Task-adaptive physical reservoir computing.

Reservoir computing is a neuromorphic architecture that may offer viable solutions to the growing energy costs of machine learning. In software-based machine learning, computing performance can be readily reconfigured to suit different computational tasks by tuning hyperparameters. This critical functionality is missing in 'physical' reservoir computing schemes that exploit nonlinear and history-dependent responses of physical systems for data processing. Here we overcome this issue with a 'task-adaptive' approach to physical reservoir computing. By leveraging a thermodynamical phase space to reconfigure key reservoir properties, we optimize computational performance across a diverse task set. We use the spin-wave spectra of the chiral magnet Cu2OSeO3 that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to different computational reservoir responses. The task-adaptive approach is applicable to a wide variety of physical systems, which we show in other chiral magnets via above (and near) room-temperature demonstrations in Co8.5Zn8.5Mn3 (and FeGe).

Emergent electromagnetic induction beyond room temperature.

Emergent electromagnetic induction based on electrodynamics of noncollinear spin states may enable dramatic miniaturization of inductor elements widely used in electric circuits, yet the research is still in its infancy and many issues must be resolved toward its application. One such problem is how to increase working temperature to room temperature, and possible thermal agitation effects on the quantum process of the emergent induction are unknown. We report here large emergent electromagnetic induction achieved around and above room temperature, making use of a few tens of micrometer-sized devices based on the high-temperature (up to 330 K) and short-period (≤ 3 nm) spin-spiral states of a metallic helimagnet. The observed inductance value L and its sign are observed to vary to a large extent, depending not only on the spin-helix structure controlled by temperature and applied magnetic field but also on the applied current density. The present finding on room-temperature operation and possible sign control of L may provide a step toward realizing microscale quantum inductors on the basis of emergent electromagnetism in spin-helix states.

Magnetic Skyrmion Materials.

Skyrmion, a concept originally proposed in particle physics half a century ago, can now find the most fertile field for its applicability, that is, the magnetic skyrmion realized in helimagnetic materials. The spin swirling vortex-like texture of the magnetic skyrmion can define the particle nature by topology; that is, all the constituent spin moments within the two-dimensional sheet wrap the sphere just one time. Such a topological nature of the magnetic skyrmion can lead to extraordinary metastability via topological protection and the driven motion with low electric-current excitation, which may promise future application to spintronics. The skyrmions in the magnetic materials frequently show up as the crystal lattice form, e.g., hexagonal lattice, but sometimes as isolated or independent particles. These skyrmions in magnets were initially found in acentric magnets, such as chiral, polar, and bilayered magnets endowed with antisymmetric spin exchange interaction, while the skyrmion host materials have been explored in a broader family of compounds including centrosymmetric magnets. This review describes the materials science and materials chemistry of magnetic skyrmions using the classification scheme of the skyrmion forming microscopic mechanisms. The emergent phenomena and functions mediated by skyrmions are described, including the generation of emergent magnetic and electric field by statics and dynamics of skrymions and the inherent magnetoelectric effect. The other important magnetic topological defects in two or three dimensions, such as biskyrmions, antiskyrmions, merons, and hedgehogs, are also reviewed in light of their interplay with the skyrmions.

Detection of Topological Spin Textures via Nonlinear Magnetic Responses.

Topologically nontrivial spin textures, such as skyrmions and dislocations, display emergent electrodynamics and can be moved by spin currents over macroscopic distances. These unique properties and their nanoscale size make them excellent candidates for the development of next-generation race-track memory and unconventional computing. A major challenge for these applications and the investigation of nanoscale magnetic structures in general is the realization of suitable detection schemes. We study magnetic disclinations, dislocations, and domain walls in FeGe and reveal pronounced responses that distinguish them from the helimagnetic background. A combination of magnetic force microscopy (MFM) and micromagnetic simulations links the response to the local magnetic susceptibility, that is, characteristic changes in the spin texture driven by the MFM tip. On the basis of the findings, which we explain using nonlinear response theory, we propose a read-out scheme using superconducting microcoils, presenting an innovative approach for detecting topological spin textures and domain walls in device-relevant geometries.

Real-Space Observation of Topological Defects in Extended Skyrmion-Strings.

Exotic topological spin textures such as emergent magnetic monopole/anti-monopoles (hedgehog/anti-hedgehog) in the metastable extended skyrmion-strings attract much attention to the fundamental physics owing to their novel electromagnetic properties. However, the direct imaging of such spin textures is lacking. Here, we report the real-space observation of emergent magnetic monopoles involved in extended skyrmion-strings by Lorentz transmission electron microscopy (TEM) in combination with micromagnetic simulations. The in-plane extended skyrmion-strings are observed directly by Lorentz TEM to accompany the topological hedgehog-like defect, where the skyrmion-string terminates or merges with another skyrmion-string, as well as the surface-related defects where skyrmion-string bends 90° and ends on the surface. We also demonstrate the transformation of a metastabilized lattice of out-of-plane short skyrmion-strings into an in-plane array of extended skyrmion-strings by tuning the magnitude of oblique fields in a room-temperature helimagnet, revealing the stability of such topological spin textures and the possibility to control them.

Topological Magnetic Phase in the Candidate Weyl Semimetal CeAlGe.

We report the discovery of topological magnetism in the candidate magnetic Weyl semimetal CeAlGe. Using neutron scattering we find this system to host several incommensurate, square-coordinated multi-k[over →] magnetic phases below T_{N}. The topological properties of a phase stable at intermediate magnetic fields parallel to the c axis are suggested by observation of a topological Hall effect. Our findings highlight CeAlGe as an exceptional system for exploiting the interplay between the nontrivial topologies of the magnetization in real space and Weyl nodes in momentum space.

Current-Driven Motion of Domain Boundaries between Skyrmion Lattice and Helical Magnetic Structure.

To utilize magnetic skyrmions, nanoscale vortex-like magnetic structures, experimental elucidation of their dynamics against current application in various circumstances such as in confined structure and mixture of different magnetic phases is indispensable. Here, we investigate the current-induced dynamics of the coexistence state of magnetic skyrmions and helical magnetic structure in a thin plate of B20-type helimagnet FeGe in terms of in situ real-space observation using Lorentz transmission electron microscopy. Current pulses with various heights and widths were applied, and the change of the magnetic domain distribution was analyzed using a machine-learning technique. The observed average driving direction of the two-magnetic-state domain boundary is opposite to the applied electric current, indicating ferromagnetic s-d exchange coupling in the spin-transfer torque mechanism. The evaluated driving distance tends to increase with increasing the pulse duration time, current density (>1 × 109 A/m2), and sample temperature, providing valuable information about hitherto unknown current-induced dynamics of the skyrmion-lattice ensemble.

Real-Space Observation of Short-Period Cubic Lattice of Skyrmions in MnGe.

Three-dimensional forms of skyrmion aggregate, such as a cubic lattice of skyrmions, are anticipated to exist, yet their direct observations remain elusive. Here, we report real-space observations of spin configurations of the skyrmion-antiskyrmion cubic-lattice in MnGe with a very short period (∼3 nm) and hence endowed with the largest skyrmion number density. The skyrmion lattices parallel to the {100} atomic lattices are directly observed using high-resolution Lorentz transmission electron microscopes, simultaneously with underlying atomic-lattice fringes.

Spontaneous Vortex-Antivortex Pairs and Their Topological Transitions in a Chiral-Lattice Magnet.

The spontaneous formation and topological transitions of vortex-antivortex pairs have implications for a broad range of emergent phenomena, for example, from superconductivity to quantum computing. Unlike magnets exhibiting collinear spin textures, helimagnets with noncollinear spin textures provide unique opportunities to manipulate topological forms such as (anti)merons and (anti)skyrmions. However, it is challenging to achieve multiple topological states and their interconversion in a single helimagnet due to the topological protection for each state. Here, the on-demand creation of multiple topological states in a helimagnet Fe0.5 Co0.5 Ge, including a spontaneous vortex pair of meron with topological charge N = -1/2 and antimeron with N = 1/2, and a vortex-antivortex bundle, that is, a bimeron (meron pair) with N = -1 is reported. The mutual transformation between skyrmions and bimerons with respect to the competitive effects of magnetic field and magnetic shape anisotropy is demonstrated. It is shown that electric currents drive the individual bimerons to form their connecting assembly and then into a skyrmion lattice. These findings signify the feasibility of designing topological states and offer new insights into the manipulation of noncollinear spin textures for potential applications in various fields.

Enhanced emergent electromagnetic inductance in Tb5Sb3 due to highly disordered helimagnetism.

In helimagnetic metals, ac current-driven spin motions can generate emergent electric fields acting on conduction electrons, leading to emergent electromagnetic induction (EEMI). Recent experiments reveal the EEMI signal generally shows a strongly current-nonlinear response. In this study, we investigate the EEMI of Tb5Sb3, a short-period helimagnet. Using small angle neutron scattering we show that Tb5Sb3 hosts highly disordered helimagnetism with a distribution of spin-helix periodicity. The current-nonlinear dynamics of the disordered spin helix in Tb5Sb3 indeed shows up as the nonlinear electrical resistivity (real part of ac resistivity), and even more clearly as a nonlinear and huge EEMI (imaginary part of ac resistivity) response. The magnitude of the EEMI reaches as large as several tens of µH for Tb5Sb3 devices on the scale of several tens of µm, originating to noncollinear spin textures possibly even without long-range helimagnetic order.

Real-space observation of skyrmion lattice in helimagnet MnSi thin samples.

Observing and characterizing the spin distributions on a nanometer scale are of vital importance for understanding nanomagnetism and its application to spintronics. The magnetic structure in MnSi thin samples prepared from a bulk, which undergoes a transition from a helix to a skyrmion lattice, was investigated by in situ observation using Lorentz microscopy. Stripe domains were observed at zero applied field below 22.5 K. A skyrmion lattice with 6-fold symmetry in real space appeared when a field of 0.18 T was applied normal to the film plane. The lattice constant was estimated to be 18 nm, almost identical to the helical period. In comparison with the marginally stable skyrmion phase in a bulk sample, the skyrmion phase was stable over a wide range of temperatures and magnetic fields in the thin samples.

Realization and Current-Driven Dynamics of Fractional Hopfions and Their Ensembles in a Helimagnet FeGe.

3D topological spin textures-hopfions-are predicted in helimagnetic systems but are not experimentally confirmed thus far. By utilizing an external magnetic field and electric current in the present study, 3D topological spin textures are realized, including fractional hopfions with nonzero topological index, in a skyrmion-hosting helimagnet FeGe. Microsecond current pulses are employed to control the dynamics of the expansion and contraction of a bundle composed of a skyrmion and a fractional hopfion, as well as its current-driven Hall motion. This research approach has demonstrated the novel electromagnetic properties of fractional hopfions and their ensembles in helimagnetic systems.

A Noble-Metal-Free Spintronic System with Proximity-Enhanced Ferromagnetic Topological Surface State of FeSi above Room Temperature.

Strongly spin-orbit coupled states at metal interfaces, topological insulators, and 2D materials enable efficient electric control of spin states, offering great potential for spintronics. However, there are still materials challenges to overcome, including the integration into advanced silicon electronics and the scarce resources of constituent heavy elements of those materials. Through magneto-transport measurements and first-principles calculations, here robust spin-orbit coupling (SOC)-induced properties of a ferromagnetic topological surface state in FeSi and their controllability via hybridization with adjacent materials are demonstrated. In comparison to the case of its naturally oxidized surface, the ferromagnetic transition temperature is greatly increased beyond room temperature and the effective SOC strength is almost doubled at the surface in proximity to a wide-bandgap fluoride insulator. Those enhanced magnetic properties enable room-temperature magnetization switching, being applicable to spin-orbit torque based spintronic devices. Realization of strong SOC in the noble-metal-free silicon-based compound will accelerate spintronic applications.

Transition between distinct hybrid skyrmion textures through their hexagonal-to-square crystal transformation in a polar magnet.

Magnetic skyrmions, topological vortex-like spin textures, garner significant interest due to their unique properties and potential applications in nanotechnology. While they typically form a hexagonal crystal with distinct internal magnetisation textures known as Bloch- or Néel-type, recent theories suggest the possibility for direct transitions between skyrmion crystals of different lattice structures and internal textures. To date however, experimental evidence for these potentially useful phenomena have remained scarce. Here, we discover the polar tetragonal magnet EuNiGe3 to host two hybrid skyrmion phases, each with distinct internal textures characterised by anisotropic combinations of Bloch- and Néel-type windings. Variation of the magnetic field drives a direct transition between the two phases, with the modification of the hybrid texture concomitant with a hexagonal-to-square skyrmion crystal transformation. We explain these observations with a theory that includes the key ingredients of momentum-resolved Ruderman-Kittel-Kasuya-Yosida and Dzyaloshinskii-Moriya interactions that compete at the observed low symmetry magnetic skyrmion crystal wavevectors. Our findings underscore the potential of polar magnets with rich interaction schemes as promising for discovering new topological magnetic phases.

Emergent zero-field anomalous Hall effect in a reconstructed rutile antiferromagnetic metal.

The anomalous Hall effect (AHE) that emerges in antiferromagnetic metals shows intriguing physics and offers numerous potential applications. Magnets with a rutile crystal structure have recently received attention as a possible platform for a collinear-antiferromagnetism-induced AHE. RuO2 is a prototypical candidate material, however the AHE is prohibited at zero field by symmetry because of the high-symmetry [001] direction of the Néel vector at the ground state. Here, we show AHE at zero field in Cr-doped rutile, Ru0.8Cr0.2O2. The magnetization, transport and density functional theory calculations indicate that appropriate doping of Cr at Ru sites reconstructs the collinear antiferromagnetism in RuO2, resulting in a rotation of the Néel vector from [001] to [110] while maintaining a collinear antiferromagnetic state. The AHE with vanishing net moment in the Ru0.8Cr0.2O2 exhibits an orientation dependence consistent with the [110]-oriented Hall vector. These results demonstrate that material engineering by doping is a useful approach to manipulate AHE in antiferromagnetic metals.

Dislocation-Driven Relaxation Processes at the Conical to Helical Phase Transition in FeGe.

The formation of topological spin textures at the nanoscale has a significant impact on the long-range order and dynamical response of magnetic materials. We study the relaxation mechanisms at the conical-to-helical phase transition in the chiral magnet FeGe. By combining macroscopic ac susceptibility measurement, surface-sensitive magnetic force microscopy, and micromagnetic simulations, we demonstrate how the motion of magnetic topological defects, here edge dislocations, impacts the local formation of a stable helimagnetic spin structure. Although the simulations show that the edge dislocations can move with a velocity up to 100 m/s through the helimagnetic background, their dynamics are observed to disturb the magnetic order on the time scale of minutes due to randomly distributed pinning sites. The results corroborate the substantial impact of dislocation motions on the nanoscale spin structure in chiral magnets, revealing previously hidden effects on the formation of helimagnetic domains and domain walls.

Emergence of spin-orbit coupled ferromagnetic surface state derived from Zak phase in a nonmagnetic insulator FeSi.

FeSi is a nonmagnetic narrow-gap insulator, exhibiting peculiar charge and spin dynamics beyond a simple band structure picture. Those unusual features have been attracting renewed attention from topological aspects. Although the surface conduction was demonstrated according to size-dependent resistivity in bulk crystals, its topological characteristics and consequent electromagnetic responses remain elusive. Here, we demonstrate an inherent surface ferromagnetic-metal state of FeSi thin films and its strong spin-orbit coupling (SOC) properties through multiple characterizations of two-dimensional conductance, magnetization, and spintronic functionality. Terminated covalent bonding orbitals constitute the polar surface state with momentum-dependent spin textures due to Rashba-type spin splitting, as corroborated by unidirectional magnetoresistance measurements and first-principles calculations. As a consequence of the spin-momentum locking, nonequilibrium spin accumulation causes magnetization switching. These surface properties are closely related to the Zak phase of the bulk band topology. Our findings propose another route to explore noble metal­free materials for SOC-based spin manipulation.

Giant anomalous Hall effect from spin-chirality scattering in a chiral magnet.

The electrical Hall effect can be significantly enhanced through the interplay of the conduction electrons with magnetism, which is known as the anomalous Hall effect (AHE). Whereas the mechanism related to band topology has been intensively studied towards energy efficient electronics, those related to electron scattering have received limited attention. Here we report the observation of giant AHE of electron-scattering origin in a chiral magnet MnGe thin film. The Hall conductivity and Hall angle, respectively, reach [Formula: see text] Ω-1 cm-1 and [Formula: see text]% in the ferromagnetic region, exceeding the conventional limits of AHE of intrinsic and extrinsic origins, respectively. A possible origin of the large AHE is attributed to a new type of skew-scattering via thermally excited spin-clusters with scalar spin chirality, which is corroborated by the temperature-magnetic-field profile of the AHE being sensitive to the film-thickness or magneto-crystalline anisotropy. Our results may open up a new platform to explore giant AHE responses in various systems, including frustrated magnets and thin-film heterostructures.

Bloch Lines Constituting Antiskyrmions Captured via Differential Phase Contrast.

Much scientific capital has been directed toward exotic magnetic spin textures called Bloch lines, that is, Néel-type line boundaries within domain walls, because their geometry promises high-density magnetic storage. While predicted to arise in high-anisotropy magnets, bulk soft magnets, and thin films with in-plane magnetization, Bloch lines also constitute magnetic antiskyrmions, that is, topological antiparticles of skyrmions. Most domain walls occur as Bloch-type or Néel-type, in which the magnetization rotates parallel or perpendicular to the domain wall across its profile, respectively. The Bloch lines' Néel-type rotation and their minute size make them difficult to directly measure. This work utilizes differential phase contrast (DPC) scanning transmission electron microscopy (STEM) to measure the in-plane magnetization of Bloch lines within antiskyrmions emergent in a non-centrosymmetric Heusler magnet with D2d symmetry, Mn1.4 Pt0.9 Pd0.1 Sn, in addition to Bloch-type skyrmions in an FeGe magnet with B20-type crystal structure to benchmark the DPC technique. Both in-focus measurement and identification of Bloch lines at the antiskyrmion's corners are provided.

Current-induced dynamics of skyrmion strings.

Dynamics of string-like objects is an important issue in a broad range of physical systems, including vortex lines in superconductors, viscoelastic polymers, and superstrings in elementary particle physics. In noncentrosymmetric magnets, string forms of magnetic skyrmions are present as topological spin objects, and their current-induced dynamics has recently attracted intense interest. We show in the chiral magnet MnSi that the current-induced deformation dynamics of skyrmion strings results in transport response associated with the real-space Berry phase. Prominent nonlinear Hall signals emerge above the threshold current only in the skyrmion phase. We clarify the mechanism for these nonlinear Hall signals by adopting spin density wave picture to describe the moving skyrmion lattice; deformation of skyrmion strings occurs in an asymmetric manner due to the Dzyaloshinskii-Moriya interaction, which leads to the nonreciprocal nonlinear Hall response originating from an emergent electromagnetic field. This finding reveals the dynamical nature of string-like objects and consequent transport outcomes in noncentrosymmetric systems.