The versatility of nanodevices dynamics may allow original architectures for computation but care should be taken to handle fluctuations arising at this scale. In the network of oscillatory units which we propose, bistability with down-quiescent and up-oscillatory states enable tolerance to noise in storage and retrieval dynamics for patterns or sequences. We illustrate this by simulations of the stochastic differential equations for a network with connectivity corresponding to stored patterns.

In the brain, learning is achieved through the ability of synapses to reconfigure the strength by which they connect neurons (synaptic plasticity). In promising solid-state synapses called memristors, conductance can be finely tuned by voltage pulses and set to evolve according to a biological learning rule called spike-timing-dependent plasticity (STDP). Future neuromorphic architectures will comprise billions of such nanosynapses, which require a clear understanding of the physical mechanisms responsible for plasticity. Here we report on synapses based on ferroelectric tunnel junctions and show that STDP can be harnessed from inhomogeneous polarization switching. Through combined scanning probe imaging, electrical transport and atomic-scale molecular dynamics, we demonstrate that conductance variations can be modelled by the nucleation-dominated reversal of domains. Based on this physical model, our simulations show that arrays of ferroelectric nanosynapses can autonomously learn to recognize patterns in a predictable way, opening the path towards unsupervised learning in spiking neural networks.

In recent years, artificial neural networks have become the flagship algorithm of artificial intelligence 1 . In these systems, neuron activation functions are static and computing is achieved through standard arithmetic operations. By contrast, a prominent branch of neuroinspired computing embraces the dynamical nature of the brain and proposes to endow each component of a neural network with dynamical functionality, such as oscillations, and to rely on emergent physical phenomena, such as synchronization 2-7 , for computing complex problems with small size networks [7][8][9][10][11] . This approach is especially interesting for hardware implementations, as emerging nanoelectronic devices can provide highly compact and energy-efficient non-linear auto-oscillators that mimic the periodic spiking activity of biological neurons [12][13][14][15][16] . The dynamical couplings between oscillators can then be used to mediate the synaptic communication between neurons. However, one major challenge towards implementing these models with nano-devices is to achieve learning, which requires finely controlling and tuning their coupled oscillations 17 . The dynamical features of nanodevices can indeed be difficult to control, and prone to noise and variability 18 . In this work, we show that the outstanding tunability of spintronic nano-oscillators, i.e. the possibility to widely and accurately control their frequency through electrical current and magnetic field, can solve this challenge. We successfully train a hardware network of four spin-torque nano-oscillators to recognize spoken vowels by tuning their frequencies according to an automatic real-time learning rule. We show that the high experimental recognition rates stem from the outstanding ability of these oscillators to synchronize. Our results demonstrate that non-trivial pattern classification tasks can be achieved with small hardware neural networks by endowing them with non-linear dynamical features: here, oscillations and synchronization. This demonstration of real-time learning with an array of four spin-torque nano-oscillators is a milestone for spintronics-based neuromorphic computing.Spin-torque nano-oscillators are natural candidates for building hardware neural networks made of coupled nanoscale oscillators [8][9][10]13,15,18,19 . These nanoscale magnetic tunnel junctions emit microwave

Spin-transfer torque magnetic memory (STT-MRAM) is currently under intense academic and industrial development, since it features non-volatility, high write and read speed and high endurance. In this work, we show that when used in a non-conventional regime, it can additionally act as a stochastic memristive device, appropriate to implement a "synaptic" function. We introduce basic concepts relating to spin-transfer torque magnetic tunnel junction (STT-MTJ, the STT-MRAM cell) behavior and its possible use to implement learning-capable synapses. Three programming regimes (low, intermediate and high current) are identified and compared. System-level simulations on a task of vehicle counting highlight the potential of the technology for learning systems. Monte Carlo simulations show its robustness to device variations. The simulations also allow comparing system operation when the different programming regimes of STT-MTJs are used. In comparison to the high and low current regimes, the intermediate current regime allows minimization of energy consumption, while retaining a high robustness to device variations. These results open the way for unexplored applications of STT-MTJs in robust, low power, cognitive-type systems.

We report on a spectroscopic study of the spin-wave eigenmodes inside an individual normally magnetized two-layer circular nanopillar (permalloy|copper|permalloy) by means of a magnetic resonance force microscope. We demonstrate that the observed spin-wave spectrum critically depends on the method of excitation. While the spatially uniform radio-frequency (rf) magnetic field excites only the axially symmetric modes having azimuthal index = 0, the rf current flowing through the nanopillar, creating a circular rf Oersted field, excites only the modes having azimuthal index = +1. Breaking the axial symmetry of the nanopillar, either by tilting the bias magnetic field or by making the pillar shape elliptical, mixes different -index symmetries, which can be excited simultaneously by the rf current. Experimental spectra are compared to theoretical prediction using both analytical and numerical calculations. An analysis of the influence of the static and dynamic dipolar coupling between the nanopillar magnetic layers on the mode spectrum is performed.

We investigate the dynamics of two coupled vortices driven by spin transfer. We are able to independently control with current and perpendicular field, and to detect, the respective chiralities and polarities of the two vortices. For current densities above J = 5.7 * 10 7 A/cm 2 , a highly coherent signal (linewidth down to 46 kHz) can be observed, with a strong dependence on the relative polarities of the vortices. It demonstrates the interest of using coupled dynamics in order to increase the coherence of the microwave signal. Emissions exhibit a linear frequency evolution with perpendicular field, with coherence conserved even at zero magnetic field.The lowest energy mode of vortex dynamics corresponds to the gyrotropic motion of the core around its equilibrium position. This mode have been studied extensively (for a review see Ref.[1]), and very recent works demonstrated that it could also be stimulated by spin transfer torque [2][3][4][5]. The resulting microwave signals are characterized by narrow linewidths (about 1 MHz) [6,7] and, for structures based on magnetic tunnel junctions instead of metallic nanopillars, large output powers [8], making these spin transfer vortex oscillators good candidates for applications as nanoscale frequency synthesizers.The reported observation of microwave emission without any applied magnetic field raises questions about the actual sources of spin torque, in particular about the role played by the static and/or dynamic behavior of the polarizer [9,10]. Here, we intentionally design samples so that both the active layer and the polarizer layer can contain a magnetic vortex, thus leading to a more complex but interesting situation of coupled vortices. The problem of interacting vortices has been rarely treated even for a field-driven excitation [11][12][13][14]21] and never for a current induced excitation. Taking benefit of this 2-vortices configuration, our objective is to establish some selection rules for the observation of highly coherent coupled vortices in terms of their relative chiralities and polarities. To do that, we first demonstrate our capability to control independently the vortices chiralities and polarities, and to detect the resulting configuration through dc transport measurements. Consequently, we can provide some clear evidence that the microwave features associated with the coupled dynamics greatly depend upon the characteristics of each vortex, notably here their relative core polarities.

Low-energy random number generation is critical for many emerging computing schemes proposed to complement or replace von Neumann architectures. However, current random number generators are always associated with an energy cost that is prohibitive for these computing schemes. In this paper, we introduce random number bit generation based on specific nanodevices: superparamagnetic tunnel junctions. We experimentally demonstrate high quality random bit generation that represents orders-of-magnitude improvements in energy efficiency compared to current solutions. We show that the random generation speed improves with nanodevice scaling, and investigate the impact of temperature, magnetic field and crosstalk. Finally, we show how alternative computing schemes can be implemented using superparamagentic tunnel junctions as random number generators. These results open the way for fabricating efficient hardware computing devices leveraging stochasticity, and highlight a novel use for emerging nanodevices.

Due to their nonlinear properties, spin transfer nano-oscillators can easily adapt their frequency to external stimuli. This makes them interesting model systems to study the effects of synchronization and brings some opportunities to improve their microwave characteristics in view of their applications in information and communication technologies and/or to design innovative computing architectures. So far, mutual synchronization of spin transfer nano-oscillators through propagating spinwaves and exchange coupling in a common magnetic layer has been demonstrated. Here we show that the dipolar interaction is also an efficient mechanism to synchronize neighbouring oscillators. We experimentally study a pair of vortex-based spin transfer nano-oscillators, in which mutual synchronization can be achieved despite a significant frequency mismatch between oscillators. Importantly, the coupling efficiency is controlled by the magnetic configuration of the vortices, as confirmed by an analytical model and micromagnetic simulations highlighting the physics at play in the synchronization process.