Current-induced torques in magnetic metals: Beyond spin-transfer

Current-induced torques (CITs) on ferromagnetic (FM) nanoparticles and on domain walls in FM nanowires are normally understood in terms of transfer of conserved spin angular momentum between spin-polarized currents and the magnetic condensate. In a series of recent articles, we have discussed a microscopic picture of CITs in which they are viewed as following from exchange fields produced by the misaligned spins of current carrying quasiparticles. This picture has the advantage that it can be applied to systems in which spin is not approximately conserved. More importantly, this point of view makes it clear that CITs can also act on the order parameter of an antiferromagnetic (AFM) metal, even though this quantity is not related to total spin. In this informal and intentionally provocative review we explain this picture and discuss its application to antiferromagnets.     

Device implications of spin-transfer torques

This article examines spin-transfer torques from the perspective of three technological applications: hard disk drives, magnetic random access memory (MRAM), and current-tunable high-frequency oscillators. In hard disk drives, spin-transfer torques are a source of noise, and we discuss the implications spin-transfer noise will have on future sensor designs. For MRAM, we evaluate the feasibility of spin-transfer-driven switching. Finally, we discuss the possibility of GHz communication applications enabled by nanoscale spin-transfer oscillators.     

Width dependence of the nonadiabatic spin-transfer torque in narrow domain walls

We analytically determine the spatially varying spin-transfer torque within a domain wall. In the case of ballistic spin and diffusive charge transport, the spin-transfer torque as well as the local degree of nonadiabaticity oscillate within a domain wall. In narrow domain walls, the degree of nonadiabaticity ceases to be a constant material parameter but depends on the domain-wall width including a possible sign change, which is crucial for experiments and the technological utilization in spin-transfer-torque-based storage devices.     

Domain-wall dynamics and spin-wave excitations with spin-transfer torques

A generalization of spin-transfer torques in ferromagnetic structures is proposed. For a spatially nonuniform magnetization, the spin torque has a form nearly identical to that in magnetic multilayers. We show that the domain-wall motion driven by the current has many unique features that do not exist in the conventional domain-wall motion driven by a magnetic field. We also demonstrate that the spin torque can generate bulk and surface spin excitations that have been seen in point-contact experiments.     

The increase of the spin-transfer torque threshold current density in coupled vortex domain walls

We have studied the dependence on the domain wall structure of the spin-transfer torque current density threshold for the onset of wall motion in curved, Gd-doped Ni(80)Fe(20) nanowires with no artificial pinning potentials. For single vortex domain walls, for both 10% and 1% Gd-doping concentrations, the threshold current density is inversely proportional to the wire width and significantly lower compared to the threshold current density measured for transverse domain walls. On the other hand for high Gd concentrations and large wire widths, double vortex domain walls are formed which require an increase in the threshold current density compared to single vortex domain walls at the same wire width. We suggest that this is due to the coupling of the vortex cores, which are of opposite chirality, and hence will be acted on by opposing forces arising through the spin-transfer torque effect.     

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     

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.     

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.     

Thermal spin-transfer torque in magnetoelectronic devices

We predict that the magnetization direction of a ferromagnet can be reversed by the spin-transfer torque accompanying spin-polarized thermoelectric heat currents. We illustrate the concept by applying a finite-element theory of thermoelectric transport in disordered magnetoelectronic circuits and devices to metallic spin valves. When thermalization is not complete, a spin heat accumulation vector is found in the normal-metal spacer, i.e., a directional imbalance in the temperature of majority and minority spins.     

All-magnonic spin-transfer torque and domain wall propagation

The spin-wave transportation through a transverse magnetic domain wall (DW) in a magnetic nanowire is studied. It is found that the spin wave passes through a DW without reflection. A magnon, the quantum of the spin wave, carries opposite spins on the two sides of the DW. As a result, there is a spin angular momentum transfer from the propagating magnons to the DW. This magnonic spin-transfer torque can efficiently drive a DW to propagate in the opposite direction to that of the spin wave.     

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.     

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.     

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)     

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.     

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)     

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.     

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)