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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.

A unified model of molecular and atomistic spin dynamics is presented enabling simulations both in microcanonical and canonical ensembles without the necessity of additional phenomenological spin damping. Transfer of energy and angular momentum between the lattice and the spin systems is achieved by a phenomenological coupling term representing the spin-orbit interaction. The characteristic spectra of the spin and phonon systems are analyzed for different coupling strength and temperatures. The spin spectral density shows magnon modes together with the uncorrelated noise induced by the coupling to the lattice. The effective damping parameter is investigated showing an increase with both coupling strength and temperature. The model paves the way to understanding magnetic relaxation processes beyond the phenomenological approach of the Gilbert damping and the dynamics of the energy transfer between lattice and spins.

L$1_0$ FePt is a technologically important material for a range of novel data storage applications. In the ordered FePt structure the normally non-magnetic Pt ion acquires a magnetic moment, which depends on the local field originating from the neighboring Fe atoms. In this work a model of FePt is constructed, where the induced Pt moment is simulated by using combined longitudinal and rotational spin dynamics. The model is parameterized to include a linear variation of the moment with the exchange field, so that at the Pt site the magnetic moment depends on the Fe ordering. The Curie temperature of FePt is calculated and agrees well with similar models that incorporate the Pt dynamics through an effective Fe-only Hamiltonian. By computing the dynamic correlation function the anisotropy field and the Gilbert damping are extracted over a range of temperatures. The anisotropy exhibits a power-law dependence with temperature with exponent $n\approx2.1$. This agrees well with what observed experimentally and it is obtained without including a two-ion anisotropy term as in other approaches. Our work shows that incorporating longitudinal fluctuations into spin dynamics calculations is crucial for understanding the properties of materials with induced moments., 9 pages, 9 figures

We propose thermally driven, voltage-controlled superparamagnetic ensembles as low-energy platforms for hardware-based reservoir computing. In the proposed devices, thermal noise is used to drive the ensembles' magnetization dynamics, while control of their net magnetization states is provided by strain-mediated voltage inputs. Using an ensemble of CoFeB nanodots as an example, we use analytical models and micromagnetic simulations to demonstrate how such a device can function as a reservoir and perform two benchmark machine learning tasks (spoken digit recognition and chaotic time series prediction) with competitive performance. Our results indicate robust performance on timescales from microseconds to milliseconds, potentially allowing such a reservoir to be tuned to perform a wide range of real-time tasks, from decision making in driverless cars (fast) to speech recognition (slow). The low energy consumption expected for such a device makes it an ideal candidate for use in edge computing applications that require low latency and power.\ud \ud The authors thank the Engineering and Physical Sciences Research Council (Grant No.: EP/S009647/1 and EP/V006339/1) for financial support. The project leading to this application has received funding from the European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 861618 (SpinENGINE).

Gilbert damping plays a significant role in magnetic reversal processes, and it determines the timescale of the switching. Here we investigate the properties of exchange-coupled composite media and the dependence of the switching time on the damping constant of the soft layer using atomistic spin dynamics. For a bilayer Fe/FePt medium, we find an anomalous increase of the switching time with increasing soft layer damping constant. The reversal occurs via a high-temperature exchange spring, and we show that the increase in the switching time is related to a corresponding increase in the time to establish the exchange spring. This phenomenon is delicately balanced in that the switching time increase occurs only in fields close to the coercivity.

Emergent behaviors occur when simple interactions between a system's constituent elements produce properties that the individual elements do not exhibit in isolation. This article reports tunable emergent behaviors observed in domain wall (DW) populations of arrays of interconnected magnetic ring‐shaped nanowires under an applied rotating magnetic field. DWs interact stochastically at ring junctions to create mechanisms of DW population loss and gain. These combine to give a dynamic, field‐dependent equilibrium DW population that is a robust and emergent property of the array, despite highly varied local magnetic configurations. The magnetic ring arrays’ properties (e.g., non‐linear behavior, “fading memory” to changes in field, fabrication repeatability, and scalability) suggest they are an interesting candidate system for realizing reservoir computing (RC), a form of neuromorphic computing, in hardware. By way of example, simulations of ring arrays performing RC approaches 100% success in classifying spoken digits for single speakers.

We present an {\it ab-initio} study of the spin-transfer torque in a Fe/MgO/FePt/Fe magnetic tunnel junctions. We consider a FePt film with a thickness up to six unit cells, either in direct contact with the MgO spacer or with an intercalated ultra-thin Fe seed layer. We find that in the FePt layer the torque is not attenuated as strongly as in the case of pure Fe. Moreover, in FePt the torque alternates sign at the Fe and Pt atomic planes throughout the stack for all FePt thicknesses considered. Finally, when Fe is intercalated between MgO and L$1_0$-FePt, the torque is sharply attenuated and it is transferred to FePt only for a Fe seed layer that is less than two-atomic-planes thick. We attribute these features to the different spatial profiles of the exchange and correlation field and the induced non-equilibrium spin accumulation. The calculated tunnelling magneto-resistance of the Fe/MgO/FePt/Fe junctions studied is enhanced with respect to the one of Fe/MgO/Fe, while it is reduced with Fe intercalation. Our work shows that L$1_0$-FePt junctions can be promising candidates for current-operated magnetic devices and that the magnetic texture at the atomic scale has an important effect on the spin transfer torque., 8 pages, 7 figures

There exists a significant challenge in developing efficient magnetic tunnel junctions with low write currents for non-volatile memory devices. With the aim of analysing potential materials for efficient current-operated magnetic junctions we have developed a multi-scale methodology combining the ab initio calculations of spin-transfer torque with large-scale time-dependent simulations using atomistic spin dynamics. In this work we introduce our multi-scale approach including a discussion on a number of possible mapping schemes the ab initio spin torques into the spin dynamics. We demonstrate this methodology on a prototype Co/MgO/Co/Cu tunnel junction showing that the spin torques are primarily acting at the interface between the Co free layer and MgO. Using spin dynamics we then calculate the reversal switching times for the free layer and the critical voltages and currents required for such switching. Our work provides an efficient, accurate and versatile framework for designing novel current-operated magnetic devices, where all the materials details are take into account., 8 pages, 7 figures, submitted to Physical Review B

Exchange coupling between magnetic grains is essential for maintaining the stability of stored information in magnetic recording media. Using an atomistic spin model, we have investigated the coupling between neighbouring magnetic grains where magnetic impurity atoms have migrated into the non-magnetic grain boundary. We find that when the impurity density is low a biquadratic term in addition to the bilinear term is required to properly describe the inter-granular exchange coupling. The temperature dependence both terms is found to follow a power law behaviour with the biquadratic exchange constant decaying faster than the bilinear. For increasing grain boundary thickness the inter-granular exchange is lower and decays faster with temperature. Further simulations of a grain at a bit boundary show an unexpected energy minimum for in-plane magnetisation which can only be reproduced using a biquadratic exchange term., Comment: 4 pages, 4 figures. The following article has been submitted to Applied Physics Letters

Magnetic recording using circularly polarised femto-second laser pulses is an emerging technology that would allow write speeds much faster than existing field driven methods. However, the mechanism that drives the magnetisation switching in ferromagnets is unclear. Recent theories suggest that the interaction of the light with the magnetised media induces an opto-magnetic field within the media, known as the inverse Faraday effect. Here we show that an alternative mechanism, driven by thermal excitation over the anisotropy energy barrier and a difference in the energy absorption depending on polarisation, can create a net magnetisation over a series of laser pulses in an ensemble of single domain grains. Only a small difference in the absorption is required to reach magnetisation levels observed experimentally and the model does not preclude the role of the inverse Faraday effect but removes the necessity that the opto-magnetic field is 10 s of Tesla in strength.

The linear reversal mechanism in FePt grains ranging from 2.316 nm to 5.404 nm has been simulated using atomistic spin dynamics, parametrized from ab-initio calculations. The Curie temperature and the critical temperature (T*), at which the linear reversal mechanism occurs, are observed to decrease with system size whilst the temperature window T* < T < TC increases. The reversal paths close to the Curie temperature have been calculated, showing that for decreasing system size the reversal path becomes more elliptic at lower temperatures, consistent with the decrease in the Curie temperature arising from finite size effects. Calculations of the minimum pulse duration show faster switching in small grains and is qualitatively described by the Landau-Lifshitz-Bloch equation with finite size atomistic parameterization, which suggests that multiscale modeling of FePt down to a grain size of ~ 3.5 nm is possible., 4 pages, 4 figures. Changes: 1) Abstract and introduction text has been updated. Some new references have been included in the introduction. 2) Figure 1 has been altered to included T* on the inset. 3) New data has been included n figure 3. Figure 3.e has been altered to include the new data and also compares to the LLB equation. 4) Main text has been altered to reflect the new figures

Using the Landau-Lifshitz-Bloch (LLB) equation for ferromagnetic materials, we derive analytic expressions for temperature dependent absorption spectra as probed by ferromagnetic resonance (FMR). By analysing the resulting expressions, we can predict the variation of the resonance frequency and damping with temperature and coupling to the thermal bath. We base our calculations on the technologically relevant L1$_0$ FePt, parameterised from atomistic spin dynamics simulations, with the Hamiltonian mapped from ab-initio parameters. By constructing a multi-macrospin model based on the LLB equation and exploiting GPU acceleration we extend the study to investigate the effects on the damping and resonance frequency in ${\mu}$m sized structures., Comment: 10 pages, 8 figures

In this paper, the ultrafast dynamic behavior of rare-earth doped permalloy is investigated using an atomistic spin model with Langevin dynamics. In line with experimental work, the effective Gilbert damping is calculated from transverse relaxation simulations, which shows that rare-earth doping causes an increase in the damping. Analytic theory suggests that this increase in damping would lead to a decrease in the demagnetization time. However, longitudinal relaxation calculations show an increase with doping concentration instead. The simulations are in a good agreement with previous experimental work of Radu et al. [Radu et al., Phys. Rev. Lett. 102, 117201 (2009)]. The longitudinal relaxation time of the magnetization is shown to be driven by the interaction between the transition metal and the laser-excited conduction electrons, whereas the effective damping is predominantly determined by the slower interaction between the rare-earth elements and the phonon heat bath. We conclude that for complex materials, it is evidently important not to expect a single damping parameter but to consider the energy transfer channel relevant to the technique and time scale of the measurement.

Atomistic modelling of magnetic materials provides unprecedented detail about the underlying physical processes that govern their macroscopic properties, and allows the simulation of complex effects such as surface anisotropy, ultrafast laser-induced spin dynamics, exchange bias, and mi- crostructural effects. Here we present the key methods used in atomistic spin models which are then applied to a range of magnetic problems. We detail the parallelisation strategies used which enable the routine simulation of extended systems with full atomistic resolution.

Low cost pollution sensors have been widely publicized, in principle offering increased information on the distribution of air pollution and a democratization of air quality measurements to amateur users. We report a laboratory study of commonly-used electrochemical sensors and quantify a number of cross-interferences with other atmospheric chemicals, some of which become significant at typical suburban air pollution concentrations. We highlight that artefact signals from co-sampled pollutants such as CO2 can be greater than the electrochemical sensor signal generated by the measurand. We subsequently tested in ambient air, over a period of three weeks, twenty identical commercial sensor packages alongside standard measurements and report on the degree of agreement between references and sensors. We then explore potential experimental approaches to improve sensor performance, enhancing outputs from qualitative to quantitative, focusing on low cost VOC photoionization sensors. Careful signal handling, for example, was seen to improve limits of detection by one order of magnitude. The quantity, magnitude and complexity of analytical interferences that must be characterised to convert a signal into a quantitative observation, with known uncertainties, make standard individual parameter regression inappropriate. We show that one potential solution to this problem is the application of supervised machine learning approaches such as boosted regression trees and Gaussian processes emulation.

The Landau-Lifshitz (LL) equation, originally proposed at the macrospin level, is increasingly used in Atomistic Spin Dynamic (ASD) models. The models are based on a spin Hamiltonian featuring atomic spins of fixed length, with the exchange introduced using the Heisenberg formalism. ASD models are proving a powerful approach to the fundamental understanding of ultrafast magnetisation dynamics, including the prediction of the thermally induced magnetisation switching phenomenon in which the magnetisation is reversed using an ultrafast laser pulse in the absence of an externally applied field. The paper outlines the ASD model approach and considers the role and limitations of the LL equation in this context., Comment: 9 pages, 1 figure