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

Neuromorphic computation with a single magnetic domain wall

Machine learning techniques are commonly used to model complex relationships but implementations on digital hardware are relatively inefficient due to poor matching between conventional computer architectures and the structures of the algorithms they are required to simulate. Neuromorphic devices, and in particular reservoir computing architectures, utilize the inherent properties of physical systems to implement machine learning algorithms and so have the potential to be much more efficient. In this work, we demonstrate that the dynamics of individual domain walls in magnetic nanowires are suitable for implementing the reservoir computing paradigm in hardware. We modelled the dynamics of a domain wall placed between two anti-notches in a nickel nanowire using both a 1D collective coordinates model and micromagnetic simulations. When driven by an oscillating magnetic field, the domain exhibits non-linear dynamics within the potential well created by the anti-notches that are analogous to those of the Duffing oscillator. We exploit the domain wall dynamics for reservoir computing by modulating the amplitude of the applied magnetic field to inject time-multiplexed input signals into the reservoir, and show how this allows us to perform machine learning tasks including: the classification of (1) sine and square waves; (2) spoken digits; and (3) non-temporal 2D toy data and hand written digits. Our work lays the foundation for the creation of nanoscale neuromorphic devices in which individual magnetic domain walls are used to perform complex data analysis tasks.

Tunable Stochasticity in an Artificial Spin Network

Metamaterials present the possibility of artificially generating advanced functionalities through engineering of their internal structure. Artificial spin networks, in which a large number of nanoscale magnetic elements are coupled together, are promising metamaterial candidates that enable the control of collective magnetic behavior through tuning of the local interaction between elements. In this work, the motion of magnetic domain-walls in an artificial spin network leads to a tunable stochastic response of the metamaterial, which can be tailored through an external magnetic field and local lattice modifications. This type of tunable stochastic network produces a controllable random response exploiting intrinsic stochasticity within magnetic domain-wall motion at the nanoscale. An iconic demonstration used to illustrate the control of randomness is the Galton board. In this system, multiple balls fall into an array of pegs to generate a bell-shaped curve that can be modified via the array spacing or the tilt of the board. A nanoscale recreation of this experiment using an artificial spin network is employed to demonstrate tunable stochasticity. This type of tunable stochastic network opens new paths toward post-Von Neumann computing architectures such as Bayesian sensing or random neural networks, in which stochasticity is harnessed to efficiently perform complex computational tasks.

Neuromorphic Spintronics

Neuromorphic computing uses basic principles inspired by the brain to design circuits that perform artificial intelligence tasks with superior energy efficiency. Traditional approaches have been limited by the energy area of artificial neurons and synapses realized with conventional electronic devices. In recent years, multiple groups have demonstrated that spintronic nanodevices, which exploit the magnetic as well as electrical properties of electrons, can increase the energy efficiency and decrease the area of these circuits. Among the variety of spintronic devices that have been used, magnetic tunnel junctions play a prominent role because of their established compatibility with standard integrated circuits and their multifunctionality. Magnetic tunnel junctions can serve as synapses, storing connection weights, functioning as local, nonvolatile digital memory or as continuously varying resistances. As nano-oscillators, they can serve as neurons, emulating the oscillatory behavior of sets of biological neurons. As superparamagnets, they can do so by emulating the random spiking of biological neurons. Magnetic textures like domain walls or skyrmions can be configured to function as neurons through their non-linear dynamics. Several implementations of neuromorphic computing with spintronic devices demonstrate their promise in this context. Used as variable resistance synapses, magnetic tunnel junctions perform pattern recognition in an associative memory. As oscillators, they perform spoken digit recognition in reservoir computing and when coupled together, classification of signals. As superparamagnets, they perform population coding and probabilistic computing. Simulations demonstrate that arrays of nanomagnets and films of skyrmions can operate as components of neuromorphic computers. While these examples show the unique promise of spintronics in this field, there are several challenges to scaling up, including the efficiency of coupling between devices and the relatively low ratio of maximum to minimum resistances in the individual devices.

A Micromagnetic Protocol for Qualitatively Predicting Stochastic Domain Wall Pinning

Understanding dynamically-induced stochastic switching effects in soft ferromagnetic nanowires is a critical challenge for realising spintronic devices with deterministic switching behaviour. Here, we present a micromagnetic simulation protocol for qualitatively predicting dynamic stochastic domain wall (DW) pinning/depinning at artificial defect sites in Ni₈₀Fe₂₀ nanowires, and demonstrate its abilities by correlating its predictions with the results of focused magneto-optic Kerr effect measurements. We analyse DW pinning configurations in both thin nanowires (t = 10 nm) and thick nanowires (t = 40 nm) with both single (asymmetric) and double (symmetric) notches, showing how our approach provides understanding of the complex DW-defect interactions at the heart of stochastic pinning behaviours. Key results explained by our model include the total suppression of stochastic pinning at single notches in thick nanowires and the intrinsic stochasticity of pinning at double notches, despite their apparent insensitivity to DW chirality.

Suppression of Stochastic Domain Wall Pinning Through Control of Gilbert Damping

Finite temperature micromagnetic simulations were used to investigate the magnetisation structure, propagation dynamics and stochastic pinning of domain walls in rare earth-doped Ni₈₀Fe₂₀ nanowires. We first show how the increase of the Gilbert damping, caused by the inclusion rare-earth dopants such as holmium, acts to suppress Walker breakdown phenomena. This allows domain walls to maintain consistent magnetisation structures during propagation. We then employ finite temperature simulations to probe how this affects the stochastic pinning of domain walls at notch-shaped artificial defect sites. Our results indicate that the addition of even a few percent of holmium allows domain walls to pin with consistent and well-defined magnetisation configurations, thus suppressing dynamically-induced stochastic pinning/depinning phenomena. Together, these results demonstrate a powerful, materials science-based solution to the problems of stochastic domain wall pinning in soft ferromagnetic nanowires.

Understanding the role of damping and Dzyaloshinskii-Moriya interaction on dynamic domain wall behaviour in platinum-ferromagnet nanowires

Heavy metal layers, exemplified by Pt, are known to play a significant role in the magnetization behaviour of thin-film ferromagnets by three distinct mechanisms that can each contribute to the reversal process. These include modifying the local magnetization state via an interfacial Dzyaloshinskii-Moriya interaction (IDMI), enhancement of the damping, via d-d hybridisation and spin-pumping across the interface, and the mediation of the magnetization switching, with the flow of current through a system, via the spin-Hall effect. Here we show for a system with weak interfacial DMI (NiFe/Pt) that the measurement of magnetic field-driven magnetization reversal, mediated by domain wall (DW) motion, is dominated by the enhanced intrinsic damping contribution as a function of the Pt capping layer thickness. But, we also show micromagnetically that the IDMI and damping also combine to modify the domain wall velocity behaviour when the damping is larger. It is also noted that Walker breakdown occurs at lower fields and peak DW velocity decreases in the presence of IDMI. These results highlight the significance of the relative contributions of the damping and the IDMI from the heavy metal layer on the magnetization reversal and provide a route to controlling the DW behaviour in nanoscale device structures.

Self-organization and FORC-based magnetic characterization of ultra-high aspect ratio epitaxial Co nanostrips produced by oblique deposition on an ordered step-bunched silicon surface

Further development of microelectronics requires novel or improved technological approaches for device nanofabrication and functional properties characterization. In this paper, we studied the crystal structure and magnetic properties of epitaxial Co nanostrips with the average width of 32.6, 45.3, and 62.6 nm grown on a step-bunched Si(111)5.55 × 5.55-Cu/Cu surface. Technological conditions, under which the ultra-high aspect ratio (∼10⁴) structurally solid, straight nanostrips of hcp-Co with crystallographic axis [0001] oriented along their long side can be grown, were determined. The dependence of the coercive force on the width of the nanostrips was demonstrated. Magnetization reversal through the transverse domain-wall nucleation and propagation in a Co nanostrip was defined with an analytical approach based on the Stoner-Wohlfarth model. Using the first-order reversal curve method, we analyzed the effect of nanostrip uniformity degree on magnetic behavior and the influence of the magnetostatic interactions on the coercive force of individual nanostrips.

Effective pinning energy landscape perturbations for propagating magnetic domain walls

The interaction between a magnetic domain wall and a pinning site is explored in a planar nanowire using micromagnetics to reveal perturbations of the pinning energetics for propagating domain walls. Numerical simulations in the high damping 'quasi-static' and low damping 'dynamic' regimes are compared and show clear differences in de-pinning fields, indicating that dynamical micromagnetic models, which incorporate precessionally limited magnetization processes, are needed to understand domain wall pinning. Differences in the micromagnetic domain wall structure strongly influence the pinning and show periodic behaviour with increasing applied field associated with Walker breakdown. In the propagating regime pinning is complicated.

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.

Creep turns linear in narrow ferromagnetic nanostrips

The motion of domain walls in magnetic materials is a typical example of a creep process, usually characterised by a stretched exponential velocity-force relation. By performing large-scale micromagnetic simulations, and analyzing an extended 1D model which takes the effects of finite temperatures and material defects into account, we show that this creep scaling law breaks down in sufficiently narrow ferromagnetic strips. Our analysis of current-driven transverse domain wall motion in disordered Permalloy nanostrips reveals instead a creep regime with a linear dependence of the domain wall velocity on the applied field or current density. This originates from the essentially point-like nature of domain walls moving in narrow, line- like disordered nanostrips. An analogous linear relation is found also by analyzing existing experimental data on field-driven domain wall motion in perpendicularly magnetised media.