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Sparked by the limitations of the Von-Neumann architecture, the burgeoning field of neuromorphic computation aims to develop systems that process information both ‘in-memory’ and in a brain-like manner. Neural networks comprise three types of layers – an input layer, hidden layers and an output layer each connected by numeric weights. Training such networks requires continuous updating of each weight requiring both time and energy. Reservoir computing (RC)&lt;sup&gt;1&lt;/sup&gt; is a subset of neuromorphic computation where training occurs only on the output layer, reducing time and energy cost significantly compared to traditional neural networks, while competing with traditional approaches for time-series classification / prediction task accuracy.&lt;br/&gt;Artificial spin networks comprising patterned nanomagnets serve as promising computational substrates for such applications, information can be stored in a single nanomagnet spin (i.e. a nanomagnetic ‘bit’) or the magnetic configuration (microstate) of the entire network. Strong dipolar coupling enables a highly non-linear history-dependent collective response to external stimuli, a key property for RC&lt;sup&gt;1&lt;/sup&gt;. Artificial spin ice (ASI) is one such network where geometric frustration gives rise to a rich microstate space and emergent collective behaviour&lt;sup&gt;2&lt;/sup&gt; highly promising for RC&lt;sup&gt;3,4&lt;/sup&gt;. However, in these systems individual nanomagnets are constrained to Ising-like states, severely limiting microstate richness. We have previously shown in simulation that combining Ising-like and vortex states allows powerful reconfigurable functionality&lt;sup&gt;5&lt;/sup&gt;.&lt;br/&gt;Modifying a subset of bars&lt;sup&gt;6,7&lt;/sup&gt; in an ASI such that the Ising and vortex states are bistable gives rise to highly non-linear responses to global- and RF-fields allowing multiple reservoir readouts, detectable by the recently developed ‘spectral fingerprinting’ technique&lt;sup&gt;8&lt;/sup&gt;. Here, we explore ASVI-based RC for forecasting and classifying time-series with varying complexity and assess the strengths and limitations of such systems compared against traditional ASI and competing neuromorphic hardware platforms.

2022 Joint MMM-INTERMAG

Reservoir computing in an artificial spin-vortex ice

The International Conference on Electron, Ion and Photon Beam Technology and Nanofabrication (EIPBN), affectionately known as "3-Beams," is the premier gathering of scientists and engineers who are dedicated to electron, ion and photon lithography, imaging, and analysis; atomically precise fabrication; nanofabrication process technologies and related emerging technologies; and their applications in a broad spectrum of fields. In its 64th meeting, researchers from academia, government laboratories, and industry from around the world meet to present and discuss recent and future trends in these technologies.
 
 
 
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EIPBN 2021

Sparked by the limitations of the Von-Neumann architecture, the burgeoning field of neuromorphic computation aims to develop systems that process information both ‘in-memory’ and in a brain-like manner. Neural networks comprise three types of layers – an input layer, hidden layers and an output layer each connected by numeric weights. Training such networks requires continuous updating of each weight requiring both time and energy. Reservoir computing (RC)1 is a subset of neuromorphic computation where training occurs only on the output layer, reducing time and energy cost significantly compared to traditional neural networks, while competing with traditional approaches for time-series classification / prediction task accuracy. Artificial spin networks comprising patterned nanomagnets serve as promising computational substrates for such applications, information can be stored in a single nanomagnet spin (i.e. a nanomagnetic ‘bit’) or the magnetic configuration (microstate) of the entire network. Strong dipolar coupling enables a highly non-linear history-dependent collective response to external stimuli, a key property for RC1. Artificial spin ice (ASI) is one such network where geometric frustration gives rise to a rich microstate space and emergent collective behaviour2 highly promising for RC3,4. However, in these systems individual nanomagnets are constrained to Ising-like states, severely limiting microstate richness. We have previously shown in simulation that combining Ising-like and vortex states allows powerful reconfigurable functionality5. Modifying a subset of bars6,7 in an ASI such that the Ising and vortex states are bistable gives rise to highly non-linear responses to global- and RF-fields allowing multiple reservoir readouts, detectable by the recently developed ‘spectral fingerprinting’ technique8. Here, we explore ASVI-based RC for forecasting and classifying time-series with varying complexity and assess the strengths and limitations of such systems compared against traditional ASI and competing neuromorphic hardware platforms.

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

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This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Strontium ferrite/polyamide12 (PA12) magnetic composite fused deposition modeling filaments made using a twin-screw extruder are being studied to be used for Magnetic Field Assisted Additive Manufacturing (MFAAM) of permanent magnets. A previous study shows that the magnetic viscosity (MV) varies with field and field angle. The Mx MV is maximum in the easy plane (1.1%) and decreases with a factor of two along the filament’s macroscopic hard axis [1]. The My MV is nearly zero along the hard axis and in the easy plane but maximum for intermediate angles. Here we study the time dependence as a function of temperature using a MicroSense EZ9 biaxial VSM to determine the melt viscosity. Samples were made by loading ~14 mg of SrO(Fe2O3)6/PA12 (26 or 40 wt%) cylindrical-shaped filament parts in pyrex glass tubes. The filament is compacted with PEEK stoppers on both sides to secure its position and avoid direct exposure to the atmosphere while heating. Our aim is to study the rotation of the magnetic particles in the molten PA12 matrix. We first heat the sample to 200 oC to orient all the particles in the y-direction using a field of 22 kOe. Then the sample temperature is lowered to the target temperature after which the field is lowered to zero. Finally, a field step is applied in the x-direction and Mx and My are monitored as a function of the time. The rotation of the moment vector with time is calculated from the data. Measurements are done for the fields of 500 and 2000 Oe, and at the temperatures of 120, 124, 128, 132, and 136°C. Up to 128°C, no strong time dependence was observed. Between 128 and 132°C, the magnetic particles orientations are no longer fixed in the matrix, but they can rotate and line up along the field direction. The time dependence of the rotation of the magnetic particles in the PA12 matrix is calculated from Mx and My (Fig. 1 and Fig. 2). The time constant decreases with temperature and field. The melt viscosity of the molten PA12 matrix at 136 oC is determined from the data is 1.4E5 Pa.s at 500 Oe field.

![](https://assets.underline.io/uploads/markdown_image/1/image/252cfa512dda08ad988cba344352f796.jpg)


![](https://assets.underline.io/uploads/markdown_image/1/image/2e86b69ac993ac1e74be8a59fc537023.jpg)

Time Dependence Analysis as a Function of the Temperature of Magnetic Polymer Composite Filaments

Soft materials embedded with hard magnetic particles have recently gained widespread recognition as small-scale actuators due to their capacity to be a rapid and precise shape-shifting material[1, 2]. Strontium ferrite (SrFe12O19) particles have been shown to be a great candidate for such applications, since it is an inert hard magnetic material [3]. The study of magnetic properties of hard-magnetic soft materials is a critical step to better design these upcoming actuators. The preparation of such material is done by mixing the particles into the uncured elastomer (PDMS), in liquid form, and then pouring the mixture in a mold for curing. If the samples are subjected to a magnetic field during the curing process, chains of particles are formed in the direction of the applied field (see Fig 1). We expect that the individual particles rotate in the fluid such that their easy axes becomes parallel to the curing field, thus creating an easy axis in the composite in this same direction. The magnetic properties of such types of composites, or for any other soft matrix, cannot yet be found in literature. In this study, we analyzed three concentrations of strontium ferrite particles in PDMS under three field configurations, resulting in 9 different samples. The concentrations used were 1:1, 2:1 and 4:1 ratios of PDMS to strontium ferrite per weight. All three samples of each concentration were cured either in a zero magnetic field, or over the north pole of a permanent magnet, or over the side of said magnet (see Fig 2). A biaxial vibrating sample magnetometer (VSM) was used to measure torque curves and the hysteresis curves parallel and perpendicular to the curing field. The samples cured in a field show a squareness ratio of up to 0.94 while the samples cured in zero field, only close to 0.5. The samples cured in a field show a magnetic anisotropy with an easy axis parallel to the curing field. Anisotropy values are compared to the crystal anisotropy of strontium ferrite to determine the shape anisotropy contribution due to the observed chaining.

![](https://assets.underline.io/uploads/markdown_image/1/image/862eb027f9f4f8e973ec3a62a4ee66d8.jpg)

Fig. 1 PDMS/strontium ferrite composite showing alignment of particles when cured under magnetic field.

![](https://assets.underline.io/uploads/markdown_image/1/image/cd5f70171405db2e6e00e095c1d763be.jpg)

Fig. 2 Curing process of samples

Magnetic Properties of PDMS Embedded with Strotium Ferrite Particles Cured Under Different Magnetic Field Conditions

Networks of interconnected magnetic nanowires offer an exciting platform to explore 3-dimensional (3D) nanomagnetism, where their structure, topology and frustration may be used as additional degrees of freedom to tailor the materials properties. We have achieved quasi-ordered metallic networks over cm-scale areas. Using a cost-effective multiple azimuthal angle ion-tracking and etching method with suitable fluence, interconnected nanoporous polycarbonate membranes were first fabricated. A subsequent electrochemical deposition process led to interconnected metallic nanowire networks, with density as low as 40 mg/cm3 (Fig. 1) [1]. New magnetization reversal mechanisms in cobalt networks (Fig. 1d) are captured by the first-order reversal curve (FORC) method, which demonstrate the evolution from strong demagnetizing dipolar interactions to intersections-mediated domain wall pinning and propagation, and eventually to shape-anisotropy dominated magnetization reversal (Fig. 2). By varying the applied magnetic field strength, orientation, and sequence, it is in principle possible to selectively address a certain subset of the nanowire networks, encode digital information into their magnetic state, and propagate it through the networks for potential 3D magnetic memory and logic applications. Such network of magnetic nanowires also has the potential to implement repeatable multi-state memristors in neuromorphic circuits, due to the expected discrete nature of domain wall motion through the intersecting networks. Interestingly, another random configuration of metallic nanowire networks has found applications in deep-submicron particulate filtration, relevant to combatting COVID-19 and air pollution, due to the extremely large surface areas and the excellent mechanical strength [2]. This work has been supported by the NSF (ECCS-1611424 and ECCS-1933527), SRC/NIST nCORE SMART center, DTRA, U.C. Davis and Georgetown University.

![](https://assets.underline.io/uploads/markdown_image/1/image/235e34862100e61fc1216607d02eed81.jpg)

Figure 1: (a) Side-view and (b) top-view SEM images of an interconnected copper network, tracked at five angles as illustrated by the schematics. Inset in (a) shows that at an intersection the wires are physically connected. Top-view SEM images of (c) a copper network and (d) a cobalt network, tracked at three angles. This produces intersections in planes that contain the three irradiated angles (which are highlighted with white dashed lines).

![](https://assets.underline.io/uploads/markdown_image/1/image/46695a346d2d61a65f1ffb4d1ef4c0ad.jpg)

Figure 2. FORC diagrams shown in 2D contour plots for (a-c) a single-angle irradiated sample, and (d-i) three-angle irradiated sample. The schematic diagrams in the lower right corner of panels (a-i) indicate the orientation of the wires (black lines) and membrane (blue box) relative to the applied field shown by the large black arrow.

3D Nanomagnetism in Interconnected Magnetic Nanowire Networks

The fabrication of micrometric magnetic materials and their integration into portable devices reveal great interests for telecommunications, automotive, biomedical and space applications, but still remain highly challenging. The bottom-up approach for nanostructured magnets is an interesting alternative route to the classical rare earth metallurgy or thin film deposition. Indeed, the recent progresses in the magnetic nanoparticle synthesis allow a good control of the particle size, shape and chemical composition. Single-crystalline Co nanorods (NRs), which combine a high magnetization and a large magnetic anisotropy, can be prepared by the polyol process [1]. These anisotropic particles constitute building blocks of primary choice for permanent magnet applications. [2] We reported recently a versatile approach for the fabrication and direct integration of nanostructured magnetic materials of controlled shaped at specific locations onto silicon substrates [3]. The magnetophoresis-assisted capillary assembly of magnetic nanoparticles leads to the fabrication of high-performance Co-based permanent magnets (Figure 1). Integrated submillimeter magnets as well as millimetric self-standing magnets exhibiting magnetic properties competing with NdFeB-based composited were obtained through this cost- and time-efficient process. The proof-of-concept of electromagnetic actuation of a MEMS cantilever by means of these supercrystals highlights their potentiality as efficient integrated magnetic materials within nomadic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/ea95a49ae8b5e560ab72881a728b9d7b.jpg)

Nanostructured magnets prepared by magnetophoresis-assisted capillary assembly of Co nanorods

Nanostructured magnets prepared by magnetophoresis-assisted capillary assembly of Co nanorods

We study the effect of thermal fluctuations on dipole coupled mesospins, the building blocks of artificial spin ice (ASI), in a micromagnetic framework. Taking into account the internal magnetic texture, we focus specifically on the fluctuations at the edges, which have previously shown to exhibit a temperature dependent switching between two states that are essentially half of a C- or S-state [1]. We study two different systems, the first being a system of two coupled magnets and the second being a fourfold coordinated ASI vertex. For the two mesospin system with parallel magnetization, we find magnonic mode splitting at the edges, which is relatively unaffected by temperature. When the magnetization in the two mesospins is opposite, we find the appearance of an asymmetric potential, which can be quantified through the magnetic texture correlations. The Arrhenius law is used to find the attempt frequency and the energy barriers associated with switching, the latter are found to be inversely proportional to the spacing. We find a logarithmic dependence of the attempt frequency on the energy barrier, which is indicative of entropy-energy compensation at small spacings (large barriers). The temperature dependent edge dynamics for the ASI vertex is evaluated for the four different types (Type I-IV), each displaying their own characteristic dynamics. An example of such dynamics is the collective switching of the handedness associated with the perpendicular edge magnetization in a type IV vertex configuration. These results indicate the presence of rich texture dynamics, even at the level of the individual building blocks of the ASI.

Magnetic Texture Fluctuations in Coupled Mesospin Systems

Artificial spin-ice systems (ASI) have been studied for 15 years, allowing detailed studies to examine the frustration, ordering and monopole transport in a variety of two-dimensional geometries [1]. The nanostructuring of magnetic materials in three-dimensions presents a new paradigm in condensed matter physics and allows access to a wide range of new physical phenomena [2]. With respect to ASI systems, there are several reasons why 3D geometries are interesting. This includes the realisation of a degenerate ice-rule, mimicking of bulk spin-ice geometries and studying the influence of surfaces upon ordering. In this talk, I will outline the realisation of a 3D artificial spin-ice system [3] which takes the geometry of a diamond-bond lattice (Fig. 1), capturing the arrangement of spins in bulk pyrochlore systems. By using magnetic force microscopy (Fig. 2), I will show that the vertex states upon the surface can be determined, and the global switching of the lattice can be measured. We find very different magnetic charge dynamics along two principal directions upon the lattice. For a field applied along the surface termination, local energetics force magnetic charges to nucleate over a larger characteristic distance, reducing their magnetic Coulomb interaction and producing lone, uncorrelated monopoles. In contrast, applying a field transverse to the surface termination yields large numbers of highly correlated monopole-antimonopole pairs. A combination of micromagnetic and Monte-Carlo simulations are used to understand the results. These suggest it is the difference in effective chemical potential that yields the striking differences in monopole transport. We anticipate that our study will inspire a new generation in artificial spin-ice research whereby the ground states in complex 3D frustrated lattices are explored.

![](https://assets.underline.io/uploads/markdown_image/1/image/68e61fe5f53c1aa5f59122b57dafa546.jpg)

Fig 1. Atomic force microscopy image of the 3DASI system. Distinct layers within the system are labelled L1 - L3.

![](https://assets.underline.io/uploads/markdown_image/1/image/6da2b1e596bc9e183b4530846549ee08.jpg)

Fig 2. Magnetic force microscopy of the 3DASI surface, showing a number of ice-rule and monopole states.

Magnetic charge propagation upon a 3D artificial spin-ice

The synthesis of single-crystalline and single-domain ferromagnetic nanowire materials has been an area of intense research,1-3 however the control of geometric parameters (diameter, lengths, tip morphology and uniformity) in nanowire syntheses is mostly empirical. Here, we demonstrate a simple method for precise control of geometric parameters in nanowire synthesis by establishing both steady-state growth conditions and a uniform rate of particle growth through the continuous and controlled additions of precursors. To prepare Co nanowires, we used both the 'LaMer' and 'extended LaMer' processes, which allows us to fine control over diameter, aspect ratio, and morphology uniformity of the nanowires with reproducibility. Meanwhile, the structural property analysis of a series of nanowires revealed both qualitative and quantitative information on the growth kinetics of the nanowires. It has been demonstrated how the precursor flow rate, metal precursor mole ratio and the reducing ability of long-chain amine affect the nanowire morphology. We then show how such fine geometric control affects the magnetic coercivity of nanowire assemblies. Based on the shape anisotropy and orientation of the nanowire assemblies, a record high room-temperature coercivity exceeding 10 kOe has been measured in Co nanowires with a diameter of 8 nm.

![](https://assets.underline.io/uploads/markdown_image/1/image/30b2d410cd16b38f3094e1caeb5b2bd1.jpg)

Fig. 1 Schematic illustration of the effect of (a) flow rate of Co-precursor, (b) mole ratio of RuCl3 to Co-precursor and (c) long-chain amine content on the growth kinetic of Co nanowires. (d-f) The TEM images of Co nanowires prepared through the continuous flow of Co-precursor at various decreasing flow rates.

Effects of growth kinetics on structural and magnetic properties of Co nanowires

Arrays of magnetically soft nanowires and microwires have potential sensor applications [1, 2]. We have reported nanowire array manufactured by electrodeposition of permalloy into polycarbonate membranes [3]. In this paper we report permalloy nanowire and microwire arrays produced using alumina and silicon membranes with hexagonally ordered pores with constant pitch. These membranes allow to optimize the nanowire array properties such as coercivity, apparent permeability and amplification factor. Finite element modelling of nanowire arrays is demanding due to the computational complexity. In [4] we calculated apparent permeability and demagnetization factor of single wire and small wire arrays. We have also proposed simplified 2D equivalent model allowing to calculate properties of wire arrays very efficiently [5] and verified the validity of this model by full 3D simulations and also experimentally on arrays of up to 91 permalloy microwires. In this paper we apply this model to manufactured arrays of 3 mm diameter containing 100 000 to 40 million wires with diameters between 180 nm and 2.5 μm and compare simulation results to measurements by SQUID. Figs. 1 and 2 show examples of the measured hysteresis loops with red line showing the slope corresponding to apparent amplitude permeability. The values calculated by FEM using constant permeability model show significant deviations especially at low density arrays. We will show that this difference is caused by the nonlinear shielding effect: the field in the outermost wires is much stronger and thus they are saturated first. Because of that the saturation process propagates fast from the periphery towards inside array which can be shown on non-linear model.

![](https://assets.underline.io/uploads/markdown_image/1/image/4818309d16f32532f9a688524ccc7d9a.jpg)

Fig. 1 Hysteresis loop of the array of 180 nm diameter 100 μm long wires with 480 nm pitch. Measured apparent amplitude permeability μa = 45, calculated incremental μai = 8.6.

![](https://assets.underline.io/uploads/markdown_image/1/image/7178e6971765f6f4dd7a495b3982dd0b.jpg)

Fig. 2 Hysteresis loop of the array of 2.5 μm diameter 200 μm long wires with 4.2 μm nominal pitch. Measured apparent amplitude permeability μa = 5.5, calculated incremental μai = 3.8.

Apparent permeability of ordered magnetically soft nanowire and microwire arrays

Multi-segmented nanowire (NW) arrays are strong candidates to improve the memory storage capacity due to their lower magnetic bit area [1]. But writing/reading information on such devices is still a challenge. Recently, micromagnetic simulations revealed that the integration of a soft magnetic segment (with lower coercivity) along the racetrack could ease the writing process by using external magnetic fields [2]. Here, we demonstrate the feasibility of using NiCu/FeCo magnetic NWs as in-line writing components in 3D racetrack memory devices. Using template-assisted DC electrodeposition [3-5], 4 samples of NW hexagonal arrays (50 nm-diameter, 100 nm of interwire distance) were produced: i) Ni90Cu10; ii) Fe20Co80; iii) bi-segmented NiCu/FeCo; and iv) multi-segmented NiCu/[FeCo/Au]3. Morphological, chemical and structural characterization revealed the formation of single, bi- and multi-segmented NW arrays with tuned dimensions and uniform compositions (Fig. 1). Magnetic hysteresis loops, ferromagnetic resonance (FMR) measurements and first-order reversal curve (FORC) diagram analysis confirmed the hard and soft magnetic properties of the FeCo and NiCu single arrays, respectively. In the interacting NiCu/FeCo bi- and multi-segmented systems, a significant reduction of the parallel coercivity occurred, while keeping the magnetization easy axis lying parallel to the NWs' axis. FORC diagrams also demonstrated a two-step reversal process in systems (Fig. 2), illustrating a FORC fingerprint typically present in soft/hard magnetic interacting bi-layered NWs [6]. Micromagnetic simulations confirmed such a two-step reversal process, revealing the presence of strong interactions at the soft/hard interface [7]. This work was supported by projects POCI-01-0145-FEDER-028676, POCI-01-0145-FEDER-031302, UIDB/04968/2020, EXPL/IF/00541/2015 and contract IF/01159/2015 from Portuguese FCT and COMPETE 2020 (FEDER); grant 02.2020/0261 from the National Research Foundation of Ukraine; and project PID2020-117024GB-C42 from the Spanish Ministerio de Ciencia e Innovacíon.

![](https://assets.underline.io/uploads/markdown_image/1/image/cd280bc8126f81abd395a71d877c76eb.jpg)

Fig. 1. Scanning electron microscopy images of the electrodeposited multi-segmented NWs.

![](https://assets.underline.io/uploads/markdown_image/1/image/22038b2a0a7bf508db8232151a5ff998.jpg)

Fig. 2. FORC diagram of the multi-segmented sample along the parallel direction.

Feasibility of Using NiCu/FeCo Coupled Bi-segmented Nanowires as In-line Writing Heads for 3D Racetrack Storage Devices

Three-dimensional (3D) magnetic assemblies can accommodate unique topological features and exotic spin textures, along with embedded magnetic frustrations [1]. Recently, we have realized interconnected cobalt nanowire networks using multiple angle ion-tracking and electrodeposition; such networks exhibit new magnetization reversal behaviors, offering an interesting platform for 3D information storage [2]. Here we report magnetoresistance (MR) studies of such interconnected networks, to explore how the magnetic configurations can be correlated with spin transport. When a sizable collection of connected nanowires is measured, typical anisotropic magnetoresistance behavior with sharp minima near the coercive fields is found, suggesting that the current is largely bypassing the high resistance intersections. However, when only a few interconnected nanowires are measured, the MR curve exhibits multiple kinks and local minima, indicative of domain wall pinning by the intersections (Fig. 1). More interestingly, during the positive to negative field sweep, a significant MR minimum is observed at positive field, which is the largest among all the MR minima. These features are not seen in parallel nanowires and are a direct consequence of the intersections. Micromagnetic simulations using an equivalent resistor model based on two intersecting nanowires reproduces the experimental observations, including the multiple kinks and a large MR minimum in positive field. Furthermore, small angle neutron scattering has been used to characterize magnetic correlations in the networks under different applied magnetic field configurations. These results show that the intersections in the networks play an important role in pinning / depinning of domain walls, which may be utilized for 3D magnetic memory and memristive devices. Work supported by the SRC/NIST nCORE SMART center and NSF.

![](https://assets.underline.io/uploads/markdown_image/1/image/33fe181bcbcc9e0f263230fd717c8566.jpg)

Figure 1: Magnetoresistance of a few interconnected Co nanowires showing multiple kinks, indicative of domain wall pinning and depinning during magnetization reversal.

Reservoir computing in an artificial spin-vortex ice

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Reservoir computing in an artificial spin-vortex ice

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