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The dynamical properties of skyrmions can be exploited to build devices with new functionalities. Here, we first investigate a skyrmion-based ring-shaped device by means of micromagnetic simulations and Thiele equation. We subsequently show three applications scenarios: (1) a clock with tunable frequency that is biased with an electrical current having a radial spatial distribution, (2) an alternator, where the skyrmion circular motion driven by an engineered anisotropy gradient is converted into an electrical signal, and (3) an energy harvester, where the skyrmion motion driven by a thermal gradient is converted into an electrical signal, thus providing a heat recovery operation. We also show how to precisely tune the frequency and amplitude of the output electrical signals by varying material parameters, geometrical parameters, number and velocity of skyrmions, and we further prove the correct device functionality under realistic conditions given by room temperature and internal material defects. Our results open a new route for the realization of energy efficient nanoscale clocks, generators, and energy harvesters.

Accelerometers have widespread applications and are an essential component in many areas such as automotive, consumer electronics and industrial applications. Most commercial accelerometers are based on micro-electromechanical system (MEMS) that are limited in downscaling and power consumption. Spintronics-based accelerometers have been proposed as alternatives, however, current proposals suffer from design limitations that result in reliability issues and high cost. Here we propose spintronic accelerometers with magnetic tunnel junctions (MTJs) as building block, which map accelerations into a measurable voltage across the MTJ terminals. The device exploits elastic and dipolar coupling as a sensing mechanism and the spintronic diode effect for the direct read out of the acceleration. The proposed technology represents a potentially competitive and scalable solution to current capacitive MEMS-based approaches that could lead to a step forward in many of the commercial applications., Comment: main document with 4 figures + supplemental information

Magnetic solitons are promising for applications due to their intrinsic properties such as small size, topological stability, ultralow power manipulation and potentially ultrafast operations. To date, research has focused on the manipulation of skyrmions, domain walls, and vortices by applied currents. The discovery of new methods to control magnetic parameters, such as the interfacial Dzyaloshinskii-Moriya interaction (DMI) by strain, geometry design, temperature gradients, and applied voltages promises new avenues for energetically efficient manipulation of magnetic structures. The latter has shown significant progress in 2d material-based technology. In this work, we present a comprehensive study using numerical and analytical methods of the stability and motion of different magnetic textures under the influence of DMI gradients. Our results show that under the influence of linear DMI gradients, N\'eel and Bloch-type skyrmions and radial vortex exhibit motion with finite skyrmion Hall angle, while the circular vortex undergoes expulsion dynamics. This work provides a deeper and crucial understanding of the stability and gradient-driven dynamics of magnetic solitons, and paves the way for the design of alternative low-power sources of magnetization manipulation in the emerging field of 2d materials., Comment: 19 pages, 5 figures

The commercial and industrial demand for the solution of hard combinatorial optimization problems push forward the development of efficient solvers. One of them is the Ising machine which can solve combinatorial problems mapped to Ising Hamiltonians. In particular, spintronic hardware implementations of Ising machines can be very efficient in terms of area and performance, and are relatively low-cost considering the potential to create hybrid CMOS-spintronic technology. Here, we perform a comparison of coherent and probabilistic paradigms of Ising machines on several hard Max-Cut instances, analyzing their scalability and performance at software level. We show that probabilistic Ising machines outperform coherent Ising machines in terms of the number of iterations required to achieve the problem s solution. Nevertheless, high frequency spintronic oscillators with sub-nanosecond synchronization times could be very promising as ultrafast Ising machines. In addition, considering that a coherent Ising machine acts better for Max-Cut problems because of the absence of the linear term in the Ising Hamiltonian, we introduce a procedure to encode Max-3SAT to Max-Cut. We foresee potential synergic interplays between the two paradigms., Comment: 26 pages, 6 Figures, submitted for publication in Phys. Rev. Applied (it will be presented at intermag 2023 in Japan)

In the "Beyond Moore's Law" era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, adopting a variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber resilience, and processing power. The time is ripe for a roadmap for unconventional computing with nanotechnologies to guide future research, and this collection aims to fill that need. The authors provide a comprehensive roadmap for neuromorphic computing using electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets, and various dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain-inspired computing for incremental learning and problem-solving in severely resource-constrained environments. These approaches have advantages over traditional Boolean computing based on von Neumann architecture. As the computational requirements for artificial intelligence grow 50 times faster than Moore's Law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon, and this roadmap will help identify future needs and challenges. In a very fertile field, experts in the field aim to present some of the dominant and most promising technologies for unconventional computing that will be around for some time to come. Within a holistic approach, the goal is to provide pathways for solidifying the field and guiding future impactful discoveries., Comment: 80 pages accepted in Nano Futures

Spintronic diodes (STDs) are emerging as a technology for the realization of high-performance microwave detectors. The key advantages of such devices are their high sensitivity, capability to work at low input power, and compactness. In this work, we show a possible use of STDs for neuromorphic computing expanding the realm of their functionalities to implement analog multiplication, which is a key operation in convolutional neural networks (CNN). In particular, we introduce the concept of degree of rectification (DOR) in injection-locked STDs. Micromagnetic simulations are used to design and identify the working range of the STDs for the implementation of the DOR. Previous experimental data confirm the applicability of the proposed solution, which is tested in image processing and in a CNN that recognizes handwritten digits., Comment: 21 pages, 6 figures, supplemental material includes 4 figures

Spintronic technology is emerging as a direction for the hardware implementation of neurons and synapses of neuromorphic architectures. In particular, a single spintronic device can be used to implement the nonlinear activation function of neurons. Here, we propose how to implement spintronic neurons with a sigmoidal and ReLU-like activation functions. We then perform a numerical experiment showing the robustness of neural networks made by spintronic neurons all having different activation functions to emulate device-to-device variations in a possible hardware implementation of the network. Therefore, we consider a vanilla neural network implemented to recognize the categories of the Mixed National Institute of Standards and Technology database, and we show an average accuracy of 98.87 % in the test dataset which is very close to the 98.89% as obtained for the ideal case (all neurons have the same sigmoid activation function). Similar results are also obtained with neurons having a ReLU-like activation function.

Spintronic diodes are emerging as disruptive candidates for impacting several technological applications ranging from the Internet of Things to Artificial Intelligence. In this letter, an overview of the recent achievements on spintronic diodes is briefly presented, underling the major breakthroughs that have led these devices to have the largest sensitivity measured up to date for a diode. For each class of spintronic diodes (passive, active, resonant, non-resonant), we indicate the remaining developments to improve the performances as well as the future directions. We also dedicate the last part of this perspective to new ideas for developing spintronic diodes in multiphysics systems by combining 2-dimensional materials and antiferromagnets.

Ultrafast dynamics of antiferromagnetic materials is an appealing feature for novel spintronic devices. Several experiments have shown that both, the static states and the dynamical behavior of the antiferromagnetic order, are strictly related to stabilization of domains and domain wall (DW) motion. Hence for a quantitative understanding of statics and dynamics of multidomain states in antiferromagnetic materials a full micromagnetic framework is necessary. Here, we use this model to study the antiferromagnetic DW motion driven by the spin-orbit torque. The main result is the derivation of analytical expressions for the DW width and velocity that exhibit a very good agreement with the numerical simulations in a wide range of parameters. We also find that a mechanism limiting the maximum applicable current in an antiferromagnetic racetrack memory is the continuous nucleation of the domains from the edge, which is qualitatively different from what is observed in ferromagnetic racetracks.

The realization of THz sources is a fundamental aspect for a wide range of applications. Over different approaches, compact THz oscillators can be realized taking advantage of dynamics in antiferromagnetic (AFMs) thin films driven by spin-Hall effect. Here we perform a systematic study of these THz oscillators within a full micromagnetic solver based on the numerical solution of two coupled Landau-Lifshitz-Gilbert-Slonczewski equations, for the case of ultra-thin films, i.e. when the N\'eel temperature of an AFM is substantially reduced. We have found two different dynamical modes depending on the strength of the Dzyaloshinskii-Moriya interaction (DMI). At low DMI, a large amplitude precession is excited where both the magnetizations of the sublattices are in a uniform state and rotate in the same direction. At large enough DMI, the ground state of the AFM becomes non-uniform and the antiferromagnetic dynamics is characterized by ultrafast domain wall motion., Comment: manuscript 15 pages 7 figures - supplemental material 3 pages 2 figures

The understanding of the dynamical properties of skyrmion is a fundamental aspect for the realization of a competitive skyrmion based technology beyond CMOS. Most of the theoretical approaches are based on the approximation of a rigid skyrmion. However, thermal fluctuations can drive a continuous change of the skyrmion size via the excitation of thermal modes. Here, by taking advantage of the Hilbert-Huang transform, we demonstrate that at least two thermal modes can be excited which are non-stationary in time. In addition, one limit of the rigid skyrmion approximation is that this hypothesis does not allow for correctly describing the recent experimental evidence of skyrmion Hall angle dependence on the amplitude of the driving force, which is proportional to the injected current. In this work, we show that, in an ideal sample, the combined effect of field-like and damping-like torques on a breathing skyrmion can indeed give rise to such a current dependent skyrmion Hall angle. While here we design and control the breathing mode of the skyrmion, our results can be linked to the experiments by considering that the thermal fluctuations and/or disorder can excite the breathing mode. We also propose an experiment to validate our findings.

The realistic modeling of STT-MRAM for the simulations of hybrid CMOS/Spintronics devices in comprehensive simulation environments require a full description of stochastic switching processes in state of the art STT-MRAM. Here, we derive an analytical formulation that takes into account the spin-torque asymmetry of the spin polarization function of magnetic tunnel junctions studying. We studied its validity range by comparing the analytical formulas with results achieved numerically within a full micromagnetic framework. We also find that a reasonable fit of the probability density function (PDF) of the switching time is given by a Pearson Type IV PDF. The main results of this work underlines the need of data-driven design of STT-MRAM that uses a full micromagnetic simulation framework for the statistical proprieties PDF of switching processes.

A strategy for a scalable synchronization of an array of spin-Hall oscillators (SHOs) is illustrated. In detail, we present micromagnetic simulations of two and five SHOs realized by means of couples of triangular golden contacts on the top of a Pt/CoFeB/Ta trilayer. Results highlight that the synchronization occurs for the whole current region that gives rise to the excitation of self-oscillations. This is linked to the role of the magnetodipolar coupling, which is the phenomenon driving the synchronization when the distance between oscillators is not too large. Synchronization turns out to be also robust against geometrical differences of the contacts, simulated by considering variable distances between the tips ranging from 100nm to 200nm. Besides, it entails an enlargement of the radiation pattern that can be useful for the generation of spin-waves in magnonics applications. Simulations performed to study the effect of the interfacial Dzyaloshinskii-Moriya interaction show nonreciprocity in spatial propagation of the synchronized spin-wave. The simplicity of the geometry and the robustness of the achieved synchronization make this design of array of SHOs scalable for a larger number of synchronized oscillators.

Nanomagnetic logic transmits information along a path of nanomagnets. The basic mechanism to drive such a transmission, known as clocking, can be achieved by exploiting the spin-Hall effect, as recently observed in experiments on Ta/CoFeB/MgO multilayers [D. Bhowmik, et al., Nat. Nano. 9, 59 (2013)]. This paper shows the fundamental mechanism of the spin-Hall driven clocking by using a full micromagnetic framework and considering two different devices, Ta/CoFeB/MgO and Pt/CoFeB/MgO. The former is used for a direct comparison of the numerical results with the experiments while the latter permits to predict the effect of the Dzyaloshinskii-Moriya interaction (DMI) in the clocking mechanism. Results show that the clocking state is non-uniform and it is characterized by the presence of domains separated by Bloch (N\'eel) domain walls depending on the absence (presence) of the DMI. Our findings point out that for the design of nanomagnetic logic a full micromagnetic approach is necessary., Comment: 12 pages, 3 figures

This paper micromagnetically studies the magnetization dynamics driven by the spin-Hall effect in a Platinum/Permalloy bi-layer. For a certain field and current range, the excitation of a uniform mode, characterized by a power with a spatial distribution in the whole ferromagnetic cross section, is observed. We suggest to use the ferromagnet of the bi-layer as basis for the realization of an array of spin-torque oscillators (STOs): the Permalloy ferromagnet will act as shared free layer, whereas the spacers and the polarizers are built on top of it. Following this strategy, the frequency of the uniform mode will be the same for the whole device, creating an intrinsic synchronization. The synchronization of an array of parallely connected STOs will allow to increase the output power, as necessary for technological applications., Comment: 7 pages, 4 figures

The role of universal memory can be successfully satisfied by magnetic tunnel junctions (MTJs) where the writing mechanism is based on spin-transfer torque (STT). An improvement in the switching properties (lower switching current density maintaining the thermal stability) has been achieved in MTJs with interfacial perpendicular anisotropy (IPA) at the interface between CoFeB and MgO. In this paper, micromagnetic simulations point out the influence of IPA and saturation magnetization (MS) on the properties of fast magnetization reversal achieved in 5, 10 and 20 ns. Both cases of in-plane and out-of-plane free layer are considered. In addition, the thermal effect is included for the in-plane switching at 20 ns and a complete analysis of energy dissipation during the switching is illustrated. This study can provide useful information for the design of STT-based memories.

Integrated power and linewidth of a propagating and a self-localized spin wave modes excited by spin-polarized current in an obliquely magnetized magnetic nanocontact are studied experimentally as functions of the angle $\theta_e$ between the external bias magnetic field and the nanocontact plane. It is found that the power of the propagating mode monotonically increases with $\theta_e$, while the power of the self-localized mode has a broad maximum near $\theta_e = 40$ deg, and exponentially vanishes near the critical angle $\theta_e = 58$ deg, at which the localized mode disappears. The linewidth of the propagating mode in the interval of angles $58<\theta_e<90$ deg, where only this mode is excited, is adequtely described by the existing theory, while in the angular interval where both modes can exist the observed linewidth of both modes is substantially broadened due to the telegraph switching between the modes. Numetical simulations and an approximate analytical model give good semi-quantitative description of the observed results., Comment: 8 pages, 6 figures