Unusual Hall effect anomaly in MnSi under pressure

Influence of the Hall-bar geometry on texture-induced topological spin transport in two-dimensional Rashba spin-orbit ferromagnets

While the recent prediction and observation of magnetic skyrmions bears inspiring promise for next-generation spintronic devices, how to detect and track their position becomes an important issue. In this work, we investigate the spin transport in a two-dimensional magnetic nanoribbon with the Hall-bar geometry in the presence of Rashba spin-orbit coupling and magnetic skyrmions. We employ the Kwant tight-binding code to compute the Hall conductance and local spin-polarized current density. We consider two versions of the model: One with single skyrmion and one with two separate skyrmions. It is found that the size and position of the skyrmions strongly modulate the Hall conductance near the Hall-bar position. The geometry of the Hall bar also has a strong influence on the Hall conductance of the system. With the decreasing of the width of Hall leads, the peak of Hall conductance becomes sharper. We also show the spatial distribution of the spin-polarized current density around a skyrmion located at different positions. We extend this study toward two separate skyrmions, where the Hall conductance also reveals a sizable dependence on the position of the skyrmions and their distance. Our numerical analysis offers the possibility of electrically detecting the skyrmion position, which could have potential applications in ultrahigh-density storage design.

Topological Spin Textures: Basic Physics and Devices

In the face of escalating modern data storage demands and the constraints of Moore's Law, exploring spintronic solutions, particularly the devices based on magnetic skyrmions, has emerged as a promising frontier in scientific research. Since the first experimental observation of skyrmions, topological spin textures have been extensively studied for their great potential as efficient information carriers in spintronic devices. However, significant challenges have emerged alongside this progress. This review aims to synthesize recent advances in skyrmion research while addressing the major issues encountered in the field. Additionally, current research on promising topological spin structures in addition to skyrmions is summarized. Beyond 2D structures, exploration also extends to 1D magnetic solitons and 3D spin textures. In addition, a diverse array of emerging magnetic materials is introduced, including antiferromagnets and 2D van der Waals magnets, broadening the scope of potential materials hosting topological spin textures. Through a systematic examination of magnetic principles, topological categorization, and the dynamics of spin textures, a comprehensive overview of experimental and theoretical advances in the research of topological magnetism is provided. Finally, both conventional and unconventional applications are summarized based on spin textures proposed thus far. This review provides an outlook on future development in applied spintronics.

Metamagnetic multiband Hall effect in Ising antiferromagnet ErGa2

Frustrated rare-earth-based intermetallics provide a promising platform for emergent magnetotransport properties through exchange coupling between conduction electrons and localized rare-earth magnetic moments. Metamagnetism, the abrupt change of magnetization under an external magnetic field, is a signature of first-order magnetic phase transitions; recently, metamagnetic transitions in frustrated rare earth intermetallics have attracted interest for their accompanying nontrivial spin structures (e.g., skyrmions) and associated nonlinear and topological Hall effects (THE). Here, we present metamagnetism-induced Hall anomalies in single-crystalline ErGa2, which recalls features arising from the THE but wherein the strong Ising-type anisotropy of Er moments prohibits noncoplanar spin structures. We show that the observed anomalies are neither due to anomalous Hall effect nor THE; instead, can be accounted for via 4f-5d interactions which produce a band-dependent mobility modulation. This leads to a pronounced multiband Hall response across the magnetization process-a metamagnetic multiband Hall effect that resembles a topological-Hall-like response but without nontrivial origins. The present findings may be of general relevance in itinerant metamagnetic systems regardless of coplanar/noncoplanar nature of spins and are important for the accurate identification of Hall signals due to emergent magnetic 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.

Current-sensitive Hall effect in a chiral-orbital-current state

Chiral orbital currents (COC) underpin a novel colossal magnetoresistance in ferrimagnetic Mn3Si2Te6. Here we report the Hall effect in the COC state which exhibits the following unprecedented features: (1) A sharp, current-sensitive peak in the magnetic field dependence of the Hall resistivity, and (2) A current-sensitive scaling relation between the Hall conductivity σxy and the longitudinal conductivity σxx, namely, σxy ∝ σxxα with α reaching up to 5, which is exceptionally large compared to α ≤ 2 typical of all solids. The novel Hall responses along with a current-sensitive carrier density and a large Hall angle of 15% point to a giant, current-sensitive Hall effect that is unique to the COC state. Here, we show that a magnetic field induced by the fully developed COC combines with the applied magnetic field to exert the greatly enhanced transverse force on charge carriers, which dictates the COC Hall responses.

Room temperature chirality switching and detection in a helimagnetic MnAu2 thin film

Helimagnetic structures, in which the magnetic moments are spirally ordered, host an internal degree of freedom called chirality corresponding to the handedness of the helix. The chirality seems quite robust against disturbances and is therefore promising for next-generation magnetic memory. While the chirality control was recently achieved by the magnetic field sweep with the application of an electric current at low temperature in a conducting helimagnet, problems such as low working temperature and cumbersome control and detection methods have to be solved in practical applications. Here we show chirality switching by electric current pulses at room temperature in a thin-film MnAu2 helimagnetic conductor. Moreover, we have succeeded in detecting the chirality at zero magnetic fields by means of simple transverse resistance measurement utilizing the spin Berry phase in a bilayer device composed of MnAu2 and a spin Hall material Pt. These results may pave the way to helimagnet-based spintronics.

Writing and Detecting Topological Charges in Exfoliated Fe5-xGeTe2

Fe5-xGeTe2 is a promising two-dimensional (2D) van der Waals (vdW) magnet for practical applications, given its magnetic properties. These include Curie temperatures above room temperature, and topological spin textures─TST (both merons and skyrmions), responsible for a pronounced anomalous Hall effect (AHE) and its topological counterpart (THE), which can be harvested for spintronics. Here, we show that both the AHE and THE can be amplified considerably by just adjusting the thickness of exfoliated Fe5-xGeTe2, with THE becoming observable even in zero magnetic field due to a field-induced unbalance in topological charges. Using a complementary suite of techniques, including electronic transport, Lorentz transmission electron microscopy, and micromagnetic simulations, we reveal the emergence of substantial coercive fields upon exfoliation, which are absent in the bulk, implying thickness-dependent magnetic interactions that affect the TST. We detected a "magic" thickness t ≈ 30 nm where the formation of TST is maximized, inducing large magnitudes for the topological charge density (∼6.45 × 1020 cm-2), and the concomitant anomalous (ρxyA,max ≃22.6 μΩ cm) and topological (ρxyu,T 1≃5 μΩ cm) Hall resistivities at T ≈ 120 K. These values for ρxyA,max and ρxyu,T are higher than those found in magnetic topological insulators and, so far, the largest reported for 2D magnets. The hitherto unobserved THE under zero magnetic field could provide a platform for the writing and electrical detection of TST aiming at energy-efficient devices based on vdW ferromagnets.

Optimizing skyrmionium movement and stability via stray magnetic fields in trilayer nanowire constructs

Skyrmioniums, known for their unique transport and regulatory properties, are emerging as potential cornerstones for future data storage systems. However, the stability of skyrmionium movement faces considerable challenges due to the skyrmion Hall effect, which is induced by deformation. In response, our research introduces an innovative solution: we utilized micro-magnetic simulations to create a sandwiched trilayer nanowire structure augmented with a stray magnetic field. This combination effectively guides the skyrmionium within the ferromagnetic (FM) layer. Our empirical investigations reveal that the use of a stray magnetic field not only reduces the size of the skyrmionium but also amplifies its stability. This dual-effect proficiently mitigates the deformation of skyrmionium movement and boosts their thermal stability. We find these positive outcomes are most pronounced at a particular intensity of the stray magnetic field. Importantly, the required stray magnetic field can be generated using a heavy metal (HM1) layer of suitable thickness, rendering the practical application of this approach plausible in real-world experiments. Additionally, we analyze the functioning mechanism based on the Landau-Lifshitz-Gilbert (LLG) equation and energy variation. We also develop a deep spiking neural network (DSNN), which achieves a remarkable recognition accuracy of 97%. This achievement is realized through supervised learning via the spike timing dependent plasticity rule (STDP), considering the nanostructure as an artificial synapse device that corresponds to the electrical properties of the nanostructure. In conclusion, our study provides invaluable insights for the design of innovative information storage devices utilizing skyrmionium technology. By tackling the issues presented by the skyrmion Hall effect, we outline a feasible route for the practical application of this advanced technology. Our research, therefore, serves as a robust platform for continued investigations in this field.

Magnon thermal Hall effect via emergent SU(3) flux on the antiferromagnetic skyrmion lattice

Complexity of quantum phases of matter is often understood theoretically by using gauge structures, as is recognized by the [Formula: see text] and U(1) gauge theory description of spin liquids in frustrated magnets. Anomalous Hall effect of conducting electrons can intrinsically arise from a U(1) gauge expressing the spatial modulation of ferromagnetic moments or from an SU(2) gauge representing the spin-orbit coupling effect. Similarly, in insulating ferro and antiferromagnets, the magnon contribution to anomalous transports is explained in terms of U(1) and SU(2) fluxes present in the ordered magnetic structure. Here, we report thermal Hall measurements of MnSc2S4 in an applied field up to 14 T, for which we consider an emergent higher rank SU(3) flux, controlling the magnon transport. The thermal Hall coefficient takes a substantial value when the material enters a three-sublattice antiferromagnetic skyrmion phase, which is in agreement with the linear spin-wave theory. In our description, magnons are dressed with SU(3) gauge field, which is a mixture of three species of U(1) gauge fields originating from the slowly varying magnetic moments on these sublattices.

Topological magneto-optical effect from skyrmion lattice

The magnetic skyrmion is a spin-swirling topological object characterized by its nontrivial winding number, holding potential for next-generation spintronic devices. While optical readout has become increasingly important towards the high integration and ultrafast operation of those devices, the optical response of skyrmions has remained elusive. Here, we show the magneto-optical Kerr effect (MOKE) induced by the skyrmion formation, i.e., topological MOKE, in Gd2PdSi3. The significantly enhanced optical rotation found in the skyrmion phase demonstrates the emergence of topological MOKE, exemplifying the light-skyrmion interaction arising from the emergent gauge field. This gauge field in momentum space causes a dramatic reconstruction of the electronic band structure, giving rise to magneto-optical activity ranging up to the sub-eV region. The present findings pave a way for photonic technology based on skyrmionics.

Instability of Magnetic Skyrmion Strings Induced by Longitudinal Spin Currents

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.

Unified theory of the anomalous and topological Hall effects with phase-space Berry curvatures

Spontaneously broken time-reversal symmetry in magnetic materials leads to a Hall response, with a nonzero voltage transverse to an applied current, even in the absence of external magnetic fields. It is common to analyze the Hall resistivity of chiral magnets as the sum of two terms: an anomalous Hall effect arising from spin-orbit coupling and a topological Hall signal coming from skyrmions, which are topologically nontrivial spin textures. The theoretical justification for such a decomposition has long remained an open problem. Using a controlled semiclassical approach that includes all phase-space Berry curvatures, we show that the solution of the Boltzmann equation leads to a Hall resistivity that is just the sum of an anomalous term arising from momentum-space curvature and a topological term related to the real-space curvature. We also present numerically exact results from a Kubo formalism that complement the semiclassical approach.

Distinguishing the Two-Component Anomalous Hall Effect from the Topological Hall Effect

In transport, the topological Hall effect (THE) presents itself as nonmonotonic features (or humps and dips) in the Hall signal and is widely interpreted as a sign of chiral spin textures, like magnetic skyrmions. However, when the anomalous Hall effect (AHE) is also present, the coexistence of two AHEs could give rise to similar artifacts, making it difficult to distinguish between genuine THE with AHE and two-component AHE. Here, we confirm genuine THE with AHE by means of transport and magneto-optical Kerr effect (MOKE) microscopy, in which magnetic skyrmions are directly observed, and find that genuine THE occurs in the transition region of the AHE. In sharp contrast, the artifact "THE" or two-component AHE occurs well beyond the saturation of the "AHE component" (under the false assumption of THE + AHE). Furthermore, we distinguish artifact "THE" from genuine THE by three methods: (1) minor loops, (2) temperature dependence, and (3) gate dependence. Minor loops of genuine THE with AHE are always within the full loop, while minor loops of the artifact "THE" may reveal a single loop that cannot fit into the "AHE component". In addition, the temperature or gate dependence of the artifact "THE" may also be accompanied by a polarity change of the "AHE component", as the nonmonotonic features vanish, while the temperature dependence of genuine THE with AHE reveals no such change. Our work may help future researchers to exercise caution and use these methods for careful examination in order to ascertain the genuine THE.

Spin-hedgehog-derived electromagnetic effects in itinerant magnets

In itinerant magnets, the indirect exchange coupling of Ruderman-Kittel-Kasuya-Yosida type is known to stabilize incommensurate spin spirals, whereas an account of higher order spin interactions favors the formation of a noncoplanar magnetic texture. This is manifested by the finite Berry phase the conduction electrons accumulate when their spins follow this texture, leading thus to the topological Hall effect. We herein utilize the effective spin model with bilinear-biquadratic exchange interactions for studying the formation of the magnetic hedgehog lattice, that represents a periodic array of magnetic anti- and monopoles and has been recently observed in the B20-type compounds, in a three-dimensional itinerant magnet. As opposed to widely used Monte Carlo simulations, we employ a neural-network-based approach for exploring the ground state spin configuration in a noncentrosymmetric crystal structure. Further, we address the topological Hall conductivity, associated with nonzero scalar spin chirality, in the itinerant magnet due to the coupling to the spin hedgehog lattice, and provide the evidence of a magneto-optic Kerr effect.

Low-Energy Excitations of Skyrmion Crystals in a Centrosymmetric Kondo-Lattice Magnet: Decoupled Spin-Charge Excitations and Nonreciprocity

We theoretically study spin and charge excitations of skyrmion crystals stabilized by conduction-electron-mediated magnetic interactions via spin-charge coupling in a centrosymmetric Kondo-lattice model by large-scale spin-dynamics simulations combined with the kernel polynomial method. We reveal clear segregation of spin and charge excitation channels and nonreciprocal nature of the spin excitations governed by the Fermi-surface geometry, which are unique to the skyrmion crystals in centrosymmetric itinerant hosts and can be a source of novel physical phenomena.

Emergent Topological Hall Effect from Exchange Coupling in Ferromagnetic Cr2Te3/Noncoplanar Antiferromagnetic Cr2Se3 Bilayers

The topological Hall effect has been observed in magnetic materials of complex spin structures or bilayers of trivial magnets and strong spin-orbit-coupled systems. In view of current attention on dissipationless topological electronics, the occurrence of the topological Hall effect in new systems or by an unexpected mechanism is fascinating. Here, we report a robust topological Hall effect generated in bilayers of a ferromagnet and a noncoplanar antiferromagnet, from the interfacial Dzyaloshinskii-Moriya interaction due to the exchange coupling of magnetic layers. Molecular beam epitaxy has been utilized to fabricate heterostructures of a ferromagnetic metal Cr₂Te₃ and a noncoplanar antiferromagnet Cr₂Se₃. A significant topological Hall effect at low temperature implies the development of nontrivial spin chirality, and density functional theory calculations explain the correlation of the Dzyaloshinskii-Moriya interaction increase and inversion symmetry breaking at the interface. The presence of noncoplanar ordering in the antiferromagnet plays a pivotal role in producing the topological Hall effect. Our results suggest that the exchange coupling in ferromagnet/noncoplanar antiferromagnet bilayers could be an alternative mechanism toward topologically protected magnetic structures.

Slowdown of photoexcited spin dynamics in the non-collinear spin-ordered phases in skyrmion host GaV4S8

Formation of magnetic order alters the character of spin excitations, which then affects transport properties. We investigate the photoexcited ultrafast spin dynamics in different magnetic phases in Néel-type skyrmion host GaV₄S₈ with time-resolved magneto-optical Kerr effect experiments. The coherent spin precession, whose amplitude is enhanced in the skyrmion-lattice phase, shows a signature of phase coexistence across the magnetic phase transitions. The incoherent spin relaxation dynamics slows down by a factor of two in the skyrmion-lattice/cycloid phases, indicating significant decrease in thermal conductivity triggered by a small change of magnetic field. The slow heat diffusion in the skyrmion-lattice/cycloid phases is attributed to the stronger magnon scattering off the domain walls formed in abundance in the skyrmion-lattice/cycloid phase. These results highlight the impact of spatial spin structure on the ultrafast heat transport in spin systems, providing a useful insight for the step toward ultrafast photocontrol of the magnets with novel spin orders.

Skyrmions are a topological magnetic texture that have garnered considerable interest for various technological applications. Here, Sekiguchi et al. investigate the ultrafast optical response of GaV4S6, and find a significant reduction in the thermal conductivity in the skyrmion phase.

A theory of skyrmion crystal formation

A generic theory about skyrmion crystal (SkX) formation in chiral magnetic thin films and its fascinating thermodynamic behaviours is presented. A chiral magnetic film can have many metastable states with an arbitrary skyrmion density up to a maximal value when the parameter κ, which measures the relative Dzyaloshinskii-Moriya interaction (DMI) strength, is large enough. The lowest energy state of an infinite film is a long zig-zag ramified stripe skyrmion occupying the whole film in the absence of a magnetic field. Under an intermediate field perpendicular to the film, the lowest energy state has a finite skyrmion density. This is why a chiral magnetic film is often in a stripy state at a low field and a SkX only around an optimal field when κ is above a critical value. The lowest energy state is still a stripy helical state no matter with or without a field when κ is below the critical value. The multi-metastable states explain the thermodynamic path dependences of the various metastable states of a film. The decrease of the κ value with the temperature explains why SkXs become metastable at low temperatures in many skyrmion systems. These findings open a new avenue for SkX manipulation and skyrmion-based applications.

Topological Hall effect in SrRuO3thin films and heterostructures

Transition metal oxides hold a wide spectrum of fascinating properties endowed by the strong electron correlations. In 4dand 5doxides, exotic phases can be realized with the involvement of strong spin-orbit coupling (SOC), such as unconventional magnetism and topological superconductivity. Recently, topological Hall effects (THEs) and magnetic skyrmions have been uncovered in SrRuO₃thin films and heterostructures, where the presence of SOC and inversion symmetry breaking at the interface are believed to play a key role. Realization of magnetic skyrmions in oxides not only offers a platform to study topological physics with correlated electrons, but also opens up new possibilities for magnetic oxides using in the low-power spintronic devices. In this review, we discuss recent observations of THE and skyrmions in the SRO film interfaced with various materials, with a focus on the electric tuning of THE. We conclude with a discussion on the directions of future research in this field.

Spin-orbit enabled all-electrical readout of chiral spin-textures

Chirality and topology are intimately related fundamental concepts, which are heavily explored to establish spin-textures as potential magnetic bits in information technology. However, this ambition is inhibited since the electrical reading of chiral attributes is highly non-trivial with conventional current perpendicular-to-plane (CPP) sensing devices. Here we demonstrate from extensive first-principles simulations and multiple scattering expansion the emergence of the chiral spin-mixing magnetoresistance (C-XMR) enabling highly efficient all-electrical readout of the chirality and helicity of respectively one- and two-dimensional magnetic states of matter. It is linear with spin-orbit coupling in contrast to the quadratic dependence associated with the unveiled non-local spin-mixing anisotropic MR (X-AMR). Such transport effects are systematized on various non-collinear magnetic states – spin-spirals and skyrmions – and compared to the uncovered spin-orbit-independent multi-site magnetoresistances. Owing to their simple implementation in readily available reading devices, the proposed magnetoresistances offer exciting and decisive ingredients to explore with all-electrical means the rich physics of topological and chiral magnetic objects.

One challenge for encoding information in chiral spin textures is how to read the information electrically. Here, Lima Fernandes et al. show that chiral spin textures exhibit a magnetoresistance signature which could allow for efficient electric readout of the chirality and helicity.

Behavior of Vortex-Like Inhomogeneities Originating in Magnetic Films with Modulated Uniaxial Anisotropy in a Planar Magnetic Field

This paper investigates the processes of magnetization reversal of a uniaxial ferromagnetic disk containing a columnar defect of the potential well type in perpendicular and planar magnetic fields. The characteristic stages of magnetization reversal of the domain structure of the disk and vortex-like inhomogeneities forming on the defect are determined. The critical fields of their existence are found and an explanation is given for the presence of a significant difference in their values for the perpendicular and planar fields of the defect magnetization reversal. The role of chirality in the behavior of a Bloch-type magnetic skyrmion during the magnetization reversal of a defect in a planar field is shown.

Unveiling the three-dimensional magnetic texture of skyrmion tubes

Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to control their motion has opened a new field of research, skyrmionics, that aims for the usage of skyrmions as information carriers. Further advances in skyrmionics call for a thorough understanding of their three-dimensional (3D) spin texture, skyrmion-skyrmion interactions and the coupling to surfaces and interfaces, which crucially affect skyrmion stability and mobility. Here, we quantitatively reconstruct the 3D magnetic texture of Bloch skyrmions with sub-10-nanometre resolution using holographic vector-field electron tomography. The reconstructed textures reveal local deviations from a homogeneous Bloch character within the skyrmion tubes, details of the collapse of the skyrmion texture at surfaces and a correlated modulation of the skyrmion tubes in FeGe along their tube axes. Additionally, we confirm the fundamental principles of skyrmion formation through an evaluation of the 3D magnetic energy density across these magnetic solitons.

Soft-Magnetic Skyrmions Induced by Surface-State Coupling in an Intrinsic Ferromagnetic Topological Insulator Sandwich Structure

A magnetic skyrmion induced on a ferromagnetic topological insulator (TI) is a real-space manifestation of the chiral spin texture in the momentum space and can be a carrier for information processing by manipulating it in tailored structures. Here, a sandwich structure containing two layers of a self-assembled ferromagnetic septuple-layer TI, Mn(Bi_1-xSb_x)₂Te₄ (MnBST), separated by quintuple layers of TI, (Bi_1-xSb_x)₂Te₃ (BST), is fabricated and skyrmions are observed through the topological Hall effect in an intrinsic magnetic topological insulator for the first time. The thickness of BST spacer layer is crucial in controlling the coupling between the gapped topological surface states in the two MnBST layers to stabilize the skyrmion formation. The homogeneous, highly ordered arrangement of the Mn atoms in the septuple-layer MnBST leads to a strong exchange interaction therein, which makes the skyrmions "soft magnetic". This would open an avenue toward a topologically robust rewritable magnetic memory.

Intrinsic Torques Emerging from Anomalous Velocity in Magnetic Textures

Momentum-space topology of electrons under strong spin-orbit coupling contributes to the electrically induced torques exerting on magnetic textures insensitively to disorder or thermal fluctuation. We present a direct connection between band topology and the torques by classifying the whole torques phenomenologically. As well as the intrinsic anomalous Hall effect, the torques also emerge intrinsically from the anomalous velocity of electrons regardless of a nonequilibrium transport current. We especially point out the intrinsic contribution arising exclusively in magnetic textures, which we call the "topological Hall torque (THT)." The THT emerges in bulk crystals without any interface or surface structures. We numerically demonstrate the enhancement of the THT in comparison with the conventional spin-transfer torque in the bulk metallic ferromagnet, which accounts for the giant current-induced torque measured in ferromagnetic SrRuO_{3}.

Above-ordering-temperature large anomalous Hall effect in a triangular-lattice magnetic semiconductor

While anomalous Hall effect (AHE) has been extensively studied in the past, efforts for realizing large Hall response have been mainly limited within intrinsic mechanism. Lately, however, a theory of extrinsic mechanism has predicted that magnetic scattering by spin cluster can induce large AHE even above magnetic ordering temperature, particularly in magnetic semiconductors with low carrier density, strong exchange coupling, and finite spin chirality. Here, we find out a new magnetic semiconductor EuAs, where Eu²⁺ ions with large magnetic moments form distorted triangular lattice. In addition to colossal magnetoresistance, EuAs exhibits large AHE with an anomalous Hall angle of 0.13 at temperatures far above antiferromagnetic ordering. As also demonstrated by model calculations, observed AHE can be explained by the spin cluster scattering in a hopping regime. Our findings shed light on magnetic semiconductors hosting topological spin textures, developing a field targeting diluted carriers strongly coupled to noncoplanar spin structures.

Phase shift in skyrmion crystals

The magnetic skyrmion crystal is a periodic array of a swirling topological spin texture. Since it is regarded as an interference pattern by multiple helical spin density waves, the texture changes with the relative phase shifts among the constituent waves. Although such a phase degree of freedom is relevant to not only magnetism but also transport properties, its effect has not been elucidated thus far. We here theoretically show that a phase shift in the skyrmion crystals leads to a tetra-axial vortex crystal and a meron-antimeron crystal, both of which show a staggered pattern of the scalar spin chirality and give rise to nonreciprocal transport phenomena without the spin-orbit coupling. We demonstrate that such a phase shift can be driven by exchange interactions between the localized spins, thermal fluctuations, and long-range chirality interactions in spin-charge coupled systems. Our results provide a further diversity of topological spin textures and open a new field of emergent electromagnetism by the phase shift engineering.

Skyrmions are a type of topological spin texture, which can exist as both an isolated state, and as a skyrmion crystal. Here, Hayami et al present a theoretical study of phase shifts in skyrmion crystals, showing how such phase shifts can lead to other crystalline topological spin textures.

Giant Topological Hall Effect in the Noncollinear Phase of Two-Dimensional Antiferromagnetic Topological Insulator MnBi4Te7

Magnetic topological insulators provide an important platform for realizing several exotic quantum phenomena, such as the axion insulating state and the quantum anomalous Hall effect, owing to the interplay between topology and magnetism. MnBi4Te7 is a two-dimensional Z2 antiferromagnetic (AFM) topological insulator with a Néel temperature of ∼13 K. In AFM materials, the topological Hall effect (THE) is observed owing to the existence of nontrivial spin structures. A material with noncollinearity that develops in the AFM phase rather than at the onset of the AFM order is particularly important. In this study, we observed that such an unanticipated THE starts to develop in a MnBi4Te7 single crystal when the magnetic field is rotated away from the easy axis (c-axis) of the system. Furthermore, the THE resistivity reaches a giant value of ∼7 μΩ-cm at 2 K when the angle between the magnetic field and the c-axis is 75°. This value is significantly higher than the values for previously reported systems with noncoplanar structures. The THE can be ascribed to the noncoplanar spin structure resulting from the canted state during the spin-flip transition in the ground AFM state of MnBi4Te7. The large THE at a relatively low applied field makes the MnBi4Te7 system a potential candidate for spintronic applications.

Giant magnetoresistance and topological Hall effect in the EuGa4antiferromagnet

We report on systematic temperature- and magnetic field-dependent studies of the EuGa₄binary compound, which crystallizes in a centrosymmetric tetragonal BaAl₄-type structure with space groupI4/mmm. The electronic properties of EuGa₄single crystals, with an antiferromagnetic (AFM) transition atT_N∼ 16.4 K, were characterized via electrical resistivity and magnetization measurements. A giant nonsaturating magnetoresistance was observed at low temperatures, reaching∼7×104% at 2 K in a magnetic field of 9 T. In the AFM state, EuGa₄undergoes a series of metamagnetic transitions in an applied magnetic field, clearly manifested in its field-dependent electrical resistivity. BelowT_N, in the ∼4-7 T field range, we observe also a clear hump-like anomaly in the Hall resistivity which is part of the anomalous Hall resistivity. We attribute such a hump-like feature to the topological Hall effect, usually occurring in noncentrosymmetric materials known to host topological spin textures (as e.g., magnetic skyrmions). Therefore, the family of materials with a tetragonal BaAl₄-type structure, to which EuGa₄and EuAl₄belong, seems to comprise suitable candidates on which one can study the interplay among correlated-electron phenomena (such as charge-density wave or exotic magnetism) with topological spin textures and topologically nontrivial bands.

Skyrmion crystals in centrosymmetric itinerant magnets without horizontal mirror plane

We theoretically investigate a new stabilization mechanism of a skyrmion crystal (SkX) in centrosymmetric itinerant magnets with magnetic anisotropy. By considering a trigonal crystal system without the horizontal mirror plane, we derive an effective spin model with an anisotropic Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction for a multi-band periodic Anderson model. We find that the anisotropic RKKY interaction gives rise to two distinct SkXs with different skyrmion numbers of one and two depending on a magnetic field. We also clarify that a phase arising from the multiple-Q spin density waves becomes a control parameter for a field-induced topological phase transition between the SkXs. The mechanism will be useful not only for understanding the SkXs, such as that in Gd[Formula: see text]PdSi[Formula: see text], but also for exploring further skyrmion-hosting materials in trigonal itinerant magnets.

Possible Topological Hall Effect above Room Temperature in Layered Cr1.2Te2 Ferromagnet

Topological Hall effect (THE) has been used as a powerful tool to unlock spin chirality in novel magnetic materials. Recent focus has been widely paid to THE and possible chiral spin textures in two-dimensional (2D) layered magnetic materials. However, the room-temperature THE has been barely reported in 2D materials, which hinders its practical applications in 2D spintronics. In this paper, we report a possible THE signal featuring antisymmetric peaks in a wide temperature window up to 320 K in Cr_1.2Te₂, a new quasi-2D ferromagnetic material. The temperature, thickness, and magnetic field dependences of the THE lead to potential spin chirality origin that is associated with the spin canting under external magnetic fields. Our work holds promise for practical applications in future chiral spin-based vdW spintronic devices.

Transverse Transport in Two-Dimensional Relativistic Systems with Nontrivial Spin Textures

Using multiple scattering theory, we show that the generally accepted expression of transverse resistivity in magnetic systems that host skyrmions, given by the linear superposition of the ordinary, the anomalous, and the topological Hall effect, is incomplete and must be amended by an additional term, the "noncollinear" Hall effect (NHE). Its angular form is determined by the magnetic texture, the spin-orbit field of the electrons, and the underlying crystal structure, allowing us to disentangle the NHE from the various other Hall contributions. Its magnitude is proportional to the spin-orbit interaction strength. The NHE is an essential term required for decoding two- and three-dimensional spin textures from transport experiments.

Real-space observation of ferroelectrically induced magnetic spin crystal in SrRuO3

Unusual features in the Hall Resistivity of thin film systems are frequently associated with whirling spin textures such as Skyrmions. A host of recent investigations of Hall Hysteresis loops in SrRuO₃ heterostructures have provided conflicting evidence for different causes for such features. We have constructed an SrRuO₃-PbTiO₃ (Ferromagnetic – Ferroelectric) bilayer that exhibits features in the Hall Hysteresis previously attributed to a Topological Hall Effect, and Skyrmions. Here we show field dependent Magnetic Force Microscopy measurements throughout the key fields where the ‘THE’ presents, revealing the emergence to two periodic, chiral spin textures. The zero-field cycloidal phase, which then transforms into a ‘double-q’ incommensurate spin crystal appears over the appearance of the ‘Topological-like’ Hall effect region, and develop into a ferromagnetic switching regime as the sample reaches saturation, and the ‘Topological-like’ response diminishes. Scanning Tunnelling Electron Microscopy and Density Functional Theory is used to observe and analyse surface inversion symmetry breaking and confirm the role of an interfacial Dzyaloshinskii–Moriya interaction at the heart of the system.

There is an ongoing debate in the origin of unusual bumps in the resistive Hall measurements in SrRuO3 systems. Here, the authors analyze surface inversion symmetry breaking and confirm the role of an interfacial Dzyaloshinskii–Moriya interaction at the heart of the system, revealing a magnetic spin crystal emergent across the unusual bumps.

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.

Unconventional Transverse Transport above and below the Magnetic Transition Temperature in Weyl Semimetal EuCd_{2}As_{2}

As exemplified by the growing interest in the quantum anomalous Hall effect, the research on topology as an organizing principle of quantum matter is greatly enriched from the interplay with magnetism. In this vein, we present a combined electrical and thermoelectrical transport study on the magnetic Weyl semimetal EuCd_{2}As_{2}. Unconventional contribution to the anomalous Hall and anomalous Nernst effects were observed both above and below the magnetic transition temperature of EuCd_{2}As_{2}, indicating the existence of significant Berry curvature. EuCd_{2}As_{2} represents a rare case in which this unconventional transverse transport emerges both above and below the magnetic transition temperature in the same material. The transport properties evolve with temperature and field in the antiferromagnetic phase in a different manner than in the paramagnetic phase, suggesting different mechanisms to their origin. Our results indicate EuCd_{2}As_{2} is a fertile playground for investigating the interplay between magnetism and topology, and potentially a plethora of topologically nontrivial phases rooted in this interplay.

Skyrmion Phase in MnSi Thin Films Grown on Sapphire by a Conventional Sputtering

Topologically protected chiral skyrmions are an intriguing spin texture that has attracted much attention because of fundamental research and future spintronic applications. MnSi with a non-centrosymmetric structure is a well-known material hosting a skyrmion phase. To date, the preparation of MnSi crystals has been investigated by using special instruments with an ultrahigh vacuum chamber. Here, we introduce a facile way to grow MnSi films on a sapphire substrate using a relatively low vacuum environment of conventional magnetron sputtering. Although the as-grown MnSi films have a polycrystalline nature, a stable skyrmion phase in a broad range of temperatures and magnetic fields is observed via magnetotransport properties including phenomenological scaling analysis of the Hall resistivity contribution. Our findings provide not only a general way to prepare the materials possessing skyrmion phases but also insight into further research to stimulate more degrees of freedom in our inquisitiveness.

Interface-induced sign reversal of the anomalous Hall effect in magnetic topological insulator heterostructures

The Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as the consequence of non-zero Berry curvature in momentum space. Here, we fabricate TI/magnetic TI heterostructures and find that the sign of the AH effect in the magnetic TI layer can be changed from being positive to negative with increasing the thickness of the top TI layer. Our first-principles calculations show that the built-in electric fields at the TI/magnetic TI interface influence the band structure of the magnetic TI layer, and thus lead to a reconstruction of the Berry curvature in the heterostructure samples. Based on the interface-induced AH effect with a negative sign in TI/V-doped TI bilayer structures, we create an artificial “topological Hall effect”-like feature in the Hall trace of the V-doped TI/TI/Cr-doped TI sandwich heterostructures. Our study provides a new route to create the Berry curvature change in magnetic topological materials that may lead to potential technological applications.

Berry curvature connects to exotic electronic phases hence it provides important insights to understand quantum materials. Here, the authors report sign change of the anomalous Hall effect resulted from Berry curvature change at the interface of a topological insulator/magnetic topological insulator heterostructure.

Magnon Landau Levels and Spin Responses in Antiferromagnets

We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose a model of an AFM topological insulator of magnons. In the long wavelength limit, the Landau levels induced by the inhomogeneous Dzyaloshinskii-Moriya interaction exhibit relativistic physics described by the Klein-Gordon equation. The spin Nernst response due to the formation of magnonic Landau levels is compared to similar topological responses in skyrmion and vortex-antivortex crystal phases of AFM insulators. Our studies show that AFM insulators exhibit rich physics associated with topological magnon excitations.

Localization to delocalization transition in a double stranded helical geometry: effects of conformation, transverse electric field and dynamics

Conformational effect on electronic localization is critically investigated for the first time considering a double-stranded helical geometry (DSHG) subjected to an electric field. In the presence of electric field the DSHG behaves like a correlated disordered system whose site potentials are modulated in a cosine form like the well known Aubry-André-Harper model. The potential distribution can be modulated further by changing the orientation of the incident field. A similar kind of cosine modulation is also introduced in the inter-strand hopping integrals of the DSHG. Suitably adjusting the orientation of the electric field, we can achieve fully extended energy eigenstates or completely localized ones or a mixture of both. The effects of short-range and long-range hopping integrals along with the chirality on localization are thoroughly studied. Finally, we inspect the role of helical dynamics to make the model more realistic. The interplay between the helical geometry and electric field may open up several notable features of electronic localization and can be verified by using different chiral molecules.

Spin Wave Radiation by a Topological Charge Dipole

The use of spin waves (SWs) as data carriers in spintronic and magnonic logic devices offers operation at low power consumption, free of Joule heating. Nevertheless, the controlled emission and propagation of SWs in magnetic materials remains a significant challenge. Here, we propose that skyrmion-antiskyrmion bilayers form topological charge dipoles and act as efficient sub-100 nm SW emitters when excited by in-plane ac magnetic fields. The propagating SWs have a preferred radiation direction, with clear dipole signatures in their radiation pattern, suggesting that the bilayer forms a SW antenna. Bilayers with the same topological charge radiate SWs with spiral and antispiral spatial profiles, enlarging the class of SW patterns. We demonstrate that the characteristics of the emitted SWs are linked to the topology of the source, allowing for full control of the SW features, including their amplitude, preferred direction of propagation, and wavelength.

Topological Nernst Effect of the Two-Dimensional Skyrmion Lattice

The topological Hall effect (THE) and its thermoelectric counterpart, the topological Nernst effect (TNE), are hallmarks of the skyrmion lattice phase (SkL). We observed the giant TNE of the SkL in centrosymmetric Gd_{2}PdSi_{3}, comparable in magnitude to the largest anomalous Nernst signals in ferromagnets. Significant enhancement (suppression) of the THE occurs when doping electrons (holes) to Gd_{2}PdSi_{3}. On the electron-doped side, the topological Hall conductivity approaches the characteristic threshold ∼1000  (Ω cm)^{-1} for the intrinsic regime. We use the filling-controlled samples to confirm Mott's relation between TNE and THE and discuss the importance of Gd-5d orbitals for transport in this compound.

Spin filtering and spin separation in 2D materials by topological spin Hall effect

The needs of high speed performance electronic devices for various applications require novel materials and new physical phenomena. For these purposes we propose to study new physical effects based on electron scattering on magnetic skyrmions and vortices distributed in a 2D ferromagnetic material. We show that the topological spin Hall effect can be efficiently employed for the filtering, switching, and separation of spin currents. For some values of the parameters (conduction electron concentrations, and skyrmion/vortex sizes) it is possible to separate Hall currents for different electron spin projections as it is like for different carrier charges (electrons and holes) in the normal Hall effect. The calculations are performed using the Boltzmann kinetic equation for the nonequilibrium distribution function and the Lippmann-Schwinger equation for the transition matrix in the whole range of the adiabaticity parameter. The spin filtering due to the skyrmion/vortex scattering can be several orders of magnitude more efficient in the narrow range of the electron concentrations than that of the ordinary ferromagnetic spin polarization in spintronics.

Interfacial tuning of chiral magnetic interactions for large topological Hall effects in LaMnO3/SrIrO3 heterostructures

Chiral interactions in magnetic systems can give rise to rich physics manifested, for example, as nontrivial spin textures. The foremost interaction responsible for chiral magnetism is the Dzyaloshinskii-Moriya interaction (DMI), resulting from inversion symmetry breaking in the presence of strong spin-orbit coupling. However, the atomistic origin of DMIs and their relationship to emergent electrodynamic phenomena, such as topological Hall effect (THE), remain unclear. Here, we investigate the role of interfacial DMIs in 3d-5d transition metal-oxide-based LaMnO₃/SrIrO₃ superlattices on THE from a chiral spin texture. By additively engineering the interfacial inversion symmetry with atomic-scale precision, we directly link the competition between interfacial collinear ferromagnetic interactions and DMIs to an enhanced THE. The ability to control the DMI and resulting THE points to a pathway for harnessing interfacial structures to maximize the density of chiral spin textures useful for developing high-density information storage and quantum magnets for quantum information science.

Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures

The quantum anomalous Hall (QAH) effect is a consequence of non-zero Berry curvature in momentum space. The QAH insulator harbours dissipation-free chiral edge states in the absence of an external magnetic field. However, the topological Hall (TH) effect, a hallmark of chiral spin textures, is a consequence of real-space Berry curvature. Here, by inserting a topological insulator (TI) layer between two magnetic TI layers, we realized the concurrence of the TH effect and the QAH effect through electric-field gating. The TH effect is probed by bulk carriers, whereas the QAH effect is characterized by chiral edge states. The appearance of the TH effect in the QAH insulating regime is a consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii-Moriya interaction and occurs during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures provides a platform for proof-of-concept dissipationless spin-textured spintronic applications.

Topological Hall Effect in Traditional Ferromagnet Embedded with Black-Phosphorus-Like Bismuth Nanosheets

Topological Hall effect is an abnormal Hall response arising from the scalar spin chirality of chiral magnetic textures. Up to now, such an effect is only observed in certain special materials, but rarely in traditional ferromagnets. In this work, we have implemented the molecular beam epitaxy technique to successfully embed black-phosphorus-like bismuth nanosheets with strong spin-orbit coupling into the bulk of chromium telluride Cr₂Te₃, as evidenced by atomically resolved energy dispersive X-ray spectroscopy mapping. Distinctive from pristine Cr₂Te₃, these Bi-embedded Cr₂Te₃ epitaxial films exhibit not only pronounced topological Hall effects, but also magnetoresistivity anomalies and differential magnetic susceptibility plateaus. All these experimental features point to the possible emergence of magnetic skyrmions in Bi-embedded Cr₂Te₃, which is further supported by our numerical simulations with all input parameters obtained from the first-principle calculations. Therefore, our work demonstrates a new efficient way to induce skyrmions in ferromagnets, as well as the topological Hall effect by embedding nanosheets with strong spin-orbit couplings.

Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications

The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last decades. In this topical review, we mainly review and discuss key results and findings in skyrmion research since the first experimental observation of magnetic skyrmions in 2009. We particularly focus on the theoretical, computational and experimental findings and advances that are directly relevant to the spintronic applications based on magnetic skyrmions, i.e. their writing, deleting, reading and processing driven by magnetic field, electric current and thermal energy. We then review several potential applications including information storage, logic computing gates and non-conventional devices such as neuromorphic computing devices. Finally, we discuss possible future research directions on magnetic skyrmions, which also cover rich topics on other topological textures such as antiskyrmions and bimerons in antiferromagnets and frustrated magnets.

Manipulating Spin Alignments of (Y,Lu)1.7Fe17 Intermetallic Compounds via Unusual Thermal Pressure

External pressure has been successfully employed to achieve desirable spin alignments in the field of materials science but is seriously restricted by the difficulty of reaching high pressure with conventional methods. The search for simple and effective ways to apply pressure on the lattice is challenging but intriguing. Here we report a new strategy to manipulate the spin alignments of (Y,Lu)_1.7Fe₁₇ intermetallic compounds through unusual thermal pressure. The spin alignments of Fe initially lie parallel inside the basal plane and then turn spirally between adjacent layers with a zone axis along the c direction under higher Lu concentration. The synchrotron and neutron powder diffraction investigations clearly reveal that the direction of spin alignments is highly correlated to large lattice contraction induced by negative thermal expansion (NTE), an unusual thermal pressure, along the c direction. The critical lattice parameter c to form spiral spin alignments is determined unambiguously. This work presents a feasible way to adjust spin alignments through NTE, which might be conducive to the future design of particular spin alignments instead of physical pressure for functional magnetic materials.

Reversible manipulation of the magnetic state in SrRuO3 through electric-field controlled proton evolution

Ionic substitution forms an essential pathway to manipulate the structural phase, carrier density and crystalline symmetry of materials via ion-electron-lattice coupling, leading to a rich spectrum of electronic states in strongly correlated systems. Using the ferromagnetic metal SrRuO3 as a model system, we demonstrate an efficient and reversible control of both structural and electronic phase transformations through the electric-field controlled proton evolution with ionic liquid gating. The insertion of protons results in a large structural expansion and increased carrier density, leading to an exotic ferromagnetic to paramagnetic phase transition. Importantly, we reveal a novel protonated compound of HSrRuO3 with paramagnetic metallic as ground state. We observe a topological Hall effect at the boundary of the phase transition due to the proton concentration gradient across the film-depth. We envision that electric-field controlled protonation opens up a pathway to explore novel electronic states and material functionalities in protonated material systems.

Electronic structure, magnetic anisotropy and Dzyaloshinskii-Moriya interaction in Janus Cr2I3X3 (X = Br, Cl) bilayers

Two-dimensional (2D) layers with a tunable electronic structure and magnetic properties have attracted much attention due to their unique characteristics and practical applications. Here, the electronic structure and magnetic properties of the 2D van der Waals Cr2I3X3 (X = Br, Cl) bilayers are investigated systematically by first-principles calculations. The Cr2I3X3 bilayers show the stacking-dependent magnetic ground state, where the band gap can be effectively tailored by the stacking and combination modes. In the Cr2I3Br3 (Cr2I3Cl3) bilayers, the electrostatic potential and electric polarization can be greatly affected by combination modes, which can be attributed to the parallel or antiparallel built-in electric fields between the monolayers. The Cr2I3X3 bilayers show a perpendicular magnetic anisotropy. The magnetic anisotropy energy of the Cr2I3Cl3 bilayer is larger than that of the Cr2I3Br3 bilayer, which can be attributed to the enhanced contribution of the hybridized I px and py orbitals of the Cr2I3Cl3 bilayer. Additionally, the Dzyaloshinskii-Moriya interaction of the Cr2I3Br3 bilayer can also be modulated by the combination modes. These results can boost the development of Janus 2D materials, which are useful in the design of multifunctional spintronic devices.

Skyrmion phase and competing magnetic orders on a breathing kagomé lattice

Magnetic skyrmion textures are realized mainly in non-centrosymmetric, e.g. chiral or polar, magnets. Extending the field to centrosymmetric bulk materials is a rewarding challenge, where the released helicity/vorticity degree of freedom and higher skyrmion density result in intriguing new properties and enhanced functionality. We report here on the experimental observation of a skyrmion lattice (SkL) phase with large topological Hall effect and an incommensurate helical pitch as small as 2.8 nm in metallic Gd₃Ru₄Al₁₂, which materializes a breathing kagomé lattice of Gadolinium moments. The magnetic structure of several ordered phases, including the SkL, is determined by resonant x-ray diffraction as well as small angle neutron scattering. The SkL and helical phases are also observed directly using Lorentz-transmission electron microscopy. Among several competing phases, the SkL is promoted over a low-temperature transverse conical state by thermal fluctuations in an intermediate range of magnetic fields.

Understanding and controlling the skyrmion lattice (SkL) phase facilitates its versatile applications. Here the direct observation of a SkL phase with large topological Hall effect in centrosymmetric Gd₃Ru₄Al₁₂ is reported, which is stabilized by thermal fluctuations and magnetic field without Dzyaloshinskii-Moriya interactions.

Magnetic skyrmions in FePt nanoparticles having Reuleaux 3D geometry: a micromagnetic simulation study

The magnetization reversal in magnetic FePt nanoelements having Reuleaux 3D geometry is studied using micromagnetic simulations employing Finite Element discretizations. Magnetic skyrmions are revealed in different systems generated by the variation of the magnitude of the magnetocrystalline anisotropy which was kept normal to the nanoelement's base and parallel to the applied external field. The topological quantity of skyrmion number is computed in order to characterize micromagnetic configurations exhibiting skyrmionic formations. Micromagnetic configurations with a wide range of skyrmion numbers between -3 and 3 are indicative for the existence of one or multiple skyrmions that have been detected and stabilized in a range of external fields. Internal magnetic structures are shown consisting of Bloch type skyrmionic entities in the bulk altered to Néel skyrmions on the nanoelement's bottom and top base surfaces. The actual sizes of the formed skyrmions and the internal magnetization structures were computed. In particular, the sizes of the generated and persistent skyrmions were calculated as functions of the magnetocrystalline anisotropy value and of the applied external magnetic field. It is shown that the size of skyrmions is linearly dependent on the external field value. The slope of the linear curve can be controlled by the magnetocrystalline anisotropy value. The magnetic skyrmions can be created for FePt magnetic systems lacking of chiral interactions by designing the geometry-shape of the nanoparticle and by controlling the value of magnetocrystalline anisotropy.