Using Brillouin light scattering microscopy, we study the rich dynamics in magnetic disks and rings governed by nonlinear interactions, focusing on the role of vortex core dynamics on the spin-wave eigenmode spectrum. By strongly exciting quantized magnon modes in magnetic vortices, self-induced magnon Floquet states are populated by the intrinsic nonlinear coupling of magnon modes to the vortex core gyration. As a result, magnon frequency combs are formed. In magnetic rings, however, this generation is suppressed even when exciting the system over a large power range. To retrieve frequency combs by the rich nonlinear dynamics in rings, we apply external in-plane magnetic fields by which the vortex core is nucleated. Our findings demonstrate how to take active control of the nonlinear processes and, thereby, the generation of magnon frequency combs in magnetic structures of different topology.

A pair of quantized spin-wave modes is driven by two-tone parallel pumping in a YIG microdisk. The nonlinear dynamics is experimentally investigated by probing the resulting steady state, which is found to critically depend on the chosen pair of modes, the detuning between the pump frequencies and the modes parametric resonance, as well as the temporal sequence of the two rf tones. A general theory of parametric excitation in confined structures based on magnetization normal modes is developed and quantitatively accounts for the observed dependence and non-commutative behaviors, which emerge from the interplay between the self and mutual nonlinear frequency shifts of the spin-wave modes. Owing to its high degree of external controllability and scalability to larger sets of modes, this dynamical system provides a model platform for exploring nonlinear phenomena and a promising route toward rf driven state mapping relevant to neuromorphic and unconventional computing.

Ordered stripe domains in ferromagnetic thin films form a natural one-dimensional crystal for propagating spin waves. Their spatial periodicity can be tuned readily with an applied magnetic field, making these systems an attractive platform for exploring how magnon band structures evolve as a function of the lattice constant a, a tuning that is difficult to achieve in physically patterned materials. In this work we employ micromagnetic simulations to calculate the spin-wave spectra of a model iron-garnet film, focusing on the influence of the external field and of cubic anisotropy. We find that band gaps at the Brillouin-zone center (k = 0) and at the zone boundary (k = ± π/a) respond differently to the applied field, appearing over a broad range of frequencies and wave vectors. When a perpendicular magnetic field or cubic anisotropy is present, additional gaps can appear at the middle of the reduced Brillouin zone (k = ± π/2a). This behavior is interpreted as a Peierls-type distortion of the domain-wall lattice, wherein “up” and “down” domains alternately expand and contract under the influence of the effective perpendicular field.

We experimentally demonstrate the generation of multiple three-magnon splitting processes in an in-plane magnetized submicron Bi-YIG disk using micro-focused Brillouin light scattering. The low magnetic damping and strong magneto-optical response of BiYIG enable the detection of nonlinear spin-wave interactions at low threshold powers. By tuning the in-plane static magnetic field, excitation frequency, and power, we observe the generation of three pairs of secondary modes symmetrically distributed around half the excitation frequency. Time-resolved BLS measurements present temporal dynamics and threshold behavior associated with the successive activation of three-magnon pairs.

We present a mechanism for self-induced Floquet states involving acoustic and optical modes in synthetic antiferromagnets. By driving optical modes off-resonantly with radiofrequency fields in the canted antiferromagnetic state, limit cycles arising from the predator-prey dynamics of the acoustic and optical mode populations can appear. The cyclic growth and decay of these mode populations induce a time-periodic modulation of the canted state, which subsequently generates Floquet states. These states appear as a rich frequency comb in the power spectrum of magnetization oscillations.

Driving condensed matter systems with periodic electromagnetic fields can result in exotic states not found in equilibrium. Termed Floquet engineering, such periodic driving applied to electronic systems can induce topological band structures and control spin interactions. In this study, we present a class of Floquet states in a magnetic vortex that arise from nonlinear interactions between the vortex core and microwave magnons. Floquet bands emerge through the periodic oscillation of the core, which can be initiated by either driving the core directly or pumping azimuthal magnon modes. For the latter, the azimuthal modes induce core gyration through nonlinear interactions, which in turn renormalizes the magnon band structure. This represents a self-induced mechanism for Floquet band engineering and opens avenues to study and control nonlinear magnon dynamics.

The dynamics of vortex states in confined geometries like thin-film disks are characterized by a subgigahertz gyration, representing the damped oscillatory motion of the vortex core about the disk center. It has recently been shown that interactions between the core and azimuthal spin waves, lying in the gigahertz range and driven by magnetic fields, can result in steady-state core gyration. The gyration in turn provides a time-periodic modulation for the spin waves, resulting in the emergence of Floquet states. Here, we present results of a theoretical and computational study in which we examine how Floquet modes sustain this core gyration. In particular, we find that multiple steady-state gyration radii are possible under certain field conditions, resulting from the nonlinear interactions between the core and Floquet modes. Different gyration radii result in distinct Floquet frequency comb spectra and allow for hysteretic effects, as reported in recent experiments.

Spin-wave spectra across transitions between uniform and textured phases can offer deep insight into both symmetry-breaking physics and self-assembled magnonic bands. However, experiments require a material platform that combines low damping, well-defined textures, and spectroscopic access. Here, we study a Bi-doped iron-garnet film with perpendicular magnetic anisotropy (PMA), which undergoes a uniform-to-stripe-domain transition as a function of in-plane magnetic field. Real-space imaging by magnetic force microscopy reveals field-reorientable stripe domains aligned with the in-plane field, while reciprocal-space measurements using thermal microfocused Brillouin light scattering (μ-BLS) reveal the softening of a low-frequency spin-wave branch near the transition and the appearance of additional modes in the stripe-domain state. Calculated dispersion relations identify finite-k softening in the Damon-Eshbach geometry (k ⊥ M), with the corresponding wavelength matching the stripe periodicity at the transition. In addition, a μ-BLS spectral model reproduces the measured mode frequencies and relative intensities at selected fixed fields. Micromagnetic simulations capture the field-driven formation of the stripe state and reproduce the experimental thermal μ-BLS spectra. Our findings establish BiYIG with PMA as a model low-damping platform for studying spin-wave freezing, stripe-domain modes, and reconfigurable magnonic band structures.

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.

Spin-torque vortex oscillators (STVOs) have been shown to exhibit rich and complex dynamical regimes, which are strongly dependent on the polarizer's configuration. Here, we give an overview of the dynamics in an STVO comprising two vortex free layers, where each layer serves as a dynamic polarizer for the other, increasing the number of degrees of freedom and therefore, the complexity of the system. The dynamics are studied through extensive micromagnetic simulations, performed using our own implementation of the coupled equations of motion, implemented in the open-source micromagnetics code Mumax3. We explore the roles of relative vortex configurations and layer asymmetry on the current-driven dynamics, and find several complex regimes, including self-modulated gyration, the emergence of C-state dynamics, as well as chaotic transitions between regular gyration and this C-state.

Interfacial Dzyaloshinskii-Moriya interaction (DMI) is a key ingredient in the stabilization of chiral magnetic states in thin films. Its sign and strength often determine crucial properties of magnetic objects, like their topology or how they can be manipulated with currents. A few experimental techniques are currently available to measure DMI quantitatively, based on the study of domain walls, spin waves, or spin-orbit torques. In this Letter, we propose a qualitative variant of spin wave methods. We rely on magnetic noise from confined thermal spin waves in domain walls and skyrmions in perpendicularly magnetized thin films, which we probe with scanning nitrogen-vacancy center relaxometry. We show both numerically and experimentally that the sign of the DMI can be inferred from the amplitude of the detected noise, which is affected by the nonreciprocity in the spin wave dispersion. Furthermore, we also demonstrate that the noise distribution around the contour of magnetic skyrmions reveals their Néel or Bloch nature, giving therefore also insight into the strength of DMI involved in their stabilization.

Vortex states in thin film disks host spin wave modes that are geometrically quantized according to their radial and azimuthal indices. Previous studies have shown that hybridization between these modes and the vortex core results in a sizeable frequency nonreciprocity between low-order clockwise and counterclockwise propagating azimuthal modes. Here, we present a computational study of these spin wave modes in submicron disks in which the spatial extension of the vortex core becomes comparable to the wavelength of certain modes. In such cases, we find that the frequency nonreciprocity can be large even for higher order radial and azimuthal indices, reaching several GHz and comparable to the mode frequencies themselves.

The extent to which non-reciprocal waves can be guided in arbitrary directions is an interesting question. We address one aspect of this problem by studying the propagation of acoustic spin waves in a narrow physical conduit made of a synthetic antiferromagnet. Through a combination of Brillouin Light Scattering microscopy and modeling, we demonstrate that even when attempting to guide waves in the reciprocal direction of the material, the system still exhibits strong signatures of non-reciprocity. This includes the excitation of high wavevector waves in the direction perpendicular to the intended channeling, as well as energy transfer in directions that often neither aligns with the physical conduit nor with the symmetry axes of the magnetic properties. These findings have implications for the modeling of propagating wave spectroscopy in non-reciprocal materials and their potential applications.

Physical reservoir computing has emerged as a powerful framework for exploiting the inherent nonlinear dynamics of physical systems to perform computational tasks. Recently, we presented the magnon-scattering reservoir, whose internal nodes are given by the fundamental wavelike excitations of ferromagnets called magnons. These excitations can be geometrically quantized and, in response to an external stimulus, show transient nonlinear scattering dynamics that can be harnessed to perform memory and nonlinear transformation tasks. Here, we test a magnon-scattering reservoir in a single magnetic disk in the vortex state against two key performance indicators for physical reservoir computing: the short-term memory and parity-check tasks. Using time-resolved Brillouin light scattering microscopy, we measure the evolution of the reservoir's spectral response to an input sequence consisting of random binary inputs encoded in microwave pulses with two distinct frequencies. Two different output spaces of the reservoir are defined: one based on the time-averaged frequency spectra and another based on temporal multiplexing. Our results demonstrate that the memory and nonlinear transformation capability do not depend on the chosen readout scheme, provided that the dimension of the output space is large enough to capture all nonlinear features provided by the magnon-magnon interactions. This further shows that it is solely the nonlinear magnons in the physical system-not the readout-that determine the reservoir's capacity.

Frequency combs represent a hallmark of coherence emerging from nonlinear dynamics, where periodic driving organizes energy into a precisely spaced spectral structure. Extending this concept to collective excitations in solids such as magnons, the quanta of spin waves in magnetically ordered materials, offers a powerful route to control energy flow, coherence, and information processing in condensed matter systems. Here, we demonstrate deterministic control of Floquet-engineered magnon frequency combs in magnetic vortices using nanosecond voltage pulses. By tuning the pulse duration and timing, we control the nonlinear energy transfer between magnons and the vortex core, enabling the Floquet-engineered initiation or suppression of magnon frequency combs far below their spontaneous instability threshold. This pulse-programmable interaction allows the vortex to sustain magnon-driven auto-oscillation with high phase stability, or to revert to its static ground state on demand. Our results establish vortex-based magnetic systems as a robust solid-state platform for Floquet engineering, bridging nonlinear spin dynamics with frequency conversion and coherent spin-based quantum devices.

Present information and communication technologies are largely based on electronic devices, which suffer from heat generation and high power consumption. Alternatives like spintronics and magnonics, which harness the spin degree of freedom, offer compelling pathways to overcome these fundamental limitations of charge-based electronics. Magnonics relies on spin waves, the collective excitations of magnetic moments in magnetically ordered materials, to achieve processing and transport of information at microwave frequencies without relying on charge currents. However, efficient means for all-electrical, high-resolution, semiconductor-compatible readout of information encoded in spin waves are still missing. Here, we demonstrate the electrical detection of spin waves using a nanoscale magnetic tunnel junction (MTJ) cell fabricated in a state-of-the-art complementary metal-oxide-semiconductor (CMOS) production line. By engineering the dynamic coupling between spin waves and the magnetization state of the MTJ, we demonstrate transduction of spin-wave excitations into measurable electrical signals with high fidelity. Moreover, through these measurements, we find spectral line widths, associated with nonlinear processes, down to a few hundreds of kHz, which opens up new perspectives for spin waves as quantum transducers.

The traditional method for exciting spin-wave dynamics in magnetic materials involves microwave magnetic fields generated by current injection into inductive antennas. However, there is a growing interest in non-inductive excitation methods. Magneto-acoustic effects present a viable alternative, where strains produced by applying voltages to a piezoelectric substrate can couple to spin-waves in a magnetic film. Recently, it has been proposed that surface acoustic waves (SAWs) can excite the gyrotropic mode of the vortex state in a magnetic disk. Here we report on experiments utilizing a magnetic resonance force microscope to investigate magnetization dynamics in CoFeB sub-micrometer disks in the vortex state, grown on a Z-cut LiNbO_3 substrate. The device design enables excitation of the gyrotropic mode either inductively, using an antenna on top of the disks, or acoustically via SAWs launched from an interdigital transducer. Our modelling indicates that the lattice rotation ωxz generates a localized magneto-acoustic field that displaces the vortex core from the disk center, initiating the gyration motion. Tuning of the magneto-acoustic torque acting on the vortex structure is achieved by a perpendicular magnetic field. These results demonstrate the clear excitation of the vortex gyrotropic mode by magneto-acoustic excitation.

Parametric spin wave excitation allows studying a variety of nonlinear phenomena, such as magnon scattering. In patterned micro- and nanostructures the magnon spectra is discrete and translational symmetry is broken, which means allowable scattering channels differ from those in continuous films. An example is non-degenerate scattering by which high-power transverse field pumping creates two magnons with distinct frequencies around half the pumping frequency. Through micromagnetics simulations, we show under certain conditions that combining two pumping frequencies generates new magnon modes through a process of stimulated magnon scattering. Such processes are found to depend on the film geometry and sequence of the pumping fields.

We present a computational study of the parametric excitation of spin waves in thin-film disks with a mode-resolved approach. The method involves projecting out the time-dependent magnetization, computed using micromagnetics simulations, onto the spatial profile of the eigenmodes that are obtained from the linearization of the equations of motion. Unlike spectral analysis in the frequency domain, the projection allows for the analysis of transient mode dynamics under parametric excitation. We apply this method to parallel pumping of quantized spin wave modes in in-plane magnetized thin-film disks, where phenomena such as frequency pulling, mutual phase locking, and higher-order magnon scattering processes are identified.

Magnons are elementary excitations in magnetic materials and undergo nonlinear multimode scattering processes at large input powers. In experiments and simulations, we show that the interaction between magnon modes of a confined magnetic vortex can be harnessed for pattern recognition. We study the magnetic response to signals comprising sine wave pulses with frequencies corresponding to radial mode excitations. Three-magnon scattering results in the excitation of different azimuthal modes, whose amplitudes depend strongly on the input sequences. We show that recognition rates as high as 99.4% can be attained for four-symbol sequences using the scattered modes, with strong performance maintained with the presence of amplitude noise in the inputs.