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Tutorial: Artificial Spin Ice and Elements of Control for Computation

Time: Wednesday, October 10th, 14:00
Speaker: Laura HEYDERMAN, ETH Zurich

Artificial spin systems [1] have received much attention in recent years, following the creation of arrays of dipolar-coupled nanomagnets with frustrated geometries analogous to that of the rare earth titanate pyrochlores [2], which are referred to as spin ices due to a geometric frustration that leads to a spin arrangement analogous to the proton ordering in water ice [3]. Such arrays of nanomagnets are appropriately named artificial spin ice [4] where single-domain elongated magnets, which have Ising-like moments pointing along one of two directions, are commonly placed on the sites of a square or kagome lattice. At every vertex where the magnets meet, there is a characteristic low energy configuration where the so-called ice rule is obeyed. Going beyond these basic designs, it is possible to devise artificial spin systems with various intricate motifs that display behaviour that is characteristic of a particular geometry.
In this tutorial, I will introduce this topic with the aim to provide the link between artificial spin ice and computation by covering a number of possibilities for control. For example, the creation and separation of emergent magnetic monopoles and their associated Dirac strings on application of a magnetic field can be controlled by modifying the shape of particular nanomagnets in the array [5]. Such modifications to individual nanomagnets can also be used to control the chirality of artificial kagome spin ice building blocks consisting of a small number of hexagonal rings of magnets [6]. Indeed, chirality control is a recurring theme, with a further example being the control of the dynamic chirality, which can be achieved in the so-called chiral ice [7], where the stray field energy associated with the magnetic configurations at the edges of the array defines the sense of rotation of the average magnetisation on thermal relaxation. In addition, the chirality of domain walls will determine how they pass through a connected artificial kagome spin ice [8].
I will address other possibilities to control and access magnetic information in artificial spin ice including further geometries, temperature, local magnetic and electric fields, fast dynamics, as well as methods for computation [9].

[1] L.J. Heyderman and R.L. Stamps, J. Phys.: Condens. Matter 25, 363201 (2013)
[2] R.F. Wang et al. Nature 439, 303 (2006)
[3] M.J. Harris et al. Phys. Rev. Letts. 79, 2554 (1997)
[4] C. Nisoli, R. Moessner and P. Schiffer, Rev. Mod. Phys. 85, 1473 (2013)
[5] E. Mengotti et al. Nat. Phys. 7, 68 (2011); R.V. Hügli et al. Phil. Trans. Roy. Soc. A 370, 5767 (2012)
[6] R.V. Chopdekar et al. New Journal of Physics 15, 125033 (2013)
[7] S. Gliga et al. Nat. Mater. 16, 1106 (2017)
[8] K. Zeissler et al. Sci. Rep. 3, 1252 (2013); A. Pushp et al. Nat. Phys. 9, 505 (2013)
[9] H. Arava et al. Nanotechnology 29, 265205 (2018); P. Gypens et al. Phys. Rev. Appl. 9, 034004 (2018)

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Associative memory operation using analog spin-orbit torque device

Time: Wednesday, October 10th, 11:10
Speaker: Shunsuke FUKAMI, Tohoku University

Neuromorphic computing has attracted great attention because of its capability to execute complex tasks that the conventional von Neumann computers cannot readily complete. Here, we present an analog spintronic device based artificial neural network. Spintronic devices, in general, offer non-volatility and virtually infinite endurance, showing promise for realization of low-power “edge” neuromorphic computing hardware with online learning capability. An antiferromagnet-ferromagnet heterostructure operated by spin-orbit torque employed here allows us to control the magnetization state in an analog manner and thus can be used as an artificial synapse [1]. Using the developed artificial neural network with the analog spintronic device, we show a proof-of-concept demonstration of an associative memory operation based on the Hopfield model, a representative model of neuromorphic computing [2].
This work is partly supported by R&D Project for ICT Key Technology of MEXT, JSPS KAKENHI No. 17H06093, JST-OPERA, and ImPACT Program of CSTI.
[1] S. Fukami et al., Nature Materials, vol. 15, 535 (2016).
[2] W. A. Borders et al., Appl. Phys. Express, vol. 10, 013007 (2017).

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Bioinspired Computing Leveraging the Non-Linearity of Magnetic Nano-Oscillators

Time: Wednesday, October 10th, 10:10
Speaker: Damien QUERLIOZ, Integnano – C2N

The brain displays many features typical of non-linear dynamical networks, such as synchronization or chaotic behavior. These observations have inspired a whole class of models that harness the power of complex non-linear dynamical networks for computing. In this framework, neurons are modeled as non-linear oscillators, and synapses as the coupling between oscillators. These abstract models are very good at processing waveforms for pattern recognition or at generating precise time sequences useful for robotic motion. However there are very few hardware implementations of these systems, because large numbers of interacting non-linear oscillators are indeed. In this talk, I will explain why coupled magnetic nano-oscillators are very promising for realizing cognitive computing at the nanometer and nanosecond scale. Then, I will present our experimental and theoretical results. In particular, I will show how we can perform speech recognition using the transient dynamics and the synchronization of a few oscillators. I will also show how this line of research can take inspiration from both neuroscience and the field of machine learning. I will finish by the open questions raised by our research.

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Critical brain dynamics, a brief overview

Time: Wednesday, October 10th, 09:00
For two decades we proposed that the most fascinating brain properties are related to the fact that it always stays close to a second order phase transition. In such conditions, the collective of neuronal groups can reliably generate robust and flexible behavior, because at the critical point is the largest number of metastable states to choose from. Here we review the motivation, arguments and recent results, as well as some implications for neuromorphics.

MemComputing: leveraging physics to compute efficiently

Time: Tuesday, October 9th, 15:00
Speaker: Massimiliano DI VENTRA, UCSD
It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum computer. There are, however, other types of (non-quantum) physical properties that one may leverage to compute efficiently a wide range of hard problems. In this talk I will discuss how to employ one such property, memory (time non-locality), in a novel physics-based approach to computation: Memcomputing [1, 2, 3, 4]. As examples, I will show the polynomial-time solution of prime factorization, the search version of the subset-sum problem [5], and approximations to the Max-SAT beyond the inapproximability gap [6] using polynomial resources and self-organizing logic gates, namely gates that self-organize to satisfy their logical proposition [5]. I will also show that these machines are described by a Witten-type topological field theory, and they compute via an instantonic phase, implying that they are robust against noise and disorder [7]. The digital memcomputing machines we propose can be efficiently simulated, are scalable and can be easily realized with available nanotechnology components. Work supported in part by MemComputing, Inc. (
[1] F. L. Traversa and M. Di Ventra, Universal Memcomputing Machines, IEEE Transactions on Neural Networks and Learning Systems 26, 2702 (2015).
[2] M. Di Ventra and Y.V. Pershin, Computing: the Parallel Approach, Nature Physics 9, 200 (2013).
[3] M. Di Ventra and Y.V. Pershin, Just add memory, Scientific American 312, 56 (2015).
[4] M. Di Ventra and F.L. Traversa, Memcomputing: leveraging memory and physics to compute efficiently, J. Appl. Phys. 123, 180901 (2018).
[5] F. L. Traversa and M. Di Ventra, Polynomial-time solution of prime factorization and NP-complete problems with digital memcomputing machines, Chaos: An Interdisciplinary Journal of Nonlinear Science 27, 023107 (2017).
[6] F. L. Traversa, P. Cicotti, F. Sheldon, and M. Di Ventra, Evidence of an exponential speed-up in the solution of hard optimization problems, Complexity 2018, 7982851 (2018).
[7] M. Di Ventra, F. L. Traversa and I.V. Ovchinnikov, Topological field theory and computing with instantons, Annalen der Physik 529,1700123 (2017).

Skyrmions based Neurmorphic Computing

Time: Tuesday, October 9th, 14:00
Speaker: Weisheng ZHAO, Beihang University

Recently, magnetic skyrmion, a swirling topological spin configuration, has been studied as a promising information carrier candidate in future ultra-dense, low-power memory and logic devices for its outstanding merits of nanoscale size, low depinning current density, high motion velocity and particle-like stability etc. One of the most potential applications is to design racetrack memory. One the other hand, we exploit the dynamics of skyrmions to design neuromorphic computing.

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Computing with Spin-Wave Solitons

Time: Tuesday, October 9th, 11:00
Speaker: Ferran MACIA, Universita de Barcelona
Collective magnetic excitations, such as spin waves are attracting a growing interest for their potential applications as memory and communication devices working at high frequency and low power. In particular the use of nanometer scale oscillators could lead to new types information processing, including neuromorphic computing. In this talk we will review some applications of spin-wave patterns created from Spin Torque Oscillators (STO) and their interactions with background oscillations [1-4]. Next, we will focus on solitonic modes that can be created in STO. First I will show that arrays of vortices can be described through the Kuramoto model, having patterns of synchronization resembling the patterns occurring in the brain [5]. Second, I will discuss some advances in the study of magnetic Droplet Solitons and Dynamical Skyrmions, which are magnetic excitations consisting of reversed oscillating spins that are strongly localized and can be controlled through the applied field and the spin current [6-9]. Droplet solitons are multistate oscillators with a hysteretic behavior making them good candidates as building blocks in neuromorphic computing

[1] F. Macià et al. Nanotechnology 22, 095301 (2011)
[2] F. Macià et al. Nanotechnology 25, 045303 (2014)
[3] F.C. Hoppensteadt, US Patent 9,582,695 (2018)
[4] F Hoppensteadt, Biosystems 136, 99-104 (2017)
[5] V. Flovick et al Scientific Reports, 6, 32528 (2016)
[6] S. M. Mohseni et al., Science 339, 1295 (2013)
[7] F. Macià et al. Nature Nanotech. (2014)
[8] J.Hang et al. Scientific Reports 8, 6847, (2018)
[9] N. Statuto et al. Nanotechnology, 29, 325302 (2018)

Mutually synchronized spin Hall nano-oscillator arrays

Time: Tuesday, October 9th, 10:10
Speaker: Johan AKERMAN, Gothenburg University

Spin Hall nano-oscillators (SHNOs) [1] are an emerging class of nano-scopic microwave signal generators with potential for new disruptive applications ranging from microwave signal generation/detection to neuromorphic computing [2,3]. SHNOs are based on an intrinsic magnetodynamic resonance with frequencies in the GHz range, which depends on material parameters, device layout, and external parameters such as magnetic field and drive current. For sufficiently high current densities, the resonance can be driven into a state of coherent auto-oscillation. Through the magnetoresistance of the device, the auto-oscillation can be used to generate a current- and field-tunable microwave voltage.
The auto-oscillation state is highly non-linear in nature, and neighbouring SHNOs can therefore interact with each other and even mutually synchronize, which further increases the power and coherence of the microwave signal [4]. This is important, as the nano-scale volume of the auto-oscillating spin wave mode is susceptible to thermal noise, leading to detrimental phase noise in the microwave signal. I will present resent results on long chains of SHNOs and the first two-dimensional SHNO arrays. We demonstrate robust mutual synchronization in chains or 21 SHNOs with record quality factors of Q=f/df of 30,000. We also demonstrate robust mutual synchronization in two-dimensional arrays of as many as 8 x 8 = 64 SHNOs. We find that the linewidth of these arrays decreases linearly with the number of SHNOs, which enables us to reach Q factors as high as 170,000, i.e. an order of magnitude higher than literature values. Based on these results I will argue that a viable path towards commercial microwave signal generators based on spintronic devices must be based on mutually synchronized SHNO arrays.
The mutual synchronization phenomenon can also be used for ultra-fast pattern matching with potential for speeding up image recognition by orders of magnitude. With the recent rapidly increasing interest in artificial intelligence and neuromorphic computing, mutually synchronized SHNO chains and arrays hence represent a highly attractive emerging technology platform for low-power, and ultrafast non-conventional computing.
[1] T. Chen, et al, Proc. IEEE 104, 1919 (2016).
[2] J. Grollier, D. Querlioz, and M. Stiles, Proc. IEEE 104, 2024 (2016).
[3] J. Torrejon et al., Nature 547, 428 (2017)
[4] A. A. Awad et al. Nature Physics 13, 292 (2017).
[5] M. Zahedinejad et al. unpublished (2018).

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Tutorial: Manipulating Magnetic Skyrmions

Time: Tuesday, October 9th, 09:00
Speaker: Axel HOFFMANN, Argonne National Laboratory
Magnetic skyrmions are topologically distinct spin textures that are stabilized by the interplay between applied magnetic fields, magnetic anisotropies, as well as symmetric and antisymmetric exchange interactions. Due to their topology magnetic skyrmions can be stable with quasi-particle like behavior, where they can be manipulated with very low electric currents. This makes them interesting for low-power information technologies, where it is envisioned that data will be encoded in topological charges, instead of electronic charges as in conventional semiconducting devices. In particular, recently there has been a lot of progress stabilizing magnetic skyrmions at room temperature in magnetic heterostructures [1]. This talk will review specific aspects that relate to the manipulation of individual magnetic skyrmions, such as their electrical generation [2,3], motion [4], and dynamical excitations.
This work was supported by the U.S. Department of Energy, Office of Science, Materials Sciences and Engineering Division.

[1] W. Jiang, et al., Phys. Rep. 704, 1 (2017).
[2] W. Jiang, et al., Science 349, 283 (2015).
[3] O. Heinonen, et al., Phys. Rev. B 93, 094407 (2016).
[4] W. Jiang, et al., Nature Phys. 13, 162 (2017).

Tutorial: Computing with magnetic dots and spintronic dynamical systems

Time: Monday, October 8th, 15:00
Speaker: Wolfgang POROD, University of Notre Dame
In this talk, we will discuss alternative approaches to computing. Instead of basing a computer on the manipulation of bits, represented by electronic switches, we will explore the possibility of harnessing spintronic dynamical systems for computation. Specifically, we will consider physical processes and dynamical systems based on coupled magnetic dots, on coupled spin-torque oscillators, and on spin waves. In such dynamical systems, the computational process more closely exploits the underlying physics, which offers the promise of lower power dissipation.