Tunable remote pinning of domain walls in magnetic nanowires

Domain wall (DW) pinning in ferromagnetic nanowires is in general a complex process. Distortions of the DW shape make quantitative agreement between modeling and experiment difficult. Here we demonstrate pinning using nanometer scale localized stray fields. This type of interaction gives well-characterized, tailorable potential landscapes that do not appreciably distort the DW. Our experimental results are in excellent quantitative agreement with an Arrhenius-Néel model of depinning--a result only possible when the modeled potential profile agrees fully with that experienced by the DW.     

Tunable resistivity of individual magnetic domain walls

Despite the relevance of current-induced magnetic domain wall (DW) motion for new spintronics applications, the exact details of the current-domain wall interaction are not yet understood. A property intimately related to this interaction is the intrinsic DW resistivity. Here, we investigate experimentally how the resistivity inside a DW depends on the wall width Δ, which is tuned using focused ion beam irradiation of Pt/Co/Pt strips. We observe the nucleation of individual DWs with Kerr microscopy, and measure resistance changes in real time. A 1/Δ(2) dependence of DW resistivity is found, compatible with Levy-Zhang theory. Also quantitative agreement with theory is found by taking full account of the current flowing through each individual layer inside the multilayer stack.     

Controlled pinning and depinning of domain walls in nanowires with perpendicular magnetic anisotropy

We investigate switching and field-driven domain wall motion in nanowires with perpendicular magnetic anisotropy comprising local modifications of the material parameters. Intentional nucleation and pinning sites with various geometries inside the nanowires are realized via a local reduction of the anisotropy constant. Micromagnetic simulations and analytical calculations are employed to determine the switching fields and to characterize the pinning potentials and the depinning fields. Nucleation sites in the simulations cause a significant reduction of the switching field and are in excellent agreement with analytical calculations. Pinning potentials and depinning fields caused by the pinning sites strongly depend on their shapes and are well explained by analytical calculations.     

Statistics of irreversible displacements of domain walls in nanowires

The process of quasistatic displacement of domain walls is considered in a nanowire represented as a one-dimensional chain of ferromagnet crystallites. The domain wall pinning due to spatial fluctuations of the anisotropy axes is analyzed. Based on the theory of overshoots of random processes, we have calculated the distribution functions of the initial susceptibility and of the maximal force of interaction of the domain wall with inhomogeneities. These functions are found to be non-Gaussian. We have derived expressions for the magnetization curve and the coercive force, which depend on the length of the chain.     

Spin-polarised currents and magnetic domain walls

Electrical currents flowing in ferromagnetic materials are spin-polarised as a result of the spin-dependent band structure. When the spatial direction of the polarisation changes, in a domain structure, the electrons must somehow accommodate the necessary change in direction of their spin angular momentum as they pass through the wall. Reflection, scattering, or a transfer of angular momentum onto the lattice are all possible outcomes, depending on the circumstances. This gives rise to a variety of different physical effects, most importantly a contribution to the electrical resistance caused by the wall, and a motion of the wall driven by the spin-polarised current.

Historical and recent research on these topics is reviewed.

Spin-polarised currents and magnetic domain walls

All authors

C. H. Marrows

https://doi.org/10.1080/00018730500442209

Published online:

19 February 2007

Table     

Metastable domain wall dynamics in magnetic nanowires

We study the formation and control of metastable states of pairs of domain walls in cylindrical nanowires of small diameter where the transverse walls are the lower energy state. We show that these pairs form bound states under certain conditions, with a lifetime as long as 200 ns, and are stabilized by the influence of a spin polarized current. Their stability is analyzed with a model based on the magnetostatic interaction and by 3D micromagnetic simulations. The apparition of bound states could hinder the operation of devices.     

Current-induced domain wall motion in magnetic nanowires with spatial variation

We model current-induced domain wall motion in magnetic nanowires with the variable width. Employing the collective coordinate method we trace the wall dynamics. The effect of the width modulation is implemented by spatial dependence of an effective magnetic field. The wall destination in the potential energy landscape due to the magnetic anisotropy and the spatial nonuniformity is obtained as a function of the current density. For a nanowire of a periodically modulated width, we identify three (pinned, nonlinear, and linear) current density regimes for current-induced wall motion. The threshold current densities depend on the pulse duration as well as the magnitude of wire modulation. In the nonlinear regime, application of ns order current pulses results in wall displacement which opposes or exceeds the prediction of the spin transfer mechanism. The finding explains stochastic nature of the domain wall displacement observed in recent experiments.     

Thermal spin-transfer torques on magnetic domain walls

We studied the spin-transfer torques acting on magnetic domain walls in the presence of a nonequilibrium thermal distribution using a generalized Landauer–Büttiker formalism, where the energy flow is described on the same footing as the electric current. First-principles transport calculations have been performed in Ni and Co domain walls as typical examples. The temperature difference between two sides of the domain wall can induce remarkable spin- transfer torques, which are comparable with the current-induced torques required for the domain wall motion.     

Tunable coplanar waveguide resonator with nanowires

A tunable superconducting half-wavelength coplanar waveguide resonator(CPWR) with Nb parallel nanowires ～300 nm in width embedded in the center conductor was designed, fabricated, and measured. The frequency shift and the amplitude attenuation of the resonance peak under irradiation of 404-nm pulse laser were observed with different light powers at 4.2 K. The RF power supplied to such a CPWR can serve as current bias, which will affect the light response of the resonator.     

Dynamics of domain walls in ultrathin magnetic films

The domain walls in ultrathin ferromagnetic films with uniaxial magnetic anisotropy are investigated theoretically. It is shown that taking account of the magnetodipole and magnetoelastic interactions leads to the appearance of an effective anisotropy with respect to the direction of the normal to the plane of the wall. The existence of a new type of domain walls—“corner” walls, at which the magnetization vector is rotated in the plane making a certain angle, which depends on the film parameters, with the plane of the domain wall and the static and dynamic properties of these walls are investigated. The dependence of the limiting velocity of the domain walls on the film thickness is found. Zh. éksp. Teor. Fiz. 112, 1476–1489 (October 1997)     

The mobility of domain walls in magnetic films

The character of the dependence of domain wall velocityv on magnetic field intensityH varies with film thickness. Possible causes of the nonlinearity ofv(H) in films of some thickness are discussed. It has been shown how the mobility of domain walls varies over a wide range of thicknesses, from ultrathin films to bulk layers. The mobility measured for films up to 500 thick is consistent with the spin damping theory. For thicknesses greater than 1 the experimental data agree well with the eddy current damping theory. The mobility in thinner films is considerably lower than predicted by this theory. It greatly depends on the domain wall structure, magnetic ripple in domains as well as on the structural defects retarding the wall.     

Interaction of domain walls in thin magnetic films

Interactions of pairs of parallel Néel walls are investigated by means of Ritz's method calculations. In the case of the symmetric, thin-film mode of Néel walls, unwinding walls show an attractive and winding walls a repulsive interaction for all distances. The functional dependence of the interaction on the distance of the walls is strongly correlated with the wall profiles of the isolated walls with their characteristic extended tails. For the asymmetric Néel wall mode which occurs in thicker films, an additional repulsive interaction of the magnetization vortices in the wall core is found. This leads for unwinding walls to stable configurations of double walls with separations between two and three times the film thickness.     

Multi-level domain wall memory in constricted magnetic nanowires

We report a new type of multibit per cell (MBPC) magnetic memory wherein the movement and position of domain wall (DW) can be controlled precisely using spin polarized current. Out of two investigated configurations, the one with in-plane magnetization offers faster DW motion, and hence is suitable for high-speed applications, although stability may be an issue. In contrast, stable DWs were observed in the perpendicular configuration. Furthermore, the DW position can be controlled through a sequence of pulses with different magnitudes. Controlling the DW position offers a novel MBPC magnetic memory with high performance compared to other solid state memories.     

Theory of retardation of magnetic domain walls in rhombic magnetic materials

We calculate the retardation of a magnetic soliton describing a magnetic domain wall by using the generalized phenomenological theory of relaxation. We show that in this theory, based on the real dynamical symmetry of magnetic materials, the dissipation function has a different structure for high and low wall velocities. Finally, we calculate the viscous force of the wall in the Walker model and show that certain features, not discussed in the literature, emerge even when the generalized theory is applied to this simple model. In particular, the dependence of the viscous friction force on the wall velocity may be highly nonlinear and regions of unstable motion may appear. Zh. éksp. Teor. Fiz. 111, 158–173 (January 1997)     

Atomic-scale magnetic domain walls in quasi-one-dimensional Fe nanostripes

Fe nanostripes on W(110) are investigated by Kerr magnetometry and spin-polarized scanning tunneling microscopy (SP-STM). An Arrhenius law is observed for the temperature dependent magnetic susceptibility indicating a one-dimensional magnetic behavior. The activation energy for creating antiparallel spin blocks indicates extremely narrow domain walls with a width on a length scale of the lattice constant. This is confirmed by imaging the domain wall by SP-STM. This information allows the quantification of the exchange stiffness and the anisotropy constant.     

Drift of domain walls in a harmonic magnetic field

It is shown that a two-step form of the dynamic magnetization curve (and the hysteresis loop) established for a multiaxial ferrite-garnet wafer with a low quality factor (Q < 1) and considerable anisotropy in the plane (K _p /K _u = 14) in the frequency range of 25–1000 Hz is explained by the reconstruction of the dynamic domain structure, particularly by the established features of the drift of domain boundaries in the harmonic magnetic field.     

Tunneling of magnetic domain walls in the quasirelativistic limit

An additional mechanism which increases the probability of tunneling of magnetic domain walls through defects of a crystal is discussed. In contrast to the thermally stimulated tunneling mechanisms described previously (c.f. Refs. 7 and 8), which arise when the wall acquires additional energy from the thermal system of the crystal, the latter mechanism is produced by the change in the structure of the walls themselves at high energies, which changes the character of their interaction with defects. The results of analytic and numerical analyses of this effect are reported. A discussion and an interpretation of existing experimental results. Fiz. Tverd. Tela (St. Petersburg) 41, 1264–1266 (July 1999)     

Spin torque on magnetic domain walls exerted by supercurrents

We calculate the spin density, spin currents and spin torque due to a spin polarized current on a magnetic domain wall juxtaposed to or inserted in a conventional superconductor. The superconductor is part of a heterostructure of the type NSN or FSF. In general, the spin torque exerted on the domain wall is weaker with respect to a normal metal. However, there are regimes where the torque is enhanced with respect to the normal metal. In these regimes the motion of the domain wall is therefore more efficient. A notable case is the passing of an unpolarized current which leads to a finite torque in the case of the superconductor.