasing K_u and lowering M_s values regardless of the non-adiabatic constant value.     

Spin-wave excitation by direct current in obliquely magnetized nanostructures

The magnetization dynamics of magnetic nanostructures magnetized at an arbitrary out-of-plane angle is investigated with the spin-wave formalism. The magnetic excitations driven by a spin-polarized direct current are considered to be standing spin-wave modes appropriate for nanopillar structures. The spin waves grow exponentially above a certain critical value of the current density and their post-threshold nonlinear dynamics leads to magnetization oscillations in the microwave range. Due to demagnetizing fields, the current-driven excitation strongly depends on the direction of the applied external magnetic field. In order to calculate the microwave oscillation frequency we derive an equation of motion for the spin-wave amplitude as a function of the out-of-plane angle of the applied field. The results are compared with recent experimental data as well as with another theoretical approach.     

Phase-coherent current-driven magnons in magnetic multilayers

We report the detection of electromagnetic waves radiated by current-driven magnons in a Co/Cu magnetic multilayer. The magnons were excited by means of a high current density ≈10⁸ A/cm² injected into the multilayer through a point contact. The point contact itself was used as a high frequency mixer to mix electromagnetic waves radiated by the current-driven magnons with externally generated microwave radiation. Here the external microwaves are used as a direct probe of the high-frequency behavior and partial phase coherence of the current-induced excitations. When the external frequency equaled the frequency of the magnons generated in the multilayer a DC voltage was found to develop across the contact. Investigation of how this voltage varies with exciting current, magnetic field, and microwave frequency provides detailed information on the spectrum of the current-driven magnons. Our observations support the feasibility of a spin-wave maser, or spin-wave amplification by stimulated emission of radiation.     

Influence of exchange coupling on current-driven domain wall motion in a nanowire

In this study, the effect of exchange stiffness constant on current-driven domain wall motion in nanowires with in-plane magnetic anisotropy (IMA) and perpendicular magnetic anisotropy (PMA) has been investigated using micromagnetic simulation. The critical current density in a nanowire with IMA decreases as the exchange stiffness constant decreases because the domain wall width at the upper edge of the nanowire narrows according to the decrease of the exchange stiffness constant. On the other hand, the critical current density in a nanowire with PMA slightly decreases contrary to that of IMA although the domain wall width reasonably decreases as the exchange stiffness constant decreases. The slight reduction rate of the critical current density is due to the increase of the effective hard-axis anisotropy of PMA nanowire.     

Domain wall motion in ferromagnetic systems with perpendicular magnetization

Although we lack clear experimental evidence, apparently out-of-plane magnetized systems are better suited for spintronic applications than the in-plane magnetized ones, mainly due to the smaller current densities required for achieving domain wall motion. [Co/Pt] multilayers belong to the first category of materials, the out-of-plane magnetization orientation arising from the strong perpendicular magnetocrystalline anisotropy. If the magnetization arranges itself out-of-plane narrow Bloch walls occur. In the present paper, both field and current-driven domain wall motion have been investigated for this system, using micromagnetic simulations. Three types of geometries have been taken into account: bulk, thin film and wire, and for all of them a full comparison is done between the effect of the applied field and injected current. The reduction of the system's dimension induces the decrease of the critical field and the critical current, but it does not influence the domain wall displacement mechanism.     

Universal magnetic domain wall dynamics in the presence of weak disorder

The motion of elastic interfaces in disordered media is a broad topic relevant to many branches of physics. Field-driven magnetic domain wall motion in ultrathin ferromagnetic Pt/Co/Pt films can be well interpreted within the framework of theories developed to describe elastic interface dynamics in the presence of weak disorder. Indeed, the three theoretically predicted dynamic regimes of creep, depinning, and flow have all been directly evidenced in this model experimental system. We discuss these dynamic regimes and demonstrate how field-driven creep can be controlled not only by temperature and pinning, but also via interactions with magnetic entities located inside or outside the magnetic layer. Consequences of confinement effects in nano-devices are briefly reviewed, as some recent results on domain wall motion driven by an electric current or assisted by an electric field. Finally new theoretical developments and perspectives are discussed.