The magnetic excitations of the skyrmion lattice in MnSi comprise a multitude of individual modes, which are non-reciprocal and thereby propagate unidirectionally. We report inelastic neutron scattering experiments for temperatures near and above the skyrmion-paramagnetic phase transition in the chiral magnet MnSi tracking the evolution from the skyrmion lattice towards the high-temperature paramagnetic state. Within the resolution of the triple-axis measurements the excitations vary smoothly across the skyrmion-paramagnetic boundary, and, the quasi-elastic paramagnetic signal under applied field retains the non-reciprocal character seen in the skyrmion phase even far above the critical temperature. Using a resolution-convolution our results are consistent with linear spin-wave theory.

In three-dimensional chiral magnets, skyrmions are line-like objects oriented parallel to the applied magnetic field. The efficient coupling of magnetic skyrmion lattices to spin currents and magnetic fields permits their dynamical manipulation. Here, we explore the dynamics of skyrmion lattices when slowly oscillating the field direction by up to a few degrees on millisecond timescales while simultaneously pushing the skyrmion lattice by electric currents. The field oscillations induce a shaking of the orientation of the skyrmion lines, leading to a phase where the critical depinning current for translational motion vanishes. We measure the transverse susceptibility of MnSi to track various depinning phase transitions induced by currents, oscillating fields, or combinations thereof. An effective slip-stick model for the bending and motion of the skyrmion lines in the presence of disorder explains main features of the experiment and predicts the existence of several dynamical skyrmion lattice phases under shaking and pushing representing phases of matter far from thermal equilibrium.

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.

The coupling between electronic nematic degrees of freedom and acoustic phonons is known to significantly alter the universality class of a nematic quantum critical point (QCP). While non-Fermi-liquid behavior emerges in the absence of lattice coupling, the inclusion of interactions with acoustic phonons results in observables such as heat capacity and single-particle scattering rate exhibiting only subleading nonanalytic corrections to dominant Fermi-liquid terms. In this work, we demonstrate that the elastocaloric effect (ECE), the adiabatic temperature change under varying strain, and the thermal expansion deviate from this pattern. Despite lattice coupling weakening the singularity of the ECE, it preserves a dominant temperature dependence that deviates from the prediction one would obtain from Fermi-liquid theory, an effect which we will refer to as an elastocaloric anomaly. By drawing analogies between nematic systems and field-tuned altermagnets, we further show that similar responses are expected for the ECE near altermagnetic QCPs. We classify the types of piezomagnetic couplings and analyze the regimes arising from field-tuned magnetoelastic interactions. Our findings are shown to be consistent with the scaling theory for elastic quantum criticality and they further emphasize the suitability of the ECE as a sensitive probe near QCPs.

Magnetic skyrmions are spatially localized whirls of spin moments in two dimensions, featuring a nontrivial topological charge and a well-defined topological charge density. We demonstrate that the quantum dynamics of magnetic skyrmions is governed by a dipole conservation law associated with the topological charge, akin to that in fracton theories of excitations with constrained mobility. The dipole conservation law enables a natural definition of the collective coordinate to specify the skyrmion’s position, which ultimately leads to a greatly simplified equation of motion in the form of the Thiele equation. In this formulation, the skyrmion mass, whose existence is often debated, actually vanishes. As a result, an isolated skyrmion is intrinsically pinned to be immobile and cannot move at a constant velocity. In a spin-wave theory, we show that such dynamics corresponds to a precise cancellation between a highly nontrivial motion of the quasiclassical skyrmion spin texture and a cloud of quantum fluctuations in the form of spin waves. Given this quenched kinetic energy of quantum skyrmions, we identify close analogies to the bosonic quantum Hall problem. In particular, the topological charge density is shown to obey the Girvin-MacDonald-Platzman algebra that describes neutral modes of the lowest Landau level in the fractional quantum Hall problem. Consequently, the conservation of the topological dipole suggests that magnetic skyrmion materials offer a promising platform for exploring fractonic phenomena with close analogies to fractional quantum Hall states.

The universality class of the Mott metal-insulator transition in electronic systems strongly coupled to lattice degrees of freedom has been the subject of recent debate. While transport scaling exponents as well as critical slowing down of resistance fluctuations point towards Ising-type criticality, a strong involvement of lattice elasticity suggests a mean-field scenario instead. We investigate the low-frequency resistance noise in model system kappa-(ET)2Cu[N(CN)2]Cl (kappa-Cl)-selected because it is known to exhibit critical elasticity-tuned to the Mott end point by hydrostatic pressure. Contrary to previous reports for the related, deuterated kappa compound, we do not find any indication of a critical slowing down, but observe a strong and anisotropic change of the relative resistance noise level in the metallic compared to the insulating phase. We speculate within framework of isostructural criticality that a critical slowing down might emerge in the presence of structural disorder.

Competing magnetic interactions may stabilize smooth magnetization textures that can be characterized by a topological winding number. Such textures, which are spatially localized within a two-dimensional plane, are commonly known as skyrmions. On the classical level, their significance for fundamental science and their potential for applications, ranging from spintronic devices to unconventional computation platforms, have been intensively investigated in recent years. This Colloquium considers quantum effects associated with skyrmion textures: their theoretical origins, the experimental and material challenges associated with their detection, and the promise of exploiting them for quantum operations. Starting with classical skyrmions, we discuss their magnon and electron excitations and show how hybrid architectures offer new platforms for engineering quantum orders, including topological superconductivity. We then focus on the quantization of the skyrmion texture itself and formulate the long-time skyrmion dynamics in terms of collective coordinates. Next, we discuss the quantization of helicity and phenomena of macroscopic quantum tunneling: key concepts that fundamentally distinguish quantum skyrmions from their classical counterparts. Looking ahead, we propose material classes suitable for the realization of skyrmions in quantum spin systems and identify device architectures with the promise of achieving quantum operations. We close by addressing the advances in experimental methods which will be a prerequisite for resolving the quantum aspects of topological spin patterns, sensing their local dynamical response, and achieving their predicted functionalities in magnetic systems.

Topological magnon bands enable uni-directional edge transport without backscattering, enhancing the robustness of magnonic circuits and providing a novel platform for exploring quantum transport phenomena. Magnetic skyrmion lattices, in particular, host a manifold of topological magnon bands with multipole character and non-reciprocal dispersions. These modes have been explored already in the short and long wavelength limit, but previously employed techniques were unable to access intermediate wavelengths comparable to inter-skyrmion distances. Here, we report the detection of such magnons with wavevectors ∣q∣ ≃ 48 rad μm−1 in the metastable skyrmion lattice phase of the bulk chiral magnet Cu2OSeO3 using Brillouin light scattering microscopy. Thanks to its high sensitivity and broad bandwidth various multipole excitation modes could be resolved over a wide magnetic field regime. Besides the known counterclockwise, breathing and clockwise modes with dipole character, quantitative comparison of frequencies and spectral weights to theoretical predictions enabled the additional identification of a quadrupole mode and, possibly, a sextupole mode. Our work highlights the potential of skyrmionic phases for the design of magnonic devices exploiting topological magnon states at GHz frequencies. Topological magnon bands in magnetic skyrmion lattices offer robust, unidirectional edge transport, crucial for advancing magnonic circuits and quantum transport studies. Here, Brillouin light scattering microscopy is used to detect intermediate wavelength magnons in Cu2OSeO3, revealing multipole excitation modes with inactive dipole character, including a novel quadrupole mode and, possibly, a sextupole mode, enhancing GHz frequency magnonic device design.

Non-collinear magnetic skyrmion lattices provide novel magnonic functionalities due to their topological magnon bands and asymmetric dispersion relations. Magnon excitations with intermediate wavelengths comparable to inter-skyrmion distances are particularly interesting but largely unexplored so far due to experimental challenges. Here, we report the detection of such magnons with wavevectors q $\simeq$ 48 rad/um in the metastable skyrmion lattice phase of the bulk chiral magnet Cu$_2$OSeO$_3$ using micro-focused Brillouin light scattering microscopy. Thanks to its high sensitivity and broad bandwidth we resolved various excitation modes of a single skyrmion lattice domain over a wide magnetic field regime. Besides the known modes with dipole character, quantitative comparison of frequencies and spectral weights to theoretical predictions enabled the identification of a quadrupole mode and observation of signatures which we attribute to a decupole and a sextupole mode. Our combined experimental and theoretical work highlights that skyrmionic phases allow for the design of magnonic devices exploiting topological magnon bands.

We show that an interacting electronic system with a single ordinary or extended Van Hove point, which crosses the Fermi energy, is unstable against triplet superconductivity. The pairing mechanism is unconventional. There is no Cooper instability. Instead, pairing is due to the divergence of the density of states at a Van Hove point, leading to a superconducting quantum critical point at a finite detuning from the Van Hove point. The transition temperature is universally determined by the exponent governing the divergence of the density of states. Enhancing this exponent drastically increases Tc. The Cooper pair wave function has a non-monotonic momentum dependence with a steep slope near the gap nodes. In the absence of spin-orbit coupling, pairing fluctuations suppress a 2e spin-triplet state, but allow pairs of triplets to condense into a charge-4e singlet state at a temperature of similar order as our result.

The nanoscopic magnetic texture forming in a monolayer of iron on the (111) surface of iridium, Fe/Ir(111), is spatially modulated and uniaxially incommensurate with respect to the crystallographic periodicities. As a consequence, a low-energy magnetic excitation is expected that corresponds to the sliding of the texture along the incommensurate direction, i.e., a phason mode, which we explicitly confirm with atomistic spin simulations. Using scanning tunneling microscopy (STM), we succeed to observe this phason mode experimentally. It can be excited by the STM tip, which leads to a random telegraph noise in the tunneling current that we attribute to the presence of two minima in the phason potential due to the presence of disorder in our sample. This provides the prospect of a floating phase in cleaner samples and, potentially, a commensurate-incommensurate transition as a function of external control parameters.

It is well established that spin-transfer torques exerted by in-plane spin currents give rise to a motion of magnetic skyrmions resulting in a skyrmion Hall effect. In films of finite thickness or in three-dimensional bulk samples the skyrmions extend in the third direction forming a string. We demonstrate that a spin current flowing longitudinally along the skyrmion string instead induces a Goldstone spin wave instability. Our analytical results are confirmed by micromagnetic simulations of both a single string as well as string lattices, suggesting that the instability eventually breaks the strings. A longitudinal current is thus able to melt the skyrmion string lattice via a nonequilibrium phase transition. For films of finite thickness or in the presence of disorder a threshold current will be required, and we estimate the latter assuming weak collective pinning.

The interplay of electronic and structural degrees of freedom in solids is a topic of intense research. More than 60 years ago, Lifshitz discussed a counterintuitive possibility: lattice softening driven by conduction electrons at topological Fermi surface transitions. The effect that he predicted, however, was small and has not been convincingly observed. Using a piezo-based uniaxial pressure cell to tune the ultraclean metal strontium ruthenate while measuring the stress-strain relationship, we reveal a huge softening of the Young's modulus at a Lifshitz transition of a two-dimensional Fermi surface and show that it is indeed driven entirely by the conduction electrons of the relevant energy band.

We have charted the phase diagram of epitaxial MnSi films grown on Si(111) by magnetometry, differential susceptibility, extended X-ray absorption fine structure, planar Hall, polarised neutron reflectometry and small-angle neutron scattering [1-3].Our experimental results are supported by micromagnetic simulations, which jointly reveal a magnetic phase diagram dominated by a field-induced cascade of single-Q soliton layers.The soliton layers are stabilized through the applied field which modifies a zero-field, out-of-plane propagating helix with λ = 11.5 nm.Field and temperature history provide specific routes for the nucleation of the distinct soliton phases, comprising of four-, three-, two-, and single-soliton layers depending on the field strength.At low temperatures (T < 10 K) a discrete phase regime can be discerned unambiguously in the susceptibility, which may be attributed to the irreversibility of the two-soliton and single-soliton regimes.These observations provide insights into the integral role of magnetic anisotropy and dimensionality on the low-temperature phase diagram of thin film MnSi.

The stability of a quantum critical point in the $O(N)$ universality class with respect to an elastic coupling, that preserves $O(N)$ symmetry, is investigated for isotropic elasticity in the framework of the renormalization group (RG) close to the upper critical dimension $d=3-\epsilon$. With respect to the Wilson-Fisher fixed point, we find that the elastic coupling is relevant in the RG sense for $1\leq N \leq 4$, and the crystal becomes microscopically unstable, i.e., a sound velocity vanishes at a finite value of the correlation length $\xi$. For $N > 4$, an additional fixed point emerges that is located at a finite value of the dimensionless elastic coupling. This fixed point is repulsive and separates the flow to weak and strong elastic coupling. As the fixed point is approached the sound velocity is found to vanish only asymptotically as $\xi \to \infty$ such that the crystal remains microscopically stable for any finite value of $\xi$. The fixed point structure we find for the quantum problem is distinct from the classical counterpart in $d=4-\epsilon$, where the crystal always remains microscopically stable for finite $\xi$.

We present important use cases and limitations when considering results obtained from cluster perturbation theory (CPT). CPT combines the solutions of small individual clusters of an infinite lattice system with the Bloch theory of conventional band theory to provide an approximation for the Green’s function in the thermodynamic limit. To this end, we are investigating single-band and multi-band Hubbard models in 1D and 2D systems. A special interest is taken in the supposed pseudogap regime of the 2D square lattice at half-filling and intermediate interaction strength ( U ≤ 3t ) as well as the metal–insulator transition. We point out that the finite-size level spacing of the cluster limits the resolution of spectral features within CPT. This restricts the investigation of asymptotic properties of the metal–insulator transition, as it would require much larger cluster sizes that are beyond computational capabilities.

Charge carriers in an engineered bilayer Mott insulator are predicted to form tightly bound, mobile pairs, glued together by string excitations of the antiferromagnetic order - a scenario that can be tested with quantum gas microscopy experiments.

In polar magnets, such as GaV 4 S 8 , GaV 4 Se 8 and VOSe 2 O 5 , modulated magnetic phases namely the cycloidal and the Néel-type skyrmion lattice states were identified over extended temperature ranges, even down to zero Kelvin. Our combined small-angle neutron scattering and magnetization study shows the robustness of the Néel-type magnetic modulations also against magnetic fields up to 2 T in the polar GaMo 4 S 8 . In addition to the large upper critical field, enhanced spin-orbit coupling stabilize cycloidal, Néel skyrmion lattice phases with sub-10 nm periodicity and a peculiar distribution of the magnetic modulation vectors. Moreover, we detected an additional single-q state not observed in any other polar magnets. Thus, our work demonstrates that non-centrosymmetric magnets with 4 d and 5 d electron systems may give rise to various highly compressed modulated states.

We report on the low-temperature thermal expansion and magnetostriction of the single-impurity quadrupolar Kondo candidate Y1-xPrxIr2Zn20. In the dilute limit, we find a quadrupolar strain that possesses a singular dependence on temperature T, epsilon(u) similar to H(2)log(1/T), for a small but finite magnetic field H. Together with the previously reported anomalous specific heat C, this implies a quadrupolar Gruneisen ratio Gamma(u) = partial derivative(T)epsilon(u)/C similar to H-2/[T(2)log(1/T)] whose divergence for finite H is consistent with the scenario of a quadrupolar Kondo effect. In addition, we find a singular behavior of the isotropic strain epsilon(B) in zero magnetic field resulting in a divergence of both the volume thermal expansion and the volume Gruneisen parameter. We speculate that this behavior might be also induced by putative Kondo correlations via elastic anharmonicities or static strain disorder.

The motion of a spin excitation across topologically nontrivial magnetic order exhibits a deflection that is analogous to the effect of the Lorentz force on an electrically charged particle in an orbital magnetic field. We used polarized inelastic neutron scattering to investigate the propagation of magnons (i.e., bosonic collective spin excitations) in a lattice of skyrmion tubes in manganese silicide. For wave vectors perpendicular to the skyrmion tubes, the magnon spectra are consistent with the formation of finely spaced emergent Landau levels that are characteristic of the fictitious magnetic field used to account for the nontrivial topological winding of the skyrmion lattice. This provides evidence of a topological magnon band structure in reciprocal space, which is borne out of the nontrivial real-space topology of a magnetic order.