The (inverse) magnetostrictive effect in ferromagnets couples the magnetic properties to the mechanical stress, allowing for an interaction between the magnetic and mechanical degrees of freedom. In this work, we present a time-integration scheme for the self-consistent simulation of coupled magnetoelastic dynamics within the framework of finite-difference micromagnetism. The proposed implementation extends the Landau-Lifshitz-Gilbert equation by a strain-induced effective field and concurrently solves the elastic equation of motion, while correctly incorporating stress and strain discontinuities at material interfaces. We then present a comprehensive set of examples, ranging from static stress configurations over material boundaries to simulations of surface-acoustic-wave attenuation in magnetically structured thin and thick films. These computational experiments both validate the implementation and underscore the significance of properly handling jump and boundary conditions in magnon-phonon interaction studies.

Filtering surface acoustic wave (SAW) signals of specified frequencies depending on the strength of an external magnetic field in a magnetostrictive material has garnered significant interest due to its potential scientific and industrial applications. Here, we propose a device that achieves selective SAW attenuation by instead programming its internal magnetic state. To this end, we perform micromagnetic simulations for the magnetoelastic interaction of the Rayleigh SAW mode with spin waves (SWs) in exchange-decoupled Co/Ni islets on a piezoelectric LiTaO3 substrate. Due to the islets exhibiting perpendicular magnetic anisotropy, the stray-field interaction between them leads to a shift in the SW dispersion depending on the magnetic alignment of neighboring islets. This significantly changes the efficiency of the magnetoelastic interaction at specified frequencies. We predict changes in SAW transmission of 52.0 dB/mm at 3.8 GHz depending on the state of the device. For the efficient simulation of the device, we extend a prior energy conservation argument based on analytical solutions of the SW to finite-difference numerical calculations, enabling the modeling of arbitrary magnetization patterns like the proposed islet-based design.

ABSTRACT A three‐dimensional magnetic field sensing concept based on the anomalous Hall effect (AHE) in chiral multilayers driven by spin–orbit torques (SOTs) is presented. In W/CoFeB/MgO stacks that host homochiral stripe and skyrmion states, SOT‐induced domain reorientation and stripe‐to‐bubble transitions are exploited to detect both in‐plane and out‐of‐plane magnetic fields. Finite‐temperature micromagnetic simulations reveal the reversible evolution from stripe domains to skyrmions under applied fields and high current densities. The symmetry of the SOT enables offset‐free in‐plane sensing, while Joule heating‐assisted domain ordering ensures linear out‐of‐plane operation. The device achieves linear ranges of (in‐plane) and (out‐of‐plane), sensitivities up to , and zero‐field offsets below for in‐plane fields. These results introduce SOT‐driven chiral multilayers as a promising platform for vector magnetic field sensing and establish a route toward offset‐free, scalable three‐dimensional Hall sensors based on chiral spin textures.

Double-helix (DH) nanowires provide a platform to study the influence of geometric chirality on spin chirality. Their three-dimensional (3D) helical architecture and tunable inter-strand coupling enable control of spin chirality, including the stabilization of topological 3D magnetic states such as helical domains and domain walls, topological stray fields, and extended helical vortex/skyrmion tubes. So far, the study of these and other 3D nanostructures is usually confined to a limited number of magnetic microscopy experiments in large facilities. Here, we investigate the reversal mechanism of a single DH nanowire using Dark-Field magneto-optical Kerr effect (DF-MOKE) magnetometry under external 3D magnetic fields. By analyzing the angular dependence of the DF-MOKE signal, we fit the reversal process using established models for domain-wall nucleation and propagation, finding a characteristic behavior similar to that reported for cylindrical nanowires. Micromagnetic simulations indicate that the reversal process goes through nucleation of the helical vortex tube in a curling manner while ptychographic X-ray magnetic circular dichroism data reveal that this helical vortex tube state forms through a mixed nucleation-propagation process. These observations provide a consistent microscopic picture of reversal mediated by a helical vortex tube extending along the nanowire. Our work provides a comprehensive characterization of magnetization reversal in DH nanowires and demonstrates that DF-MOKE magnetometry is effective for probing reversal mechanisms in single 3D nanostructures. This lab-based approach expands the range of accessible experiments beyond large-scale facilities, enabling extensive exploration of the rich spin states supported by 3D nano-geometries.

Inverse design - specifying a desired functionality and letting a computational algorithm find the optimal structure - has emerged as a powerful paradigm for magnonic device engineering. In this article, we survey the rapidly growing field of inverse-design magnonics, organising it along two axes: the design variables (topology, material parameters, and magnetic field landscape) and the algorithmic toolbox (gradient-free, gradient-based, and neural-network-based methods) together with the differentiable micromagnetic solvers that enable them. We then identify open frontiers that we consider most promising for the next phase of the field: sensitivity analysis and robust design to bridge the gap between simulation and experiment; input shaping and transducer optimisation; the incorporation of nonlinear spin-wave effects as an explicit design resource; spatially structured amplification; self-adapting media and machine-learning-based design; and the long-term vision of a universal, reconfigurable magnonic platform. We argue that magnonics and artificial intelligence are converging from two directions - machine-learning tools for designing magnonic devices, and magnonic devices as hardware for neuromorphic computation - and propose the term AI magnonics to describe this emerging paradigm.

Bloch points are three-dimensional topological singularities in magnetization that play a key role in topological transformations of spin textures, such as skyrmion creation or annihilation. While topology often enforces the existence of Bloch points in confined geometries like cylindrical nanowires, deterministic control over their position and magnetic configuration remains challenging. Here we demonstrate the generation of Bloch points with controlled spin texture by engineering geometrical boundary conditions in three-dimensional nanomagnets. By introducing a chirality interface between two three-dimensional double-helix nanowires of opposite handedness, forming a kinked, non-collinear structure, we impose competing topological constraints that uniquely define the magnetization configuration surrounding the Bloch point. A saturating magnetic field nucleates head-to-head or tail-to-tail domain configurations at the chirality interface, producing a Bloch-point domain wall with deterministic polarity, circulation and helicity. This geometrical approach enables full three-dimensional control of Bloch point domain walls allowing deterministic engineering of their spin texture and its selective coupling to current-induced Oersted fields.

The extension of magnetic nanostructures to three dimensions (3D) has been predicted to result in phenomena such as non-reciprocal collective dynamics and ultra-fast motion of textures. However, while first indications of dynamics in 3D have been explored in microstructures, the experimental investigation of magnetization dynamics in complex-shaped 3D nanostructures remains challenging. Here, 3D nanoprinted cobalt double-helix nanostructures are investigated with time-resolved X-ray microscopy at nanoscale spatial and picosecond temporal resolution to study their magnetization dynamics. Within the helices, the dynamics of coupled domain walls are observed, and a clear resonant response identified. Micromagnetic simulations confirm that the experimentally observed resonance arises from a harmonic oscillatory mode of the coupled domain walls and predict additional higher-frequency modes, revealing a rich dynamic spectrum. By systematically varying the helix geometry in simulations, we find that the resonant modes can be engineered. This geometrical control promises an alternative to conventional tuning strategies based on tailored magnetic anisotropies, DC bias, or externally applied fields. Together, these experimental and simulated results of magnetization dynamics in complex 3D nanostructures provide a pathway for programmable functionalities, relevant for potential technologies including information processing architectures based on tunable spin texture dynamics.

Engineering the dispersion relation is one of the key ingredients enabling the application of spin waves in computational elements. One way to engineer the spin-wave band structure is to create an artificial magnonic crystal, which can be used to design specific band gaps or dispersion branches. However, creating a two-dimensional magnonic crystal usually requires removing material, which dramatically decreases the decay lengths of spin waves. Here, we present a method to manipulate the demagnetizing field landscape by utilizing large-area curvilinear nanotemplates consisting of three-dimensional nanopyramids arranged in a square lattice with a period of 400 nm. In a 50-nm-thick Permalloy film grown on these curvilinear templates, we experimentally observe a complete in-plane band gap together with flat-band modes that exhibit strong real-space localization of the spin waves in the pyramid valleys. Micro-focused Brillouin light scattering measurements corroborate the numerically predicted dispersion and reveal the possibility of opening and closing this gap by varying the external magnetic field. Our results establish three-dimensional-templated continuous films as a versatile platform for two-dimensional signal processing and magnonic computing elements.

Reliable operation of perpendicular spin-transfer-torque magnetic random-access memory (p-STT-MRAM) requires control of magnetic alignment within the synthetic antiferromagnet (SAF) reference layer. At nanopillar dimensions, however, devices can exhibit magnetic states that are absent in extended thin films. We present a systematic micromagnetic study of 30 nm-diameter three-layer p-STT-MRAM nanopillars using experimentally motivated material parameters, and map equilibrium states as functions of bilinear and biquadratic interlayer exchange coupling. Phase diagrams show that introducing asymmetry between the SAF layers in saturation magnetization, anisotropy, and thickness reduces the coupling strength required to stabilize antiparallel SAF states and suppress competing configurations. Minimum-energy path calculations show that, for noncollinear antiparallel SAF states, increasing SAF asymmetry can raise SAF reversal barriers while lowering the free-layer barrier; this trade-off is absent for collinear antiparallel SAF states. Stray fields also significantly modify both SAF and free-layer energy barriers. To support the design of p-STT-MRAM devices with either collinear or noncollinear antiparallel SAF reference states, we publicly release the simulation dataset covering 4374 distinct device configurations.

Controlling wave-vector-selective coupling between microwave antennas and spin waves is a central challenge in magnonic transducer design. In all-electrical propagating spin-wave spectroscopy, the launched -spectrum is set by Fourier transform of the perpendicular near-field component of the antenna, but realistic sub-micron antennas exhibit skin and proximity effects, impedance mismatch, and electromagnetic leakage from feed tapers that uniform-current models cannot capture. We introduce a coupled finite-element-finite-difference (FE-FD) framework linking impedance-matched nanoantenna geometries to propagating spin-wave dynamics. Finite-element simulations yield the full complex vector RF near field, projected onto the precession-driving perpendicular component, discretised onto a grid, and injected into micromagnetic Landau-Lifshitz-Gilbert simulations. The antenna wave-vector weighting and excitation intensity are extracted by Fourier analysis and compared with experiment. Applying this framework to coplanar-waveguide and stripline nanoantennas on a yttrium-iron-garnet film, we achieve quantitative agreement in dispersion ridges, group velocities, and wave-vector peak positions. The simulations resolve how antenna width, ground-return symmetry, taper geometry, and leakage shape the launched -spectrum, providing design rules for wave-vector-selective spin-wave excitation in classical and quantum magnonic devices. We further quantify leakage from feed tapers, identify dominant loss channels, and compare CPW and stripline performance, providing routes to efficiency optimization.

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.

We introduce jaxFMM, an open-source, adaptive, highly parallel point-charge Fast Multipole Method implementation for the Laplace kernel written in JAX. It is based on a non-uniform refinement strategy with on-the-fly rotation-based transforms tailored around JAX’s just-in-time compiler, which results in extremely concise and simple code. Benchmarks show that the algorithm performs well at moderate accuracies, even for highly non-uniform charge distributions. JaxFMM already massively speeds up stray-field computations in micromagnetics and with JAX features like autodiff, novel applications such as inverse-design problems and machine-learning tasks can be tackled with ease in the future.

Reconstructing complex magnetization textures from nitrogen-vacancy (NV) magnetometry stray-field measurements presents a challenging inverse problem. In this work, we introduce a physics-informed method that addresses this by incorporating the full micromagnetic energy directly into the variational formulation. Built on a PyTorch backend, our forward model integrates an auto-differentiable finite-differences micromagnetic framework with FFT-based stray-field calculations and Fourier-space upward continuation. This enables efficient gradient-based optimization via the adjoint method and allows the sensor-sample distance to be treated as an optimization parameter. By doing so, we eliminate the experimental uncertainty arising from unknown NV implantation depths and surface oxidation layers. Validation on synthetic data demonstrates high-fidelity reconstruction of spin textures and precise sensor height estimation. Furthermore, when applied to NV measurements of the van der Waals ferromagnet Fe_3-xGaTe_2, the method reconstructs the previously unknown NV-sample distance and physically plausible magnetization textures, which accurately reproduce the experimental observations.

We present framework for extracting internal magnetic structures and intrinsic magnetic material parameters from stray field measurements. The approach introduces a tunable bias field into Landau-Lifshitz-Gilbert dynamics and identifies optimal parameters by minimizing the mismatch between simulated and target stray fields or magnetic force microscopy (MFM) frequency shift contrast. Using synthetic data, we demonstrate recovery of global parameters including the uniaxial anisotropy constant [Formula: see text], saturation magnetization [Formula: see text], exchange stiffness [Formula: see text], and Dzyaloshinskii-Moriya interaction constant [Formula: see text]. A sensitivity analysis reveals that [Formula: see text] has the strongest influence on the optimization loss, while [Formula: see text] and [Formula: see text] exhibit relatively shallow minima. We further assess robustness to noise in the input stray field and find that accurate parameter estimation remains feasible at moderate noise levels. We further analyze the inverse reconstruction of magnetization textures and show that, while the strong stray-field side of Néel skyrmions allows for reliable reconstructions, the weak stray-field side poses significant challenges. These difficulties can be mitigated by employing a convolutional neural network (U-Net) trained on synthetic micromagnetic data to learn the mapping from stray-field slices to magnetization textures. The network provides a robust initialization for the subsequent physics-based relaxation, thereby improving convergence and reconstruction accuracy in challenging scenarios such as the weak stray-field side of Néel skyrmions. The framework is implemented using automatic differentiation in PyTorch, enabling gradient-based optimization and suggesting future extensions toward spatially resolved parameter reconstruction. This hybrid learning-and-physics method offers a flexible and robust strategy for material characterization based on micromagnetic forward models and experimental magnetic imaging data.

Magnonic logic gates represent a crucial step toward realizing fully magnonic data processing systems without reliance on conventional electronic or photonic elements. Recently, a universal and reconfigurable inverse-design device has been developed, featuring a 7 by 7 array of independent current loops that create local inhomogeneous magnetic fields to scatter spin waves in an yttrium-iron-garnet film. Although initially used for linear radio frequency components, we now demonstrate key nonlinear logic gates, NOT, OR, NOR, AND, NAND, and a half-adder, sufficient for building a full processor. In this system, binary data (“0” and “1”) are encoded in the spin-wave amplitude. The contrast ratio, representing the difference between logic states, achieved values of 34, 53.9, 11.8, 19.7, 17, and 9.8 decibels for these gates, respectively.

Topological defects, or singularities, play a key role in the statics and dynamics of complex systems. In magnetism, Bloch point singularities represent point defects that mediate the nucleation of textures such as skyrmions and hopfions. While these textures are typically stabilised in chiral magnets, the influence of chirality and symmetry breaking on Bloch point singularities remains relatively unexplored. Here, we harness advanced three-dimensional nanofabrication to explore the influence of symmetry breaking on Bloch point textures by introducing controlled nano-curvature in a ferromagnetic nanowire. Combining X-ray magnetic microscopy with the application of in situ magnetic fields, we demonstrate that Bloch point singularity-containing domain walls are stabilised in straight regions of the sample, and determine that curvature can be used to tune the energy landscape of the Bloch points. Not only are we able to pattern pinning points but, by controlling the gradient of curvature, we define asymmetric potential wells to realise a robust Bloch point texture shift-register with non-reciprocal behaviour. These insights into the influence of symmetry on singularities offer a route to the controlled nucleation and propagation of topological textures, providing opportunities for logic and computing devices.

This work provides a complete numeric framework, with which soft magnetic composite materials can be numerically analyzed through a combination of two distinct numerical methods. Key soft magnetic properties connected to energy efficiency, namely the permeability and the energy-loss can be predicted. The latter consists of different contributions. These contributions are treated separately in our work and therefore 2 decoupled numerical models are required to fully encompass these materials. Experimentally established concepts with the aim to improve magnetic properties for soft magnetic materials have been simulated, resulting in trends that agree well with the experimentally measured improvements. Moreover, we analyze the distinct loss contributions-an uncommon practice in experimental physics-providing valuable insights into the working principles of these materials, and therefore understanding which contributions become dominant under which conditions. Furthermore measurements of iron powders were conducted, in order to compare the numerical simulations with experimental data.

Magnons have inspired potential applications in modern quantum technologies and hybrid quantum systems due to their intrinsic nonlinearity, nanoscale scalability, and a unique set of experimentally accessible parameters for manipulating their dispersion. Such magnon-based quantum technologies demand long decoherence times, millikelvin temperatures, and minimal dissipation. Due to its low magnetic damping, the ferrimagnet yttrium iron garnet (YIG), grown on gadolinium gallium garnet (GGG), is the most promising material for this objective. To comprehend the magnetic losses of propagating magnons in such YIG-GGG heterostructures at cryogenic temperatures, we investigate magnon transport in a micrometer-thick YIG sample via propagating spin-wave spectroscopy measurements for temperatures between 4 K to 26 mK. We demonstrate an increase in the dissipation rate with wavenumber at cryogenic temperatures, caused by dipolar coupling to the partially magnetized GGG substrate. Additionally, we observe a temperature-dependent decrease in spin-wave transmission, attributed to rare earth ion relaxations. The critical role of the additional dissipation channels at cryogenic temperatures is underpinned by the comparison of the experimental results with theoretical calculations and micromagnetic simulations. Our findings strengthen the understanding of magnon losses at millikelvin temperatures, which is essential for the future detection of individual propagating magnons.

The inverse design approach in magnonics exploits the wave nature of magnons and machine learning to develop logical devices with functionalities that exceed the capabilities of analytical methods. While promising for analog, Boolean, and neuromorphic computing, current implementations face memory limitations that hinder the design of complex systems. This study presents a level-set parameterization method for topology optimization, combined with an adjoint-state approach for memory-efficient simulation of magnetization dynamics. The framework is implemented in NeuralMag, a GPU-accelerated micromagnetic solver featuring a nodal finite-difference scheme and automatic differentiation tools. To validate the method, we optimized the shape of a magnetic nanoparticle by applying constraints to the objective function, and designed a 300 nm-wide yttrium iron garnet demultiplexer achieving frequency-selective spin-wave separation. These results highlight the algorithm’s efficiency in exploring local minima across various initial configurations, establishing its utility as a versatile tool for the inverse design of magnonic logic devices.