Nonadiabatic spin torque investigated using thermally activated magnetic domain wall dynamics

Coherent correlation imaging for resolving fluctuating states of matter

Fluctuations and stochastic transitions are ubiquitous in nanometre-scale systems, especially in the presence of disorder. However, their direct observation has so far been impeded by a seemingly fundamental, signal-limited compromise between spatial and temporal resolution. Here we develop coherent correlation imaging (CCI) to overcome this dilemma. Our method begins by classifying recorded camera frames in Fourier space. Contrast and spatial resolution emerge by averaging selectively over same-state frames. Temporal resolution down to the acquisition time of a single frame arises independently from an exceptionally low misclassification rate, which we achieve by combining a correlation-based similarity metric^1,2 with a modified, iterative hierarchical clustering algorithm^3,4. We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state with nanometre-scale resolution. We uncover an intricate network of transitions between more than 30 discrete states. Our spatiotemporal data enable us to reconstruct the pinning energy landscape and to thereby explain the dynamics observed on a microscopic level. CCI massively expands the potential of emerging high-coherence X-ray sources and paves the way for addressing large fundamental questions such as the contribution of pinning^5-8 and topology^9-12 in phase transitions and the role of spin and charge order fluctuations in high-temperature superconductivity^13,14.

Quantification of Competing Magnetic States and Switching Pathways in Curved Nanowires by Direct Dynamic Imaging

For viable applications, spintronic devices based, for example, on domain wall motion need to be highly reliable with stable magnetization states and highly reproducible switching pathways transforming one state to another. The existence of multiple stable states and switching pathways in a system is a definitive barrier for device operation, yet rare and stochastic events are difficult to detect and understand. We demonstrate an approach to quantify competing magnetic states and stochastic switching pathways based on time-resolved scanning electron microscopy with polarization analysis, applied to the technologically relevant control of vortex domain wall chirality via field and curvature in curved wires. As a pump-probe technique, our analysis scheme nonetheless allows for the disentanglement of different occurring dynamic pathways, and we can even identify the rare events leading to changes from one magnetization switching pathway to another pathway via temperature- and geometry-dependent measurements. The experimental imaging is supported by micromagnetic simulations to reveal the mechanisms responsible for the change of the pathway. Together the results allow us to explain the origin and details of the domain wall chirality control and to quantify the frequency and the associated energy barriers of thermally activated changes of the states and switching pathways.

Theory for spin torque in Weyl semimetal with magnetic texture

The spin-transfer torque is a fundamental physical quantity to operate the spintronics devices such as racetrack memory. We theoretically study the spin-transfer torque and analyze the dynamics of the magnetic domain walls in magnetic Weyl semimetals. Owing to the strong spin-orbit coupling in Weyl semimetals, the spin-transfer torque can be significantly enhanced, because of which they can provide a more efficient means of controlling magnetic textures. We derive the analytical expression of the spin-transfer torque and find that the velocity of the domain wall is one order of magnitude greater than that of conventional ferromagnetic metals. Furthermore, due to the suppression of longitudinal conductivity in the thin domain-wall configuration, the dissipation due to Joule heating for the spin-transfer torque becomes much smaller than that in bulk metallic ferromagnets. Consequently, the fast-control of the domain wall can be achieved with smaller dissipation from Joule heating in the Weyl semimetals as required for application to low-energy-consumption spintronics devices.

Synthetic ferrimagnet nanowires with very low critical current density for coupled domain wall motion

Domain walls in ferromagnetic nanowires are potential building-blocks of future technologies such as racetrack memories, in which data encoded in the domain walls are transported using spin-polarised currents. However, the development of energy-efficient devices has been hampered by the high current densities needed to initiate domain wall motion. We show here that a remarkable reduction in the critical current density can be achieved for in-plane magnetised coupled domain walls in CoFe/Ru/CoFe synthetic ferrimagnet tracks. The antiferromagnetic exchange coupling between the layers leads to simple Néel wall structures, imaged using photoemission electron and Lorentz transmission electron microscopy, with a width of only ~100 nm. The measured critical current density to set these walls in motion, detected using magnetotransport measurements, is 1.0 × 10¹¹ Am⁻², almost an order of magnitude lower than in a ferromagnetically coupled control sample. Theoretical modelling indicates that this is due to nonadiabatic driving of anisotropically coupled walls, a mechanism that can be used to design efficient domain-wall devices.

Enhanced Nonadiabaticity in Vortex Cores due to the Emergent Hall Effect

We present a combined theoretical and experimental study, investigating the origin of the enhanced nonadiabaticity of magnetic vortex cores. Scanning transmission x-ray microscopy is used to image the vortex core gyration dynamically to measure the nonadiabaticity with high precision, including a high confidence upper bound. We show theoretically, that the large nonadiabaticity parameter observed experimentally can be explained by the presence of local spin currents arising from a texture induced emergent Hall effect. This study demonstrates that the magnetic damping α and nonadiabaticity parameter β are very sensitive to the topology of the magnetic textures, resulting in an enhanced ratio (β/α>1) in magnetic vortex cores or Skyrmions.

Geometrically pinned magnetic domain wall for multi-bit per cell storage memory

Spintronic devices currently rely on magnetic switching or controlled motion of domain walls (DWs) by an external magnetic field or a spin-polarized current. Controlling the position of DW is essential for defining the state/information in a magnetic memory. During the process of nanowire fabrication, creating an off-set of two parts of the device could help to pin DW at a precise position. Micromagnetic simulation conducted on in-plane magnetic anisotropy materials shows the effectiveness of the proposed design for pinning DW at the nanoconstriction region. The critical current for moving DW from one state to the other is strongly dependent on nanoconstricted region (width and length) and the magnetic properties of the material. The DW speed which is essential for fast writing of the data could reach values in the range of hundreds m/s. Furthermore, evidence of multi-bit per cell memory is demonstrated via a magnetic nanowire with more than one constriction.

Intrinsic Nature of Stochastic Domain Wall Pinning Phenomena in Magnetic Nanowire Devices

Finite temperature micromagnetic simulations are used to probe stochastic domain wall pinning behaviours in magnetic nanowire devices. By exploring field-induced propagation both below and above the Walker breakdown field it is shown that all experimentally observed phenomena can be comprehensively explained by the influence of thermal perturbations on the domain walls' magnetisation dynamics. Nanowires with finite edge roughness are also investigated, and these demonstrate how this additional form of disorder couples with thermal perturbations to significantly enhance stochasticity. Cumulatively, these results indicate that stochastic pinning is an intrinsic feature of DW behaviour at finite temperatures, and would not be suppressed even in hypothetical systems where initial DW states and experimental parameters were perfectly defined.

Model of spin accumulation and spin torque in spatially varying magnetisation structures: limitations of the micromagnetic approach

We study the spin-transfer torque acting on the magnetisation when injecting polarised conduction electrons into a magnetic system. The spin accumulation is calculated self-consistently and naturally includes the adiabatic and non-adiabatic contributions which depend on the rate of change of magnetisation in relation to the spin diffusion length. As an example we consider a system where a spin-polarised current is injected into a structure containing a domain wall. We calculate the spin torque and related parameters corresponding to the adiabatic and non-adiabatic terms directly from the spin accumulation, and find that the dynamic micromagnetic approach based on adiabatic and non-adiabatic terms with constant coefficients is valid only for systems with slowly spatially varying magnetisation.

Gilbert damping in noncollinear ferromagnets

The precession and damping of a collinear magnetization displaced from its equilibrium are well described by the Landau-Lifshitz-Gilbert equation. The theoretical and experimental complexity of noncollinear magnetizations is such that it is not known how the damping is modified by the noncollinearity. We use first-principles scattering theory to investigate transverse domain walls (DWs) of the important ferromagnetic alloy Ni80Fe20 and show that the damping depends not only on the magnetization texture but also on the specific dynamic modes of Bloch and Néel DWs in ways that were not theoretically predicted. Even in the highly disordered Ni80Fe20 alloy, the damping is found to be remarkably nonlocal.

Domain wall transformations and hopping in La(0.7)Sr(0.3)MnO(3) nanostructures imaged with high resolution x-ray magnetic microscopy

We investigate the effect of electric current pulse injection on domain walls in La(0.7)Sr(0.3)MnO(3) (LSMO) half-ring nanostructures by high resolution x-ray magnetic microscopy at room temperature. Due to the easily accessible Curie temperature of LSMO, we can employ reasonable current densities to induce the Joule heating necessary to observe effects such as hopping of the domain walls between different pinning sites and nucleation/annihilation events. Such effects are the dominant features close to the Curie temperature, while spin torque is found to play a small role close to room temperature. We are also able to observe thermally activated domain wall transformations and we find that, for the analyzed geometries, the vortex domain wall configuration is energetically favored, in agreement with micromagnetic simulations.

Elementary depinning processes of magnetic domain walls under fields and currents

The probability laws associated to domain wall depinning under fields and currents have been studied in NiFe and FePt nanowires. Three basic domain wall depinning processes, associated to different potential landscapes, are found to appear identically in those systems with very different anisotropies. We show that these processes constitute the building blocks of any complex depinning mechanism. A Markovian analysis is proposed, that provides a unified picture of the depinning mechanism and an insight into the pinning potential landscape.

Correlation between spin structure oscillations and domain wall velocities

Magnetic sensing and logic devices based on the motion of magnetic domain walls rely on the precise and deterministic control of the position and the velocity of individual magnetic domain walls in curved nanowires. Varying domain wall velocities have been predicted to result from intrinsic effects such as oscillating domain wall spin structure transformations and extrinsic pinning due to imperfections. Here we use direct dynamic imaging of the nanoscale spin structure that allows us for the first time to directly check these predictions. We find a new regime of oscillating domain wall motion even below the Walker breakdown correlated with periodic spin structure changes. We show that the extrinsic pinning from imperfections in the nanowire only affects slow domain walls and we identify the magnetostatic energy, which scales with the domain wall velocity, as the energy reservoir for the domain wall to overcome the local pinning potential landscape.

Quantitative magneto-mechanical detection and control of the Barkhausen effect

Quantitative characterization of intrinsic and artificial defects in ferromagnetic structures is critical to future magnetic storage based on vortices or domain walls moving through nanostructured devices. Using torsional magnetometry, we observe finite size modifications to the Barkhausen effect in the limiting case of a single vortex core interacting with individual pointlike pinning sites in a magnetic thin film. The Barkhausen effect in this limit becomes a quantitative two-dimensional nanoscale probe of local energetics in the film. Tailoring the pinning potential using single-point focused ion beam implantation demonstrates control of the effect and points the way to integrated magneto-mechanical devices incorporating quantum pinning effects.

Understanding nanoscale temperature gradients in magnetic nanocontacts

We have determined the temperature profile in magnetic nanocontacts under applied current densities typical of spin-torque oscillators (∼10(8)  A/cm2). The study combines experimental measurements of the electrical and magnetic properties of the nanocontacts and full three-dimensional simulations of the heat and current flow in these systems. It is found that the quadratic current-induced increase of the resistance due to Joule heating is independent of the applied temperature from 6 to 300 K. In terms of magnetization dynamics, the measured current-induced vortex nucleation, a thermally activated process, is found to be consistent with local temperatures increases of between 147 and 225 K. Simulations reproduce the experimental findings and show that significant thermal gradients exist out to 450 nm from the nanocontact.

Current-induced torques in magnetic materials

The magnetization of a magnetic material can be reversed by using electric currents that transport spin angular momentum. In the reciprocal process a changing magnetization orientation produces currents that transport spin angular momentum. Understanding how these processes occur reveals the intricate connection between magnetization and spin transport, and can transform technologies that generate, store or process information via the magnetization direction. Here we explain how currents can generate torques that affect the magnetic orientation and the reciprocal effect in a wide variety of magnetic materials and structures. We also discuss recent state-of-the-art demonstrations of current-induced torque devices that show great promise for enhancing the functionality of semiconductor devices.

Determination of the spin torque non-adiabaticity in perpendicularly magnetized nanowires

Novel nanofabrication methods and the discovery of an efficient manipulation of local magnetization based on spin polarized currents has generated a tremendous interest in the field of spintronics. The search for materials allowing for fast domain wall dynamics requires fundamental research into the effects involved (Oersted fields, adiabatic and non-adiabatic spin torque, Joule heating) and possibilities for a quantitative comparison. Theoretical descriptions reveal a material and geometry dependence of the non-adiabaticity factor β, which governs the domain wall velocity. Here, we present two independent approaches for determining β: (i) measuring the dependence of the dwell times for which a domain wall stays in a metastable pinning state on the injected current and (ii) the current-field equivalence approach. The comparison of the deduced β values highlights the problems of using one-dimensional models to describe two-dimensional dynamics and allows us to ascertain the reliability, robustness and limits of the approaches used.

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.

Dynamics of magnetic domain walls under their own inertia

The motion of magnetic domain walls induced by spin-polarized current has considerable potential for use in magnetic memory and logic devices. Key to the success of these devices is the precise positioning of individual domain walls along magnetic nanowires, using current pulses. We show that domain walls move surprisingly long distances of several micrometers and relax over several tens of nanoseconds, under their own inertia, when the current stimulus is removed. We also show that the net distance traveled by the domain wall is exactly proportional to the current pulse length because of the lag derived from its acceleration at the onset of the pulse. Thus, independent of its inertia, a domain wall can be accurately positioned using properly timed current pulses.

Direct determination of large spin-torque nonadiabaticity in vortex core dynamics

We use a pump-probe photoemission electron microscopy technique to image the displacement of vortex cores in Permalloy discs due to the spin-torque effect during current pulse injection. Exploiting the distinctly different symmetries of the spin torques and the Oersted-field torque with respect to the vortex spin structure we determine the torques unambiguously, and we quantify the amplitude of the strongly debated nonadiabatic spin torque. The nonadiabaticity parameter is found to be β=0.15±0.07, which is more than an order of magnitude larger than the damping constant α, pointing to strong nonadiabatic transport across the high magnetization gradient vortex spin structures.

Domain-wall depinning assisted by pure spin currents

We study the depinning of domain walls by pure diffusive spin currents in a nonlocal spin valve structure based on two ferromagnetic Permalloy elements with copper as the nonmagnetic spin conduit. The injected spin current is absorbed by the second Permalloy structure with a domain wall, and from the dependence of the wall depinning field on the spin current density we find an efficiency of 6×10{-14}  T/(A/m{2}), which is more than an order of magnitude larger than for conventional current induced domain-wall motion. Theoretically we find that this high efficiency arises from the surface torques exerted by the absorbed spin current that lead to efficient depinning.