Dynamic transition and Galilean relativity of current-driven skyrmions.

The coupling of conduction electrons and magnetic textures leads to quantum transport phenomena described by the language of emergent electromagnetic fields1-3. For magnetic skyrmions, spin-swirling particle-like objects, an emergent magnetic field is produced by their topological winding4-6, resulting in the conduction electrons exhibiting the topological Hall effect (THE)7. When the skyrmion lattice (SkL) acquires a drift velocity under conduction electron flow, an emergent electric field is also generated8,9. The resulting emergent electrodynamics dictate the magnitude of the THE by the relative motion of SkL and conduction electrons. Here we report the emergent electrodynamics induced by SkL motion in Gd2PdSi3, facilitated by its giant THE10,11. With increasing current excitation, we observe the dynamic transition of the SkL motion from the pinned to creep regime and finally to the flow regime, in which the THE is totally suppressed. We argue that the Galilean relativity required for the total cancellation of the THE may be generically recovered in the flow regime, even in complex multiband systems such as the present compound. Moreover, the observed THE voltages are large enough to enable real-time measurement of the SkL velocity-current profile, which shows the inertial-like motion of the SkL in the creep regime, appearing as the current hysteresis of the skyrmion velocity.

Confined antiskyrmion motion driven by electric current excitations.

Current-driven dynamics of topological spin textures, such as skyrmions and antiskyrmions, have garnered considerable attention in condensed matter physics and spintronics. As compared with skyrmions, the current-driven dynamics of their antiparticles - antiskyrmions - remain less explored due to the increased complexity of antiskyrmions. Here, we design and employ fabricated microdevices of a prototypical antiskyrmion host, (Fe0.63Ni0.3Pd0.07)3P, to allow in situ current application with Lorentz transmission electron microscopy observations. The experimental results and related micromagnetic simulations demonstrate current-driven antiskyrmion dynamics confined within stripe domains. Under nanosecond-long current pulses, antiskyrmions exhibit directional motion along the stripe regardless of the current direction, while the antiskyrmion velocity is linearly proportional to the current density. Significantly, the antiskyrmion mobility could be enhanced when the current flow is perpendicular to the stripe direction. Our findings provide novel and reliable insights on dynamical antiskyrmions and their potential implications on spintronics.

Bloch Point Quadrupole Constituting Hybrid Topological Strings Revealed with Electron Holographic Vector Field Tomography.

Topological magnetic (anti)skyrmions are robust string-like objects heralded as potential components in next-generation topological spintronics devices due to their low-energy manipulability via stimuli such as magnetic fields, heat, and electric/thermal current. While these 2D topological objects are widely studied, intrinsically 3D electron-spin real-space topology remains less explored despite its prevalence in bulky magnets. 2D-imaging studies reveal peculiar vortex-like contrast in the core regions of spin textures present in antiskyrmion-hosting thin plate magnets with S4 crystal symmetry, suggesting a more complex 3D real-space structure than the 2D model suggests. Here, holographic vector field electron tomography captures the 3D structure of antiskyrmions in a single-crystal, precision-doped (Fe0.63Ni0.3Pd0.07)3P (FNPP) lamellae at room temperature and zero field. These measurements reveal hybrid string-like solitons composed of skyrmions with topological number W = -1 on the lamellae's surfaces and an antiskyrmion (W = + 1) connecting them. High-resolution images uncover a Bloch point quadrupole (four magnetic (anti)monopoles that are undetectable in 2D imaging) which enables the observed lengthwise topological transitions. Numerical calculations corroborate the stability of hybrid strings over their conventional (anti)skyrmion counterparts. Hybrid strings result in topological tuning, a tunable topological Hall effect, and the suppression of skyrmion Hall motion, disrupting existing paradigms within spintronics.

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).

Heat current-driven topological spin texture transformations and helical q-vector switching.

The use of magnetic states in memory devices has a history dating back decades, and the experimental discovery of magnetic skyrmions and subsequent demonstrations of their control via magnetic fields, heat, and electric/thermal currents have ushered in a new era for spintronics research and development. Recent studies have experimentally discovered the antiskyrmion, the skyrmion's antiparticle, and while several host materials have been identified, control via thermal current remains elusive. In this work, we use thermal current to drive the transformation between skyrmions, antiskyrmions and non-topological bubbles, as well as the switching of helical states in the antiskyrmion-hosting ferromagnet (Fe0.63Ni0.3Pd0.07)3P at room temperature. We discover that a temperature gradient [Formula: see text] drives a transformation from antiskyrmions to non-topological bubbles to skyrmions while under a magnetic field and observe the opposite, unidirectional transformation from skyrmions to antiskyrmions at zero-field, suggesting that the antiskyrmion, more so than the skyrmion, is robustly metastable at zero field.

Spin-Lattice and Magnetoelectric Couplings Enhanced by Orbital Degrees of Freedom in Polar Multiferroic Semiconductors.

Orbital degrees of freedom mediating an interaction between spin and lattice were predicted to raise strong magnetoelectric effect, i.e., to realize an efficient coupling between magnetic and ferroelectric orders. However, the effect of orbital fluctuations has been considered only in a few magnetoelectric materials, as orbital-degeneracy driven Jahn-Teller effect rarely couples to polarization. Here, we explore the spin-lattice coupling in multiferroic Swedenborgites with mixed valence and Jahn-Teller active transition metal ions on a stacked triangular and Kagome lattice using infrared and dielectric spectroscopy. On one hand, in CaBaM_{4}O_{7} (M=Co, Fe), we observe a strong magnetic-order-induced shift in the phonon frequencies and a corresponding large change in the dielectric response. Remarkably, as an unusual manifestation of the spin-phonon coupling, the spin fluctuations reduce the phonon lifetime by one order of magnitude at the magnetic phase transitions. On the other hand, lattice vibrations, dielectric response, and electric polarization show no variation at the Néel temperature of CaBaFe_{2}Co_{2}O_{7}, which is built up by orbital singlet ions. Our results provide a showcase for orbital degrees of freedom enhanced magnetoelectric coupling via the example of Swedenborgites.

Positive temperature coefficient of the thermal conductivity above room temperature in a perovskite cobaltite.

The thermal conductivity above room temperature is investigated for LaCoO3-based materials showing spin-state and insulator-metal crossovers. A positive temperature coefficient (PTC) of the thermal conductivity is observed during the insulator-metal crossover around 500 K. Our analysis indicates that the phononic thermal transport is also enhanced in addition to the electronic contribution as the insulator-metal crossover takes place. The enhancement of the phononic component is ascribed to the reduction of the incoherent local lattice distortion coupled with the spin/orbital state of each Co3+ ion, which is induced by the enhanced spin-state fluctuation between low and excited spin-states. Moreover, fine tunability for the PTC of the thermal conductivity is demonstrated via doping hole-type carriers into LaCoO3. The observed enhancement ratio of the thermal conductivity κ T (773 K) / κ T (323 K) = 2.6 in La0.95Sr0.05CoO3 is the largest value among oxide materials which exhibit a PTC of their thermal conductivity above room temperature. The thermal rectification ratio is estimated to reach 61% for a hypothetical thermal diode consisting of La0.95Sr0.05CoO3 and LaGaO3, the latter of which is a typical band insulator. These results indicate that utilizing spin-state and orbital degrees of freedom in strongly correlated materials is a useful strategy for tuning thermal transport properties, especially for designing thermal diodes.

Real-Space Observations of Three-Dimensional Antiskyrmions and Skyrmion Strings.

Nanometric topological spin textures, such as skyrmions (Sks) and antiskyrmions (antiSks), have attracted much attention recently. However, most studies have focused on two-dimensional spin textures in films with inherent or synthetic antisymmetric spin-exchange interaction, termed Dzyaloshinskii-Moriya interaction, although three-dimensional (3D) topological spin textures, such as antiSks composed of alternating Bloch- and Néel-type spin spirals, chiral bobbers carrying emergent magnetic monopoles, and deformed Sk strings, are ubiquitous. To elucidate these textures, we have developed a 3D nanometric magnetic imaging technique, tomographic Lorentz transmission electron microscopy (TEM). The approach enables the visualization of the 3D shape of magnetic objects and their 3D vector field mapping. Here we report 3D vector field maps of deformed Sk-strings and antiSk using the technique. This research approach will lead to discoveries and understanding of fertile 3D magnetic structures in a broad class of magnets, providing insight into 3D topological magnetism.

Small-angle neutron scattering study of mesoscale magnetic disordering and skyrmion phase suppression in the frustrated chiral magnet Co6.75Zn6.75Mn6.5.

Co-Zn-Mn chiral cubic magnets display versatile magnetic skyrmion phases, including equilibrium phases stable far above and far below room temperature, and the facile creation of robust far-from-equilibrium skyrmion states. In this system, compositional disorder and magnetic frustration are key ingredients that have profound effects on the chiral magnetism. Reported here are studies of the magnetism in Co6.75Zn6.75Mn6.5 by magnetometry, small-angle neutron scattering (SANS), magnetic diffuse neutron scattering and Lorentz transmission electron microscopy (LTEM). While features in magnetometry and LTEM often give standard indications for skyrmion formation, they are not readily observed from the measurements on this system. Instead, skyrmion lattice correlations are only revealed by SANS, and they are found to form an orientationally disordered structure in a minority fraction of the sample. The majority fraction of the sample always displays orientationally disordered helical spin correlations, which undergo further disordering along the radial direction on cooling below the critical temperature (T c ≃ 102 K). The near-complete suppression of the skyrmion phase, and the process of disordering on cooling, are attributed to competing magnetic interactions that dominate over the ferromagnetic interaction expected to favour chiral magnetism in this system. These competing interactions start to develop above T c and become further enhanced towards low temperatures. The present observations of co-existing and disordered magnetic correlations over multiple length scales are not unique to Co6.75Zn6.75Mn6.5 but are seemingly common to the family of Co-Zn-Mn compounds with finite Mn, and their accurate description presents a challenge for theoretical modelling. In addition, this study highlights a need for neutron instrumentation capable of the comprehensive measurement of magnetic correlations over expanded ranges of momentum transfer in such multiple-length-scale magnets.

Real-space determination of the isolated magnetic skyrmion deformation under electric current flow.

The manipulation and control of electron spins, the fundamental building blocks of magnetic domains and spin textures, are at the core of spintronics. Of particular interest is the effect of the electric current on topological magnetic skyrmions, such as the current-induced deformation of isolated skyrmions. The deformation has consequences ranging from perturbed dynamics to modified packing configurations. In this study, we measured the current-driven real-space deformation of isolated, pinned skyrmions within Co10Zn10 at room temperature. We observed that the skyrmions are surprisingly soft, readily deforming during electric current application into an elliptical shape with a well-defined deformation axis (semimajor axis). We found that this axis rotates unidirectionally toward the current direction irrespective of electric current polarity and that the elliptical deformation reverses back upon current termination. We quantified the average distortion δ, which increased by ∼90% during the largest applied current density |j| = 8.46 ×109 A/m2 when compared with the skyrmion's intrinsic shape ([Formula: see text]). Additionally, we demonstrated an approximately 120% average skyrmion core size expansion during current application, highlighting the skyrmions' inherent topological protection. This evaluation of in situ electric current-induced skyrmion deformation paints a clearer picture of spin-polarized electron-skyrmion interactions and may prove essential in designing spintronic devices.

Magnetoelectric transfer of a domain pattern.

The utility of ferroic materials is determined by the formation of domains and their poling behavior under externally applied fields. For multiferroics, which exhibit several types of ferroic order at once, it is also relevant how the domains of the coexisting ferroic states couple and what kind of functionality this might involve. In this work, we demonstrate the reversible transfer of a domain pattern between magnetization and electric-polarization space in the multiferroic Dy0.7Tb0.3FeO3. A magnetic field transfers a ferromagnetic domain pattern into an identical ferroelectric domain pattern while erasing it at its magnetic origin. Reverse transfer completes the cycle. To assess the generality of our experiment, we elaborate on its conceptual origin and aspects of application.

Entropy-Assisted, Long-Period Stacking of Honeycomb Layers in an AlB2-Type Silicide.

Configurational entropy can impact crystallization processes, tipping the scales between structures of nearly equal internal energy. Using alloyed single crystals of Gd2PdSi3 in the AlB2-type structure, we explore the formation of complex layer sequences made from alternating, two-dimensional triangular and honeycomb slabs. A four-period and an eight-period stacking sequence are found to be very close in internal energy, the latter being favored by entropy associated with covering the full configuration space of interlayer bonds. Possible consequences of polytype formation on magnetism in Gd2PdSi3 are discussed.

Formation and Control of Zero-Field Antiskyrmions in Confining Geometries.

Magnetic skyrmions and antiskyrmions have attracted much interest owing to their topological features and spintronic functionalities. In contrast to skyrmions, the generation of antiskyrmions relies on tunning both the magnitude and direction of the external magnetic field. Here, it is reported that antiskyrmions can be efficiently created via quenching and robustly persist at zero field in the Fe1.9 Ni0.9 Pd0.2 P magnet with the S4 -symmetry. It is demonstrated that well-ordered antiskyrmions form in a square lattice in a confining micrometer-scale square geometry, while the antiskyrmion lattice distorts in triangular, circular, or rotated-square geometry; the distortion depends on the relative configuration between sample edges and the two q-vectors arising from the anisotropic Dzyaloshinskii-Moriya interaction, in good agreement with micromagnetic simulations. It is also characterized transformations from antiskyrmions to skyrmions and nontopological bubbles at different directions and values of external field. These results demonstrate a roadmap for generating and controlling antiskyrmions in a confining geometry.

Doping Control of Magnetic Anisotropy for Stable Antiskyrmion Formation in Schreibersite (Fe,Ni)3 P with S4 symmetry.

Magnetic skyrmions, vortex-like topological spin textures, have attracted much interest in a wide range of research fields from fundamental physics to spintronics applications. Recently, growing attention is also paid to antiskyrmions emerging with opposite topological charge in non-centrosymmetric magnets with D2d or S4 symmetry. In these magnets, complex interplay among anisotropic Dzyaloshinskii-Moriya interaction, uniaxial magnetic anisotropy, and magnetic dipolar interactions generates various magnetic textures. However, the precise role of these magnetic interactions in stabilizing antiskyrmions remains to be elucidated. In this work, the uniaxial magnetic anisotropy of schreibersite (Fe,Ni)3 P with S4 symmetry is controlled by doping and its impact on the stability of antiskyrmions is investigated. The authors' magnetometry study, supported by ferromagnetic resonance spectroscopy, shows that the variation of the Ni content and slight doping with 4d transition metals considerably change the magnetic anisotropy. In particular, doping with Pd induces easy-axis anisotropy, giving rise to formation of antiskyrmions, while a temperature-induced spin reorientation is observed in an Rh-doped compound. In combination with Lorentz transmission electron microscopy and micromagnetic simulations, the stability of antiskyrmion as functions of uniaxial anisotropy and demagnetization energy is quantitatively analyzed, and demonstrated that subtle balance between them is necessary to stabilize the antiskyrmions.

Dynamic transition of current-driven single-skyrmion motion in a room-temperature chiral-lattice magnet.

Driving and controlling single-skyrmion motion promises skyrmion-based spintronic applications. Recently progress has been made in moving skyrmionic bubbles in thin-film heterostructures and low-temperature chiral skyrmions in the FeGe helimagnet by electric current. Here, we report the motion tracking and control of a single skyrmion at room temperature in the chiral-lattice magnet Co9Zn9Mn2 using nanosecond current pulses. We have directly observed that the skyrmion Hall motion reverses its direction upon the reversal of skyrmion topological number using Lorentz transmission electron microscopy. Systematic measurements of the single-skyrmion trace as a function of electric current reveal a dynamic transition from the static pinned state to the linear flow motion via a creep event, in agreement with the theoretical prediction. We have clarified the role of skyrmion pinning and evaluated the intrinsic skyrmion Hall angle and the skyrmion velocity in the course of the dynamic transition. Our results pave a way to skyrmion applications in spintronic devices.

Large Hall and Nernst responses from thermally induced spin chirality in a spin-trimer ferromagnet.

The long-range order of noncoplanar magnetic textures with scalar spin chirality (SSC) can couple to conduction electrons to produce an additional (termed geometrical or topological) Hall effect. One such example is the Hall effect in the skyrmion lattice state with quantized SSC. An alternative route to attain a finite SSC is via the spin canting caused by thermal fluctuations in the vicinity of the ferromagnetic ordering transition. Here, we report that for a highly conducting ferromagnet with a two-dimensional array of spin trimers, the thermally generated SSC can give rise to a gigantic geometrical Hall conductivity even larger than the intrinsic anomalous Hall conductivity of the ground state. We also demonstrate that the SSC induced by thermal fluctuations leads to a strong response in the Nernst effect. A comparison of the sign and magnitude of fluctuation-Nernst and Hall responses in fundamental units indicates the need for a momentum-space picture to model these thermally induced signals.

Nano-to-micro spatiotemporal imaging of magnetic skyrmion's life cycle.

Magnetic skyrmions are self-organized topological spin textures that behave like particles. Because of their fast creation and typically long lifetime, experimental verification of skyrmion's creation/annihilation processes has been challenging. Here, we successfully track skyrmion dynamics in defect-introduced Co9Zn9Mn2 by using pump-probe Lorentz transmission electron microscope. Following the nanosecond photothermal excitation, we resolve 160-nm skyrmion's proliferation at <1 ns, contraction at 5 ns, drift from 10 ns to 4 µs, and coalescence at ~5 µs. These motions relay the multiscale arrangement and relaxation of skyrmion clusters in a repeatable cycle of 20 kHz. Such repeatable dynamics of skyrmions, arising from the weakened but still persistent topological protection around defects, enables us to visualize the whole life of the skyrmions and demonstrates the possible high-frequency manipulations of topological charges brought by skyrmions.

Intrinsic coupling between spatially-separated surface Fermi-arcs in Weyl orbit quantum Hall states.

Topological semimetals hosting bulk Weyl points and surface Fermi-arc states are expected to realize unconventional Weyl orbits, which interconnect two surface Fermi-arc states on opposite sample surfaces under magnetic fields. While the presence of Weyl orbits has been proposed to play a vital role in recent observations of the quantum Hall effect even in three-dimensional topological semimetals, actual spatial distribution of the quantized surface transport has been experimentally elusive. Here, we demonstrate intrinsic coupling between two spatially-separated surface states in the Weyl orbits by measuring a dual-gate device of a Dirac semimetal film. Independent scans of top- and back-gate voltages reveal concomitant modulation of doubly-degenerate quantum Hall states, which is not possible in conventional surface orbits as in topological insulators. Our results evidencing the unique spatial distribution of Weyl orbits provide new opportunities for controlling the novel quantized transport by various means such as external fields and interface engineering.

Room-temperature antiskyrmions and sawtooth surface textures in a non-centrosymmetric magnet with S4 symmetry.

Topological spin textures have attracted much attention both for fundamental physics and spintronics applications. Among them, antiskyrmions possess a unique spin configuration with Bloch-type and Néel-type domain walls owing to anisotropic Dzyaloshinskii-Moriya interaction in the non-centrosymmetric crystal structure. However, antiskyrmions have thus far only been observed in a few Heusler compounds with D2d symmetry. Here we report a new material, Fe1.9Ni0.9Pd0.2P, in a different symmetry class (S4), in which antiskyrmions exist over a wide temperature range that includes room temperature, and transform into skyrmions on changing magnetic field and lamella thickness. The periodicity of magnetic textures greatly depends on the crystal thickness, and domains with anisotropic sawtooth fractals were observed at the surface of thick crystals and attributed to the interplay between the dipolar interaction and the Dzyaloshinskii-Moriya interaction as governed by crystal symmetry. Our findings provide an arena in which to study antiskyrmions, and should stimulate further research on topological spin textures and their applications.

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.