Physical reservoir computing represents an energy efficient approach for processing temporal signals by exploiting the intrinsic nonlinear dynamics and fading memory of a physical system. Recently, ferroelectric semiconductors moved into focus as reservoir materials motivated by their versatile electronic responses to external stimuli. Here, we explore the fundamental possibility to recognize time-varying light pulses via photo-induced currents, using the small-band-gap p-type semiconductor ErMnO_3 as a model system. Under white light illumination, ErMnO_3 exhibits non-linearly evolving photo-induced currents and controllable relaxation dynamics that naturally realize the high-dimensional projection and fading memory capabilities required for reservoir computing. The reservoir capability of ErMnO_3 is reflected by the improved recognition accuracy of "Past" input pulses, which increases from 33

Three-dimensional topological spin textures have attracted growing interest due to their rich geometry and potential for functional magnetic phenomena. In this work, we introduce a new class of magnetic models, termed screw chiral magnets. We show that these systems support metastable Hopfions and other three-dimensional topological textures in a ferromagnetic background. These solitons exhibit distinctive physical properties, including unconventional Goldstone modes. The models are obtained via a systematic symmetry transformation of the bulk chiral magnet. Our results establish screw chiral magnets as a new class of magnetic models supporting Hopfions in ferromagnetic backgrounds and identify symmetry transformations as a general route to generate systems with nontrivial three-dimensional textures.

Knots and links play a crucial role in understanding topology and discreteness in nature. In magnetic systems, twisted, knotted and braided vortex tubes manifest as Skyrmions, Hopfions, or screw dislocations. These complex textures are characterized by topologically non-trivial quantities, such as a Skyrmion number, a Hopf index H, a Burgers vector (quantified by an integer ν), and linking numbers. In this work, we introduce a discrete geometric definition of H for periodic magnetic textures, which can be separated into contributions from the self-linking and inter-linking of flux tubes. We show that fractional Hopfions or textures with non-integer values of H naturally arise and can be interpreted as states of “mixed topology" that are continuously transformable to one of the multiple possible topological sectors. Our findings demonstrate a solid physical foundation for the Hopf index to take integer, non-integer, or specific fractional values, depending on the underlying topology of the system.

Magnetic material parameters such as the exchange stiffness and magnetic anisotropy govern the behavior and functionality of magnetic systems, yet their local inference from magnetization data remains challenging, particularly in strongly fluctuating regimes with polycrystalline or multiphase microstructure, where conventional texture-based methods become unreliable. We introduce a magnetization-only framework for inferring material parameters from thermally driven magnetization dynamics. Using micromagnetic simulations, we extract statistical quantities such as temporal mean and latent entropy from the magnetization dynamics, fit models to these descriptors, and invert the models to infer material parameters. We show that this framework enables material-parameter inference as well as grain-boundary detection in a heterogeneous sample. Among the descriptors considered, latent entropy yields more accurate parameter estimates than the temporal mean. Our results establish latent entropy as an efficient descriptor for inferring magnetic material parameters from dynamical magnetization data and point toward its use for experimental parameter extraction at high temperatures and, more broadly, under strongly fluctuating conditions.

Abstract DNA is the largest biopolymer in nature, and chromatin contact maps are widely interpreted as quantitative readouts of its three-dimensional organization. However, the validity of such interpretations critically depends on how these maps are processed. Here, we identify a previously overlooked but fundamental source of bias in chromatin contact data analysis. We demonstrate that a widely adopted preprocessing convention, namely whole-matrix percentile clipping, systematically distorts sparse contact maps by collapsing their dynamic range. This effect is strongest in near-diagonal interactions, precisely the regime encoding chromatin domains and looping structures, thereby compromising quantitative interpretation while preserving superficial structural features. We show that this distortion represents a sparsity-dependent failure mode of current preprocessing standards and affects the comparability of datasets and computational methods across technologies and sequencing depths. To address this, we introduce a statistically consistent preprocessing framework based on nonzero-percentile clipping and log-space normalization, which preserves the intrinsic dynamic range of observed contacts. Building on this foundation, we present CCUT, a modular deep learning framework for chromatin contact map reconstruction. Under corrected preprocessing, reconstructed maps recover domain organization, contact decay, and scaling behavior consistent with polymer physics. Importantly, we demonstrate quantitative agreement between reconstructed maps and simulated contact patterns derived from a kinetic Monte Carlo loop extrusion model, enabling direct comparison between experimental data and physical models. Together, our results establish preprocessing as a decisive determinant of the physical interpretability of chromatin contact maps and provide a principled framework for robust and comparable analysis across chromatin conformation capture technologies.

Drawing inspiration from swarm intelligence, we show that short-range attractive interactions between thermally driven Brownian quasiparticles enable energy-efficient optimization. As quasiparticles can be generated directly within a material, the swarm size can be adjusted with minimal energy overhead. Using an optimization task defined by a spatially varying temperature landscape, we quantitatively show that interacting swarms reliably identify global optima and significantly outperform non-interacting searchers within a well-defined regime of interaction strength and swarm size. This improvement arises from emergent cooperative behavior, where local interactions guide the swarm toward high-quality solutions without central coordination. To link our physical model to experimental realizations, we coarse-grain the quasiparticle dynamics onto a sensor lattice and generate trajectories emulating particle-tracking measurements. We further show that the interacting swarm adapts robustly to landscapes that evolve over time. These findings establish interacting Brownian quasiparticles as a physical platform for scalable and energy-efficient unconventional computing.

Topological classification of physical vector fields conventionally relies on field normalization and homotopy-based invariants. However, when field amplitudes vanish, normalization becomes ill-defined, preventing a direct topological characterization. Here, we introduce a general framework for the topological classification of non-normalizable n-dimensional vector fields with compactifiable base spaces by transforming them into (n+1)-dimensional normalized vector fields. This construction extends homotopy-based classification to fields containing amplitude zeros. We explicitly demonstrate the approach for one-, two-, and three-dimensional non-normalized vector fields and derive the corresponding topological invariants. The resulting topological charges are robust under continuous deformations and can change only when the embedding structure becomes singular. Our framework provides a unified route to the topological characterization of non-normalizable fields and opens the door to the study of topological phenomena in a broad range of systems, including magnetic textures, ferroelectrics, electromagnetic fields, and wave systems.

Magnetic skyrmions and related topological spin textures have emerged as a central topic in condensed-matter physics, combining fundamental significance with potential for transformative applications in spintronics, magnonics, and beyond. Over the past decade, advances in material platforms, imaging techniques, theoretical modeling, and device concepts have established skyrmionics as a rapidly expanding field. At the same time, challenges remain in stabilizing, controlling, and integrating such textures into functional architectures, while novel phenomena such as antiskyrmions, higher-order skyrmions, hopfions, and antiferromagnetic textures arise. The 2026 Skyrmionics Roadmap represents a collective effort of many authors, providing a comprehensive perspective on the current state-of-the-art and the outlook for the coming years. In 33 focused sections, each co-authored by two researchers, we chart progress in theory and modeling, material systems, skyrmion dynamics, and skyrmion technologies. By offering a consolidated vision, this Roadmap aims to guide both fundamental research and application-driven efforts, accelerating the transition of skyrmionics from conceptual breakthroughs toward practical technologies.

Localized topological defects inherently possess a multiscale character. While their microstructure configuration depends on the specific physical system, their topological features and mutual interactions can be described on the macroscale in terms of a particle representation. However, determining the physical properties associated with a given defect pattern often requires knowledge of the underlying microscopic structure. In this study, we extend a Wasserstein generative adversarial neural network by incorporating physical constraints and Fourier-space information to generate microscopic spin configurations consistent with prescribed macroscopic patterns and thermodynamic parameters. Using the two-dimensional XY model as a test case, where vortex-antivortex pairs act as long-range interacting defects, we show that the model generates spin configurations that accurately reproduce magnetization, susceptibility, helicity modulus, and spin-spin correlations over a wide range of temperatures below the Kosterlitz-Thouless transition. At the same time, deviations in the specific heat reveal limitations in reproducing higher-order energy fluctuations. A complementary analysis based on topological data analysis uncovers subtle differences in global spin-correlation structures at near-critical temperatures that are not apparent from conventional correlation functions alone. These results demonstrate both the promise and current limitations of generative approaches for multiscale studies of defect-dominated spin systems and, at the same time, highlight topological methods as valuable tools for characterizing critical behavior.

Topological concepts are frequently used to describe structured optical fields, including plasmonic near fields. Topological descriptions in terms of skyrmion numbers implicitly assume the compactness of the underlying manifold. Even when skyrmion-like textures appear locally, the compactness is usually not fulfilled in extended optical fields. Here, we use photoemission electron microscopy to investigate a plasmonic nano-focus that exhibits a sequence of radially extending alternating skyrmion and antiskyrmion textures. The full spatio-temporal reconstruction of the electric field vectors and their topology is accessible by vector polarimetry. The experiments confirm the expected oscillatory behavior of the skyrmion number and demonstrate that a global skyrmion number cannot be assigned in such non-compact fields.

Local material inhomogeneities can strongly influence magnetization dynamics and macroscopic magnetic properties, yet detecting such defects from magnetic imaging data remains challenging when thermal fluctuations and experimental noise obscure static contrast. Here, we investigate defect detection in strongly fluctuating magnetization regimes where signatures of inhomogeneities largely average out in time-resolved measurements. Using finite-temperature micromagnetic simulations with randomly distributed defects and material parameters representative of Ni80Fe20, we compute per-pixel temporal mean, temporal standard deviation, and latent entropy and use them as inputs for U-Net-based semantic segmentation models. We find that the most effective descriptor depends on the noise level and, importantly, that robust detection requires training data that reflect the expected noise statistics. These results provide practical guidance for designing noise-robust defect-detection workflows in magnetic imaging.

Spin-based computing is emerging as a powerful approach for energy-efficient and high-performance solutions to future data processing hardware. Spintronic devices function by electrically manipulating the collective dynamics of the electron spin, that is inherently non-volatile, nonlinear and fast-operating, and can couple to other degrees of freedom such as photonic and phononic systems. This review explores key advances in integrating magnetic and spintronic elements into computational architectures, ranging from fundamental components like radio-frequency neurons/synapses and spintronic probabilistic-bits to broader frameworks such as reservoir computing and magnetic Ising machines. We discuss hardware-specific and task-dependent metrics to evaluate the computing performance of spin-based components and associate them with physical properties. Finally, we discuss challenges and future opportunities, highlighting the potential of spin-based computing in next-generation technologies.

To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterization has proven essential. In particular, while the skyrmion number is a well-established topological invariant for two-dimensional magnetic textures, the Hopf index serves as a key topological descriptor for three-dimensional magnetic structures. In this paper, we present and compare various methods for numerically calculating the Hopf index, provide implementations, and offer a detailed analysis of their accuracy and computational efficiency. Additionally, we identify and address common pitfalls and challenges associated with the numerical computation of the Hopf index, offering insights for improving the robustness of these techniques.

The explosive growth of data in the modern digital era has placed unprecedented demands on information and communication technologies, driving up energy consumption and revealing critical limitations in conventional computing architectures. This Editorial introduces a Special Topic dedicated to the exploration of next-generation memory technologies aimed at addressing these challenges through energy-efficient, high-speed, and scalable computing solutions. Emphasizing the convergence of neuromorphic and in-memory computing paradigms, this collection highlights innovative materials and device architectures, including spintronic, ferroelectric, resistive switching, photonic, molecular, and two-dimensional systems, that enable new modes of data storage and processing. Featured contributions encompass advances in skyrmionics and spin–orbit torque magnetic random-access memories, advanced ferroelectric nitrides, antiferromagnetic topological systems, and bio-inspired optoelectronic synapses, among others. Together, these works illuminate a vibrant landscape of research at the intersection of condensed matter physics, materials science, and electrical engineering, offering critical insights into the design of sustainable, brain-like, and high-performance memory technologies for the era of artificial intelligence, edge computing, and green electronics.

Topological spin textures in magnetic materials and arrangements of electric dipoles in ferroelectrics are considered to be promising candidates for next-generation information technology and unconventional computing. Exciting examples are magnetic skyrmions and ferroelectric domain walls. We discuss how the physical properties of these topological nanoscale systems can be leveraged for reservoir computing, that is, for translating non-linear problems into linearly solvable ones. They fulfill the requirements for non-linearity, complexity, short-term memory and reproducibility, giving new opportunities for the downscaling of devices, enhanced complexity and versatile input and readout options. We also discuss the practical challenges and opportunities for exploiting the unique properties of these systems. This Perspective explores how the physical properties of these topological nanoscale systems, such as magnetic skyrmions and ferroelectric domain walls, can be leveraged for reservoir computing.

Physical reservoir computing (PRC) is a computing framework that harnesses the intrinsic dynamics of physical systems for computation. It offers a promising energy-efficient alternative to traditional von Neumann computing for certain tasks, particularly those demanding both memory and nonlinearity. As PRC is implemented across a broad variety of physical systems, the need increases for standardised tools for data processing and model training. In this manuscript, we introduce PRCpy, an open-source Python library designed to simplify the implementation and assessment of PRC for researchers. The package provides a high-level interface for data handling, preprocessing, model training, and evaluation. Key concepts are described and accompanied by experimental data on two benchmark problems: nonlinear transformation and future forecasting of chaotic signals. Throughout this manuscript, which will be updated as a rolling release, we aim to facilitate researchers from diverse disciplines to prioritise evaluating the computational benefits of the physical properties of their systems by simplifying data processing, model training and evaluation.

ZusammenfassungBeim physikalischen Reservoir‐Computing wird die natürliche Dynamik eines Materials für Berechnungen genutzt. Jedes System, das weniger als eine Handvoll Eigenschaften erfüllt, eignet sich als physikalisches Reservoir, dem zentralen Bestandteil eines Reservoir‐Computers. Selbst Wassereimer können so recht komplexe Aufgaben lösen. Besonders interessant sind magnetische Muster auf der Nanoskala. Dazu zählen insbesondere magnetische Wirbel, Skyrmionen, weil diese topologisch stabilisiert werden. Daraus lassen sich energieeffiziente und leicht zu steuernde Reservoirs konstruieren, die mit unserer derzeitigen Computer‐Hardware kompatibel sind. Magnetische Reservoir‐Computer demonstrierten zum Beispiel Spracherkennung und diverse Benchmark‐Probleme mit Bestleistungen.

Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime magnetic hopfions: magnetic textures in two spatial dimensions that when excited by a time-periodic drive develop spacetime topology. We uncover two complementary construction routes using skyrmions by braiding their center of mass position and by controlling their internal low-energy excitations. Spacetime magnetic hopfions can be realized in nanopatterned grids to braid skyrmions and in frustrated magnets under an applied AC electric field. Their topological invariant, the spacetime Hopf index, can be tuned by the applied electric field as demonstrated by our collective coordinate modeling and micromagnetic simulations. The principles we have introduced to actively control spacetime topology are not limited to magnetic solitons, opening avenues to explore spacetime topology of general order parameters and fields.