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Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation of an experimental physical system. Here we show that a dynamical neural network, trained on a minimal amount of data, can predict the behavior of spintronic devices with high accuracy and an extremely efficient simulation time, compared to the micromagnetic simulations that are usually employed to model them. For this purpose, we re-frame the formalism of Neural Ordinary Differential Equations (ODEs) to the constraints of spintronics: few measured outputs, multiple inputs and internal parameters. We demonstrate with Spin-Neural ODEs an acceleration factor over 200 compared to micromagnetic simulations for a complex problem -- the simulation of a reservoir computer made of magnetic skyrmions (20 minutes compared to three days). In a second realization, we show that we can predict the noisy response of experimental spintronic nano-oscillators to varying inputs after training Spin-Neural ODEs on five milliseconds of their measured response to different excitations. Spin-Neural ODE is a disruptive tool for developing spintronic applications in complement to micromagnetic simulations, which are time-consuming and cannot fit experiments when noise or imperfections are present. Spin-Neural ODE can also be generalized to other electronic devices involving dynamics., Comment: 16 pages, 4 figures

The reservoir computing neural network architecture is widely used to test hardware systems for neuromorphic computing. One of the preferred tasks for bench-marking such devices is automatic speech recognition. However, this task requires acoustic transformations from sound waveforms with varying amplitudes to frequency domain maps that can be seen as feature extraction techniques. Depending on the conversion method, these may obscure the contribution of the neuromorphic hardware to the overall speech recognition performance. Here, we quantify and separate the contributions of the acoustic transformations and the neuromorphic hardware to the speech recognition success rate. We show that the non-linearity in the acoustic transformation plays a critical role in feature extraction. We compute the gain in word success rate provided by a reservoir computing device compared to the acoustic transformation only, and show that it is an appropriate benchmark for comparing different hardware. Finally, we experimentally and numerically quantify the impact of the different acoustic transformations for neuromorphic hardware based on magnetic nano-oscillators., Comment: 13 pages, 5 figures

Spin-torque nano-oscillators can emulate neurons at the nanoscale. Recent works show that the non-linearity of their oscillation amplitude can be leveraged to achieve waveform classification for an input signal encoded in the amplitude of the input voltage. Here we show that the frequency and the phase of the oscillator can also be used to recognize waveforms. For this purpose, we phase-lock the oscillator to the input waveform, which carries information in its modulated frequency. In this way we considerably decrease amplitude, phase and frequency noise. We show that this method allows classifying sine and square waveforms with an accuracy above 99% when decoding the output from the oscillator amplitude, phase or frequency. We find that recognition rates are directly related to the noise and non-linearity of each variable. These results prove that spin-torque nano-oscillators offer an interesting platform to implement different computing schemes leveraging their rich dynamical features.

Neurons in the brain behave as non-linear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behavior to realize high density, low power neuromorphic computing will require huge numbers of nanoscale non-linear oscillators. Indeed, a simple estimation indicates that, in order to fit a hundred million oscillators organized in a two-dimensional array inside a chip the size of a thumb, their lateral dimensions must be smaller than one micrometer. However, despite multiple theoretical proposals, there is no proof of concept today of neuromorphic computing with nano-oscillators. Indeed, nanoscale devices tend to be noisy and to lack the stability required to process data in a reliable way. Here, we show experimentally that a nanoscale spintronic oscillator can achieve spoken digit recognition with accuracies similar to state of the art neural networks. We pinpoint the regime of magnetization dynamics leading to highest performance. These results, combined with the exceptional ability of these spintronic oscillators to interact together, their long lifetime, and low energy consumption, open the path to fast, parallel, on-chip computation based on networks of oscillators.

We study effects originating from the strong spin orbit coupling in CoFeB/MgO heterostructures with heavy metal (HM) underlayers. The perpendicular magnetic anisotropy at the CoFeB/MgO interface, the spin Hall angle of the heavy metal layer, current induced torques and the Dzyaloshinskii-Moriya interaction at the HM/CoFeB interfaces are studied for films in which the early 5d transition metals are used as the HM underlayer. We show how the choice of the HM layer influences these intricate spin orbit effects that emerge within the bulk and at interfaces of the heterostructures.

The time it takes to accelerate an object from zero to a given velocity depends on the applied force and the environment. If the force ceases, it takes exactly the same time to completely decelerate. A magnetic domain wall (DW) is a topological object that has been observed to follow this behavior. Here we show that acceleration and deceleration times of chiral Neel walls driven by current are different in a system with low damping and moderate Dzyaloshinskii-Moriya (DM) exchange constant. The time needed to accelerate a DW with current via the spin Hall torque is much faster than the time it needs to decelerate once the current is turned off. The deceleration time is defined by the DM exchange constant whereas the acceleration time depends on the spin Hall torque, enabling tunable inertia of chiral DWs. Such unique feature of chiral DWs can be utilized to move and position DWs with lower current, key to the development of storage class memory devices.

The motion of magnetic domain walls in ultrathin magnetic heterostructures driven by current via the spin Hall torque is described. We show results from perpendicularly magnetized CoFeB|MgO heterostructures with various heavy metal underlayers. The domain wall moves along or against the current flow depending on the underlayer material. The direction to which the domain wall moves is associated with the chirality of the domain wall spiral formed in these heterostructures. The one-dimensional model is used to describe the experimental results and extract parameters such as the Dzyaloshinskii-Moriya exchange constant which is responsible for the formation of the domain wall spiral. Fascinating effects arising from the control of interfaces in magnetic heterostructures are described., Comment: To appear in "Magnetic Nano- and Microwires", Editor M. Vazquez, Woodhead publishing

The flow of in-plane current through ultrathin magnetic heterostructures can cause magnetization switching or domain wall nucleation owing to bulk and interfacial effects. Within the magnetic layer, the current can create magnetic instabilities via spin transfer torques (STT). At interface(s), spin current generated from the spin Hall effect in a neighboring layer can exert torques, referred to as the spin Hall torques, on the magnetic moments. Here, we study current induced magnetization switching in perpendicularly magnetized CoFeB/MgO heterostructures with a heavy metal (HM) underlayer. Depending on the thickness of the HM underlayer, we find distinct differences in the inplane field dependence of the threshold switching current. The STT is likely responsible for the magnetization reversal for the thinner underlayer films whereas the spin Hall torques cause the switching for thicker underlayer films. For the latter, we find differences in the switching current for positive and negative currents and initial magnetization directions. We find that the growth process during the film deposition introduces an anisotropy that breaks the symmetry of the system and causes the asymmetric switching. The presence of such symmetry breaking anisotropy enables deterministic magnetization switching at zero external fields.

Recent advances in the understanding of spin orbital effects in ultrathin magnetic heterostructures have opened new paradigms to control magnetic moments electrically. The Dzyaloshinskii-Moriya interaction (DMI) is said to play a key role in forming a Neel-type domain wall that can be driven by the spin Hall torque, a torque resulting from the spin current generated in a neighboring non-magnetic layer via the spin Hall effect. Here we show that the strength and sign of the DMI can be changed by modifying the adjacent heavy metal underlayer (X) in perpendicularly magnetized X|CoFeB|MgO heterstructures. Albeit the same spin Hall angle, a domain wall moves along or against the electron flow depending on the underlayer. We find that the sense of rotation of a domain wall spiral11 is reversed when the underlayer is changed from Hf to W and the strength of DMI varies as the number of 5d electrons of the heavy metal layer changes. The DMI can even be tuned by adding nitrogen to the underlayer, thus allowing interface engineering of the magnetic texture in ultrathin magnetic heterostructures., Comment: Extended version of arXiv:1308.1751

Recent advances in the understanding of spin orbital effects in ultrathin magnetic heterostructures have opened new paradigms to control magnetic moments electrically. The Dzyaloshinskii-Moriya interaction (DMI) is said to play a key role in forming a Neel-type domain wall that can be driven by the spin Hall torque, a torque resulting from the spin current generated in a neighboring non-magnetic layer via the spin Hall effect. Here we show that the sign of the DMI, which determines the direction to which a domain wall moves with current, can be changed by modifying the adjacent non-magnetic layer. We find that the sense of rotation of a domain wall spiral is reversed when the Ta underlayer is doped with nitrogen in Ta|CoFeB|MgO heterostructures. The spin Hall angle of the Ta and nitrogen doped Ta underlayers carry the same sign, suggesting that the sign of the DMI is defined at the interface. Depending on the sense of rotation, spin transfer torque and spin Hall torque can either compete or assist each other, thus influencing the efficiency of moving domain walls with current.