Neuromorphic computing uses basic principles inspired by the brain to design circuits that perform artificial intelligence tasks with superior energy efficiency. Traditional approaches have been limited by the energy area of artificial neurons and synapses realized with conventional electronic devices. In recent years, multiple groups have demonstrated that spintronic nanodevices, which exploit the magnetic as well as electrical properties of electrons, can increase the energy efficiency and decrease the area of these circuits. Among the variety of spintronic devices that have been used, magnetic tunnel junctions play a prominent role because of their established compatibility with standard integrated circuits and their multifunctionality. Magnetic tunnel junctions can serve as synapses, storing connection weights, functioning as local, nonvolatile digital memory or as continuously varying resistances. As nano-oscillators, they can serve as neurons, emulating the oscillatory behavior of sets of biological neurons. As superparamagnets, they can do so by emulating the random spiking of biological neurons. Magnetic textures like domain walls or skyrmions can be configured to function as neurons through their non-linear dynamics. Several implementations of neuromorphic computing with spintronic devices demonstrate their promise in this context. Used as variable resistance synapses, magnetic tunnel junctions perform pattern recognition in an associative memory. As oscillators, they perform spoken digit recognition in reservoir computing and when coupled together, classification of signals. As superparamagnets, they perform population coding and probabilistic computing. Simulations demonstrate that arrays of nanomagnets and films of skyrmions can operate as components of neuromorphic computers. While these examples show the unique promise of spintronics in this field, there are several challenges to scaling up, including the efficiency of coupling between devices and the relatively low ratio of maximum to minimum resistances in the individual devices. I-Neuromorphic computing is the path to low energy Artificial Intelligence Artificial Intelligence has experienced unprecedented progress in recent years, promising to transform multiples areas of how we live and how we work. However, this development comes with a considerable challenge: the energy consumption associated with existing approaches 1 , making it

Within a decade, the field of magnetic skyrmionics has developed from a niche prediction to a huge and active research field. Not only do magnetic skyrmions—magnetic whirls with a unique topology—reveal fundamentally new physics, but they have also risen to prominence as up-and-coming candidates for next-generation high-density efficient information encoding. Within a few years, it has been possible to efficiently create, manipulate, and destroy nanometer-size skyrmions in device-compatible materials at room-temperature by all electrical means. Despite the incredibly rapid progress, several challenges still remain to obtain fully functional and competitive skyrmion devices, as discussed in this perspective article with a focus on recent results.

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The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potential for major breakthroughs ranging from fundamental questions to applications as driven by an interdisciplinary exchange of ideas between areas in magnetism which traditionally have been pursued rather independently. The skyrmionics roadmap provides a review of the present state of the art and the wide range of research directions and strategies currently under way. These are, for instance, motivated by the identification of the fundamental structural properties of skyrmions and related textures, processes of nucleation and annihilation in the presence of non-trivial topological winding, an exceptionally efficient coupling to spin currents generating spin transfer torques at tiny current densities, as well as the capability to purposedesign broad-band spin dynamic and logic devices. arXiv:2001.00026v3 [cond-mat.str-el]

Inspired by the human brain, there is a strong effort to find alternative models of information processing capable of imitating the high energy efficiency of neuromorphic information processing. One possible realization of cognitive computing are reservoir computing networks. These networks are built out of non-linear resistive elements which are recursively connected. We propose that a skyrmion network embedded in frustrated magnetic films may provide a suitable physical implementation for reservoir computing applications.The significant key ingredient of such a network is a two-terminal device with non-linear voltage characteristics originating from single-layer magnetoresistive effects, like the anisotropic magnetoresistance or the recently discovered non-collinear magnetoresistance. The most basic element for a reservoir computing network built from "skyrmion fabrics" is a single skyrmion embedded in a ferromagnetic ribbon. In order to pave the way towards reservoir computing systems based on skyrmion fabrics, here we simulate and analyze i) the current flow through a single magnetic skyrmion due to the anisotropic magneto-resistive effect and ii) the combined physics of local pinning and the anisotropic magneto-resistive effect. 1 arXiv:1702.04298v2 [cond-mat.dis-nn]

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Andreas Berger CICnanoGUNE BRTA Following the success and relevance of the 2014 and 2017 Magnetism Roadmap articles, this 2020 Magnetism Roadmap edition takes yet another timely look at newly relevant and highly active areas in magnetism research. The overall layout of this article is unchanged, given that it has proved the most appropriate way to convey the most relevant aspects of today’s magnetism research in a wide variety of sub-fields to a broad readership. A different group of experts has again been selected for this article, representing both the breadth of new research areas, and the desire to incorporate different voices and viewpoints. The latter is especially relevant for thistype of article, in which one’s field of expertise has to be accommodated on two printed pages only, so that personal selection preferences are naturally rather more visible than in other types of articles. Most importantly, the very relevant advances in the field of magnetism research in recent years make the publication of yet another Magnetism Roadmap a very sensible and timely endeavour, allowing its authors and readers to take another broad-based, but concise look at the most significant developments in magnetism, their precise status, their challenges, and their anticipated future developments. While many of the contributions in this 2020 Magnetism Roadmap edition have significant associations with different aspects of magnetism, the general layout can nonetheless be classified in terms of three main themes: (i) phenomena, (ii) materials and characterization, and (iii) applications and devices. While these categories are unsurprisingly rather similar to the 2017 Roadmap, the order is different, in that the 2020 Roadmap considers phenomena first, even if their occurrences are naturally very difficult to separate from the materials exhibiting such phenomena. Nonetheless, the specifically selected topics seemed to be best displayed in the order presented here, in particular, because many of the phenomena or geometries discussed in (i) can be found or designed into a large variety of materials, so that the progression of the article embarks from more general concepts to more specific classes of materials in the selected order. Given that applications and devices are based on both phenomena and materials, it seemed most appropriate to close the article with the application and devices section (iii) once again. The 2020 Magnetism Roadmap article contains 14 sections, all of which were written by individual authors and experts, specifically addressing a subject in terms of its status, advances, challenges and perspectives in just two pages. Evidently, this two-page format limits the depth to which each subject can be described. Nonetheless, the most relevant and key aspects of each field are touched upon, which enables the Roadmap as whole to give its readership an initial overview of and outlook into a wide variety of topics and fields in a fairly condensed format. Correspondingly, the Roadmap pursues the goal of giving each reader a brief reference frame of relevant and current topics in modern applied magnetism research, even if not all sub-fields can be represented here. The first block of this 2020 Magnetism Roadmap, which is focussed on (i) phenomena, contains five contributions, which address the areas of interfacial Dzyaloshinskii–Moriya interactions, and two-dimensional and curvilinear magnetism, as well as spin-orbit torque phenomena and all optical magnetization reversal. All of these contributions describe cutting edge aspects of rather fundamental physical processes and properties, associated with new and improved magnetic materials’ properties, together with potential developments in terms of future devices and technology. As such, they form part of a widening magnetism ‘phenomena reservoir’ for utilization in applied magnetism and related device technology. The final block (iii) of this article focuses on such applications and device-related fields in four contributions relating to currently active areas of research, which are of course utilizing magnetic phenomena to enable specific functions. These contributions highlight the role of magnetism or spintronics in the field of neuromorphic and reservoir computing, terahertz technology, and domain wall-based logic. One aspect common to all of these application-related contributions is that they are not yet being utilized in commercially available technology; it is currently still an open question, whether or not such technological applications will be magnetism-based at all in the future, or if other types of materials and phenomena will yet outperform magnetism. This last point is actually a very good indication of the vibrancy of applied magnetism research today, given that it demonstrates that magnetism research is able to venture into novel application fields, based upon its portfolio of phenomena, effects and materials. This materials portfolio in particular defines the central block (ii) of this article, with its five contributions interconnecting phenomena with devices, for which materials and the characterization of their properties is the decisive discriminator between purely academically interesting aspects and the true viability of real-life devices, because only available materials and their associated fabrication and characterization methods permit reliable technological implementation. These five contributions specifically address magnetic films and multiferroic heterostructures for the purpose of spin electronic utilization, multi-scale materials modelling, and magnetic materials design based upon machine-learning, as well as materials characterization via polarized neutron measurements. As such, these contributions illustrate the balanced relevance of research into experimental and modelling magnetic materials, as well the importance of sophisticated characterization methods that allow for an ever-more refined understanding of materials. As a combined and integrated article, this 2020 Magnetism Roadmap is intended to be a reference point for current, novel and emerging research directions in modern magnetism, just as its 2014 and 2017 predecessors have been in previous years.

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutoriallike article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures -skyrmions -are tailormade to study these Berry phase effects.Over the last decades physicists have realized that a seemingly harmless phase -the Berry phase -leads to a lot of interesting physical consequences like quantum, This paper is structured as follows: First, we review the general concept of Berry phases and introduce the main formulas. In Sec. II, we focus on real-space Berry phase effects. Here we discuss the example of a free electron traversing a spatially or temporally inhomogeneous, smooth magnetic structure. In the adiabatic limit, the magnetic moment of the electron adjusts constantly to the local magnetization direction and thereby the electron picks up a Berry phase. To interpret the physical consequences of these Berry phases, we review the mapping onto a problem, where the electron moves in a uniform Zeeman magnetic field, but instead "feels" an emergent electric field and an emergent orbital magnetic field, leading, for example, to the topological Hall effect 4 . In Sec. III, we first introduce skyrmions in a formal way and then later focussing on skyrmions in magnetic systems, in particular those in a certain material class denoted as B20 materials. We discuss that those magnetic textures are tailormade to observe the emergent electric fields introduced in Sec. II A. In Sec. III C we switch the perspective and discuss the back reaction of the electronic Berry phase effects on the skyrmion lattice. I. BERRY PHASESBerry phases occur in all parts of physics and arise whenever a system adiabatically evolves along a cyclic process C in some parameter space X. A simple classical example is the parallel transport of a vector along a closed curve on a sphere (see Fig. 1). Although the system returns to its initial state it aquires a geometric phase characterized by the enclosed area on the sphere (Gauss-Bonnet theorem).A quantum-mechanical example is a system whose states are non-degenerate and which evolves adiabatically in the parameter space X = X(t). In that case, the solution of the time-dependent Schrödinger equation i ∂ t |ψ(t) = H(X(t)) |ψ(t) is given by 11 |ψ(t) = n a n (t 0 )e iγn(C) e − i t 0 dt n (X(t )) |ψ n (t) , (1) where |ψ n (t) and n (X(t)) are the time-evolved eigenstates and energies of the Hamiltonian H(X(t)), |ψ(t 0 ) = n a n (t 0 ) |ψ n (t 0