About the SpinENGINE project

The SpinENGINE project will lay the foundations for a new, massively parallel, platform based on emergent behaviour in nanomagnet ensembles. The project will an efficient, highly scalable, and easily reproducible platform meeting the data challenges in our increasingly data-rich society. We will build upon our recent discoveries and use complex, nonlinear, and highly tunable interactions in such ensembles to realize a hardware platform for “Reservoir Computing”, a biologically-inspired computational approach. Our critical hypothesis is that the synergies between the inherent properties of nanomagnet ensembles and those required for reservoir computing will enable the efficient creation of a highly adaptive computational platform for the analysis of complex, dynamic data sets. This has the potential to greatly outperform current approaches using conventional CMOS hardware.

SpinENGINE will bring together a multidisciplinary team of researchers with expertise in computer science, condensed matter physics, material science, computational modelling, and high-resolution microscopy. This will enable us to simultaneously explore the fundamental behaviours of nanomagnet ensembles and understand how these can be harnessed for useful computation. By the end of the project, we aim to fabricate a proof-of-concept device capable of solving pattern recognition and classification problems, and, in collaboration with our industrial partner, IBM, produce a roadmap to the further scaling and commercialization of our computational platform. Success in the SpinENGINE project will have vast implications for data analysis at all scales, ranging from low power computation in the simplest sensor node to accelerated data processing in the most complex supercomputer.

Micromagnetically-calculated domain wall arrangements at ring junctions with 100-nm-wide wires and (a) 10 % and (b) 100 % wire overlap. Colour represents magnetisation direction.


  1. flatspin: A Large-Scale Artificial Spin Ice Simulator
    Johannes H. Jensen, Anders Strømberg, Odd Rune Lykkebø, Arthur Penty, Jonathan Leliaert, Magnus Själander, Erik Folven, and Gunnar Tufte
    Phys. Rev. B 106, 064408, August 2022

    Abstract: We present flatspin, a novel simulator for systems of interacting mesoscopic spins on a lattice, also known as artificial spin ice (ASI). A generalization of the Stoner-Wohlfarth model is introduced, and combined with a well-defined switching protocol to capture realistic ASI dynamics using a point-dipole approximation. Temperature is modelled as an effective thermal field, based on the Arrhenius-Néel equation. Through GPU acceleration, flatspin can simulate the dynamics of millions of magnets within practical time frames, enabling exploration of large-scale emergent phenomena at unprecedented speeds. We demonstrate flatspin's versatility through the reproduction of a diverse set of established experimental results from literature. In particular, the field-driven magnetization reversal of “pinwheel” ASI is reproduced, for the first time, in a dipole model. Finally, we use flatspin to explore aspects of “square” ASI by introducing dilution defects and measuring the effect on the vertex population.

  2. Quantifying the Computational Capability of a Nanomagnetic Reservoir Computing Platform with Emergent Magnetisation Dynamics
    Ian Vidamour, Matthew O.A. Ellis, David Griffin, Guru Venkat, Charles Swindells, Richard W. S. Dawidek, Thomas J Broomhall, Nina-Juliane Steinke, Joshaniel Cooper, Francesco Maccherozzi, Sarnjeet Dhesi, Susan Stepney, Eleni Vasilaki, Dan A Allwood and Tom James Hayward
    Nanotechnology, August 2022

    Abstract: Devices based on arrays of interconnected magnetic nano-rings with emergent magnetization dynamics have recently been proposed for use in reservoir computing applications, but for them to be computationally useful it must be possible to optimise their dynamical responses. Here, we use a phenomenological model to demonstrate that such reservoirs can be optimised for classification tasks by tuning hyperparameters that control the scaling and input-rate of data into the system using rotating magnetic fields. We use task-independent metrics to assess the rings' computational capabilities at each set of these hyperparameters and show how these metrics correlate directly to performance in spoken and written digit recognition tasks. We then show that these metrics, and performance in tasks, can be further improved by expanding the reservoir's output to include multiple, concurrent measures of the ring arrays' magnetic states.

  3. A Representation of Artificial Spin Ice for Evolutionary Search
    Arthur Penty and Gunnar Tufte
    Proceedings of the International Conference on Unconventional Computation and Natural Computation, October 2021

    Abstract: Ensembles of interacting nanomagnets known as Artificial Spin Ice (ASI) have become a promising new substrate for computation. Properties such as emergence and non-linear local interactions make it of particular interest for unconventional and material computation. Previously, we have proposed a method to represent and grow new ASI geometries, suited for use in an Evolutionary Algorithm (EA). Here we use our representation and evolution to further investigate towards computational properties including memory and classification. The richness of geometries found with sought computational properties indicates that ASI geometry is a fruitful tuning parameter for computational ASI systems.

  4. Effects of array shape and disk ellipticity in dipolar-coupled magnetic metamaterials
    Sam D. Slöetjes, Einar S. Digernes, Anders Strømberg, Fredrik K. Olsen, Ambjørn D. Bang, Alpha T. N’Diaye, Rajesh V. Chopdekar, Erik Folven, and Jostein K. Grepstad
    Physics Review B Vol.104, No. 134421, October 2021

    Abstract: Two-dimensional lattices of dipolar-coupled thin film ferromagnetic nanodisks give rise to emergent superferromagnetic (SFM) order when the spacing between dots becomes sufficiently small. In this paper, we define micron-sized arrays of permalloy nanodisks arranged on a hexagonal lattice. The arrays were shaped as hexagons, squares, and rectangles to investigate finite-size effects in the SFM domain structure for such arrays. The resulting domain patterns were examined using x-ray magnetic circular dichroism photoemission electron microscopy. At room temperature, we find these SFM metamaterials to be below their blocking temperature. Distinct differences were found in the magnetic switching characteristics of horizontally and vertically oriented rectangular arrays. The results are corroborated by micromagnetic simulations.

  5. A Representation of Artificial Spin Ice for Evolutionary Search
    Arthur Penty and Gunnar Tufte
    Proceedings of the Artificial Life Conference, July 2021

    Abstract: Arrangements of nanomagnets known as artificial spin ices show great potential for use in unconventional computation. The majority of exploratory work done in this area considers just a small handful of well studied geometries (nanomagnetic arrangements), and uses them as if they were a black box. Here we detail a novel representation of artificial spin ice geometries, which lends itself to the tuning and evolutionary search of geometries. Using our representation we present geometries tuned to exhibit a desired computational or meta-material property. This is the first example of such a search performed on artificial spin ice.

  6. Synchronization of Chiral Vortex Nano-Oscillators
    Zhiyang Zeng, Zhaochu Luo, Laura J. Heyderman, Joo-Von Kim, and Aleš Hrabec
    Applied Physics Letters Vol. 118, No. 222405, June 2021

    Abstract: The development of spintronic oscillators is driven by their potential applications in radio frequency telecommunication and neuromorphic computing. In this work, we propose a spintronic oscillator based on the chiral coupling in thin magnetic films with patterned anisotropy. With an in-plane magnetized disk imprinted on an out-of-plane magnetized slab, the oscillator takes a polar vortex-like magnetic structure in the disk stabilized by a strong Dzyaloshinskii–Moriya interaction. By means of micromagnetic simulations, we investigate its dynamic properties under applied spin current, and by placing an ensemble of oscillators in the near vicinity, we demonstrate their synchronization with different resonant frequencies. Finally, we show their potential application in neuromorphic computing using a network with six oscillators.

  7. Anisotropy and Domain Formation in a Dipolar Magnetic Metamaterial
    Einar Digernes, Anders Strømberg, Carlos A. F. Vaz, Armin Kleibert, Jostein K. Grepstad and Erik Folven
    Applied Physics. Letters Vol. 118, No. 202404, May 2021

    Abstract: Long-range magnetic ordering can be stabilized in arrays of single-domain nanomagnets through dipolar interactions. In these metamaterials, the magnetic properties are determined by geometric parameters such as the nanomagnet shape and lattice symmetry. Here, we demonstrate engineering of the anisotropy in a dipolar magnetic metamaterial by tuning of the lattice parameters. Furthermore, we show how a modified Kittel's law explains the resulting domain configurations of the dipolar ferromagnetic arrays.

  8. Voltage-controlled superparamagnetic ensembles for low-power reservoir computing
    A. Welbourne, A. L. R. Levy, M. O. A. Ellis, H. Chen, M. J. Thompson, E. Vasilaki, D. A. Allwood, T. J. Hayward
    Applied Physics Letters Vol. 118, No. 202402, May 2021

    Abstract: 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.

  9. Dynamically Driven Emergence in a Nanomagnetic System
    Richard W. Dawidek, Thomas J. Hayward, Ian T. Vidamour, Thomas J. Broomhall, Guru Venkat, Mohanad Al Mamoori, Aidan Mullen, Stephan J. Kyle, Paul W. Fry, Nina-Juliane Steinke, Joshaniel F. K. Cooper, Francesco Maccherozzi, Sarnjeet S. Dhesi, Lucia Aballe, Michael Foerster, Jordi Prat, Eleni Vasilaki, Matthew O. A. Ellis, and Dan A. Allwood
    Advanced Functional Materials Vol. 31, No. 15, February 2021

    Abstract: 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.



flatspin is a GPU-accelerated simulator for systems of interacting nanomagnet spins arranged on a 2D lattice, also known as Artificial Spin Ice (ASI). flatspin can simulate the dynamics of large ASI systems with thousands of interacting elements. flatspin is written in Python and uses OpenCL for GPU acceleration. flatspin comes with extra bells and whistles for analysis and visualization. flatspin is open-source software and released under a GNU GPL license.


Norwegian University of Science and Technology

Erik Folven

Gunnar Tufte

Magnus Själander

The University of Sheffield

Dan Allwood

Tom Hayward


Laura Heyderman

Ghent University

Bartel Van Waeyenberge


Rolf Allenspach