Large topological Hall effect in a short-period helimagnet MnGe

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.

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.

Field-Modulated Anomalous Hall Conductivity and Planar Hall Effect in Co3Sn2S2 Nanoflakes

Time-reversal-symmetry-breaking Weyl semimetals (WSMs) have attracted great attention recently because of the interplay between intrinsic magnetism and topologically nontrivial electrons. Here, we present anomalous Hall and planar Hall effect studies on Co₃Sn₂S₂ nanoflakes, a magnetic WSM hosting stacked Kagome lattice. The reduced thickness modifies the magnetic properties of the nanoflake, resulting in a 15-time larger coercive field compared with the bulk, and correspondingly modifies the transport properties. A 22% enhancement of the intrinsic anomalous Hall conductivity (AHC), as compared to bulk material, was observed. A magnetic field-modulated AHC, which may be related to the changing Weyl point separation with magnetic field, was also found. Furthermore, we showed that the PHE in a hard magnetic WSM is a complex interplay between ferromagnetism, orbital magnetoresistance, and chiral anomaly. Our findings pave the way for a further understanding of exotic transport features in the burgeoning field of magnetic topological phases.

Direct Observation of the Statics and Dynamics of Emergent Magnetic Monopoles in a Chiral Magnet

In the three-dimensional (3D) Heisenberg model, topological point defects known as spin hedgehogs behave as emergent magnetic monopoles, i.e., quantized sources and sinks of gauge fields that couple strongly to conduction electrons, and cause unconventional transport responses such as the gigantic Hall effect. We observe a dramatic change in the Hall effect upon the transformation of a spin hedgehog crystal in a chiral magnet MnGe through combined measurements of magnetotransport and small-angle neutron scattering (SANS). At low temperatures, well-defined SANS peaks and a negative Hall signal are each consistent with expectations for a static hedgehog lattice. In contrast, a positive Hall signal takes over when the hedgehog lattice fluctuates at higher temperatures, with a diffuse SANS signal observed upon decomposition of the hedgehog lattice. Our approach provides a simple way to both distinguish and disentangle the roles of static and dynamic emergent monopoles on the augmented Hall motion of conduction electrons.

Formation Mechanism of the Helical Q Structure in Gd-Based Skyrmion Materials

Using the ab initio local force method, we investigate the formation mechanism of the helical spin structure in GdRu_{2}Si_{2} and Gd_{2}PdSi_{3}. We calculate the paramagnetic spin susceptibility and find that the Fermi surface nesting is not the origin of the incommensurate modulation, in contrast to the naive scenario based on the Ruderman-Kittel-Kasuya-Yosida mechanism. We then decompose the exchange interactions between the Gd spins into each orbital component, and show that spin-density-wave type interaction between the Gd-5d orbitals is ferromagnetic, but the interaction between the Gd-4f orbitals is antiferromagnetic. We conclude that the competition of these two interactions, namely, the interorbital frustration, stabilizes the finite-Q structure.

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.

Theory of an electron asymmetric scattering on skyrmion textures in two-dimensional systems

We discuss in detail the electron scattering pattern on skyrmion-like magnetic textures in two-dimensional geometry. The special attention is focused on analyzing the scattering asymmetry, which is a precursor of the topological Hall effect. We present analytical results valid in the limiting regimes of strong and weak coupling, we analyze analytically the conditions when the transverse response acquires a quantized character determined by the topological charge of a magnetic texture, we also derive the numerical scheme that gives access to the exact solution of the scattering problem. We describe how the electron scattering asymmetry is modified due to an additional short-range impurity located inside a magnetic skyrmion. Based on the numerical computations we investigate the properties of the asymmetric scattering for an arbitrary magnitude of the interaction strength and the topology of a magnetic texture, we also account for the presence or absence of a scalar impurity.

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.

Room Temperature Skyrmions in Strain-Engineered FeGe thin films

Skyrmions hold great promise for low-energy consumption and stable high density information storage, and stabilization of the skyrmion lattice (SkX) phase at or above room temperature is greatly desired for practical use. The topological Hall effect can be used to identify candidate systems above room temperature, a challenging regime for direct observation by Lorentz electron microscopy. Atomically ordered FeGe thin films are grown epitaxially on Ge(111) substrates with ~ 4 % tensile strain. Magnetic characterization reveals enhancement of Curie temperature to 350 K due to strain, well above the bulk value of 278 K. Strong topological Hall effect was observed between 10 K and 330 K, with a significant increase in magnitude observed at 330 K. The increase in magnitude occurs just below the Curie temperature, a similar relative temperature position as the onset of Skx phase in bulk FeGe. The results suggest that strained FeGe films may host a SkX phase above room temperature when significant tensile strain is applied.

Giant Topological Hall Effect and Superstable Spontaneous Skyrmions below 330 K in a Centrosymmetric Complex Noncollinear Ferromagnet NdMn2Ge2

Skyrmions with topologically nontrivial spin textures are promising information carriers in next-generation ultralow power consumption and high-density spintronic devices. To promote their further development and utilization, the search for new room temperature skyrmion-hosting materials is crucial. Considering that most of the previous skyrmion-hosting materials are noncollinear magnets, here, the detection of the topological Hall effect (THE) and the discovery of skyrmions at room temperature are first reported in a centrosymmetric complex noncollinear ferromagnet NdMn₂Ge₂. Below 330 K, the compound can host stable Bloch-type skyrmions with about 75 nm diameter in a wide window of magnetic field and temperature, including zero magnetic field and room temperature. Moreover, the skyrmions can induce a giant topological Hall effect in a wide temperature range with a maximum value of -2.05 μΩ cm. These features make the compound attractive for both fundamental research and potential application in novel spintronic devices.

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.

Observation of Robust Néel Skyrmions in Metallic PtMnGa

Over the past decade the family of chiral noncollinear spin textures has continued to expand with the observation in metallic compounds of Bloch-like skyrmions in several B20 compounds, and antiskyrmions in a tetragonal inverse Heusler. Néel like skyrmions in bulk crystals with broken inversion symmetry have recently been seen in two distinct nonmetallic compounds, GaV₄ S₈ and VOSe₂ O₅ at low temperatures (below ≈13 K) only. Here, the first observation of bulk Néel skyrmions in a metallic compound PtMnGa and, moreover, at high temperatures up to ≈220 K is reported. Lorentz transmission electron microscopy reveals the chiral Néel character of the skyrmions. A strong variation is reported of the size of the skyrmions on the thickness of the lamella in which they are confined, varying by a factor of 7 as the thickness is varied from ≈90 nm to ≈4 µm. Moreover, the skyrmions are highly robust to in-plane magnetic fields and can be stabilized in a zero magnetic field using suitable field-cooling protocols over a very broad temperature range to as low as 5 K. These properties, together with the possibility of manipulating skyrmions in metallic PtMnGa via current induced spin-orbit torques, make them extremely exciting for future spintronic applications.

Dynamical magnetoelectric phenomena of skyrmions in multiferroics

Magnetic skyrmions, nanoscopic spin vortices carrying a quantized topological number in chiral-lattice magnets, are recently attracting great research interest. Although magnetic skyrmions had been observed only in metallic chiral-lattice magnets such as B20 alloys in the early stage of the research, their realization was discovered in 2012 also in an insulating chiral-lattice magnet Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ . A characteristic of the insulating skyrmions is that they can host multiferroicity, that is, the noncollinear magnetization alignment of skyrmion induces electric polarizations in insulators with a help of the relativistic spin-orbit interaction. It was experimentally confirmed that the skyrmion phase in Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ is indeed accompanied by the spin-induced ferroelectricity. The resulting strong magnetoelectric coupling between magnetizations and electric polarizations can provide us with a means to manipulate and activate magnetic skyrmions by application of electric fields. This is in sharp contrast to skyrmions in metallic systems, which are driven through injection of electric currents. The magnetoelectric phenomena specific to the skyrmion-based multiferroics are attracting intensive research interest, and, in particular, those in dynamical regime are widely recognized as an issue of vital importance because their understanding is crucial both for fundamental science and for technical applications. In this article, we review recent studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulating chiral-lattice magnet Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ . It is argued that the multiferroic skyrmions show unique resonant excitation modes of coupled magnetizations and polarizations, so-called electromagnon excitations, which can be activated both magnetically with a microwave magnetic field and electrically with a microwave electric field. The interference between these two activation processes gives rise to peculiar phenomena in the gigahertz regime. As its representative example, we discuss a recent theoretical prediction of unprecedentedly large nonreciprocal directional dichroism of microwaves in the skyrmion phase of Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ . This phenomenon can be regarded as a one-way window effect on microwaves, that is, the extent of microwave absorption changes significantly when its incident direction is reversed. This dramatic effect was indeed observed by subsequent experiments. These studies demonstrated that the multiferroic skyrmions can be a promising building block for microwave devices.

Topological-chiral magnetic interactions driven by emergent orbital magnetism

Two hundred years ago, Ampère discovered that electric loops in which currents of electrons are generated by a penetrating magnetic field can mutually interact. Here we show that Ampère's observation can be transferred to the quantum realm of interactions between triangular plaquettes of spins on a lattice, where the electrical currents at the atomic scale are associated with the orbital motion of electrons in response to the non-coplanarity of neighbouring spins playing the role of a magnetic field. The resulting topological orbital moment underlies the relation of the orbital dynamics with the topology of the spin structure. We demonstrate that the interactions of the topological orbital moments with each other and with the spins form a new class of magnetic interactions [Formula: see text] topological-chiral interactions [Formula: see text] which can dominate over the Dzyaloshinskii-Moriya interaction, thus opening a path for realizing new classes of chiral magnetic materials with three-dimensional magnetization textures such as hopfions.

Nonlocal accumulation, chemical potential, and Hall effect of skyrmions in Pt/Co/Ir heterostructure

Magnetic skyrmion is a swirling topological spin texture behaving as an individual particle. It shows a gyro-motion similarly to that of a charged particle under a magnetic field, being led to the transverse shift to the electric current, i.e., skyrmion Hall effect. With the open boundaries of a sample, this results in an accumulation of skyrmions on one side and their depletion on the other side. Here we demonstrate experimentally that this effect propagates non-locally over tens of micrometers even where the electric current is absent, when the narrow wires bridge bar-shaped Pt/Co/Ir heterostructure thin film systems. This nonlocality can be understood in terms of the “chemical potential” gradient for the skyrmion bubble induced by the skyrmion Hall effect in the nonequilibrium steady state under the electric current. The present result shows that the skyrmion Hall effect acts as the skyrmion pump and the thermodynamic concepts can be applied to the aggregate of skyrmion bubbles.

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.

Complex magnetism of B20-MnGe: from spin-spirals, hedgehogs to monopoles

B20 compounds are the playground for various non-trivial magnetic textures such as skyrmions, which are topologically protected states. Recent measurements on B20-MnGe indicate no clear consensus on its magnetic behavior, which is characterized by the presence of either spin-spirals or three-dimensional objects interpreted to be a cubic lattice of hedgehogs and anti-hedgehogs. Utilizing a massively parallel linear scaling all-electron density functional algorithm, we find from full first-principles simulations on cells containing thousands of atoms that upon increase of the compound volume, the state with lowest energy switches across different magnetic phases: ferromagnetic, spin-spiral, hedgehog and monopole.

Spin chirality fluctuation in two-dimensional ferromagnets with perpendicular magnetic anisotropy

Non-coplanar spin textures with scalar spin chirality can generate an effective magnetic field that deflects the motion of charge carriers, resulting in a topological Hall effect (THE)^1-3. However, spin chirality fluctuations in two-dimensional ferromagnets with perpendicular magnetic anisotropy have not been considered so far. Here, we report evidence of spin chirality fluctuations by probing the THE above the Curie temperature in two different ferromagnetic ultra-thin films, SrRuO₃ and V-doped Sb₂Te₃. The temperature, magnetic field, thickness and carrier-type dependence of the THE signal, along with Monte Carlo simulations, suggest that spin chirality fluctuations are a common phenomenon in two-dimensional ferromagnets with perpendicular magnetic anisotropy. Our results open a path for exploring spin chirality with topological Hall transport in two-dimensional magnets and beyond^4-7.

Skyrmions and Hall transport

We review recent progresses towards an understanding of the skyrmion Hall transport in insulating as well as conducting materials. First, we consider a theoretical breakthrough based on the quantum field theory ward identity, a first principle analysis, relying on symmetries and conservation laws. Broken parity (inversion) symmetry plays a crucial role in skyrmion Hall transport. In addition to the well known thermal and electric Hall conductivities, our analysis has led us to the discovery of a new and unforeseen physical quantity, Hall viscosity-an anti-symmetric part of the viscosity tensor. We propose a simple way to confirm the existence of Hall viscosity in the measurements of Hall conductivity as a function of momentum. We provide various background materials to assist the readers to understand the quantum field theory ward identity. In the second part, we review recent theoretical and experimental advancements of the skyrmion Hall effects and the topological (magnon) Hall effects for conducting (insulting) magnets. For this purpose, we consider two enveloping themes: spin torque and thermo-electromagnetic effect. First, we overview various spin torques, such as spin transfer torque, spin-orbit torque, and spin Hall torque, and generalized Landau-Lifshitz-Gilbert equations and Thiele equations using a phenomenological approach. Second, we consider irreversible thermodynamics to survey possible thermo-electromagnetic effects, such as Seebeck, Peltier and Thompson effects in the presence of the electric currents, along with the Hall effects in the presence of a background magnetic field. Recently developed spin Seebeck effects are also a significant part of the survey. We also accommodate extensive background materials to make this review self-contained. Finally, we revisit the skyrmion Hall transport from the ward identity view point.

Emergent Topological Hall Effect in La0.7Sr0.3MnO3/SrIrO3 Heterostructures

Recently, perovskite oxide heterostructures have drawn great attention because multiple and complex coupling at the heterointerface may produce novel magnetic and electric phenomena that are not expected in homogeneous materials either in the bulk or in films. In this work, we report for the first time that an emergent giant topological Hall effect (THE), associated with a noncoplanar (NC) spin texture, can be induced in ferromagnetic (FM) La_0.7Sr_0.3MnO₃ thin films in a wide temperature range of up to 200 K by constructing La_0.7Sr_0.3MnO₃/SrIrO₃ epitaxial heterostructures on (001) SrTiO₃ substrates. This THE is not observed in La_0.7Sr_0.3MnO₃ single-layer films or La_0.7Sr_0.3MnO₃/SrTiO₃/SrIrO₃ trilayer heterostructures, indicating the relevance of the La_0.7Sr_0.3MnO₃/SrIrO₃ interface, where the Dzyaloshinskii-Moriya interaction due to strong spin-orbital coupling in SrIrO₃ may play a crucial role. The fictitious field associated with THE is independent of temperature in La_0.7Sr_0.3MnO₃/SrIrO₃ heterostructures, suggesting that the NC spin texture may be magnetic skyrmions. This work demonstrates the feasibility of using SrIrO₃ to generate novel magnetic and transport characteristics by interfacing with other correlated oxides, which might be useful to novel spintronic applications.

All Electrical Access to Topological Transport Features in Mn1.8PtSn Films

The presence of nontrivial magnetic topology can give rise to nonvanishing scalar spin chirality and consequently a topological Hall or Nernst effect. In turn, topological transport signals can serve as indicators for topological spin structures. This is particularly important in thin films or nanopatterned materials where the spin structure is not readily accessible. Conventionally, the topological response is determined by combining magnetotransport data with an independent magnetometry experiment. This approach is prone to introduce measurement artifacts. In this study, we report the observation of large topological Hall and Nernst effects in micropatterned thin films of Mn_1.8PtSn below the spin reorientation temperature T_SR ≈ 190 K. The magnitude of the topological Hall effect ρ _xy^T = 8 nΩm is close to the value reported in bulk Mn₂PtSn, and the topological Nernst effect S _xy^T = 115 nV K^-1 measured in the same microstructure has a similar magnitude as reported for bulk MnGe ( S _xy^T ∼ 150 nV K^-1), the only other material where a topological Nernst was reported. We use our data as a model system to introduce a topological quantity, which allows one to detect the presence of topological transport effects without the need for independent magnetometry data. Our approach thus enables the study of topological transport also in nanopatterned materials without detrimental magnetization related limitations.

Topological transitions among skyrmion- and hedgehog-lattice states in cubic chiral magnets

Manipulating topological spin textures is a key for exploring unprecedented emergent electromagnetic phenomena. Whereas switching control of magnetic skyrmions, e.g., the transitions between a skyrmion-lattice phase and conventional magnetic orders, is intensively studied towards development of future memory device concepts, transitions among spin textures with different topological orders remain largely unexplored. Here we develop a series of chiral magnets MnSi1-xGex, serving as a platform for transitions among skyrmion- and hedgehog-lattice states. By neutron scattering, Lorentz transmission electron microscopy and high-field transport measurements, we observe three different topological spin textures with variation of the lattice constant controlled by Si/Ge substitution: two-dimensional skyrmion lattice in x = 0-0.25 and two distinct three-dimensional hedgehog lattices in x = 0.3-0.6 and x = 0.7-1. The emergence of various topological spin states in the chemical-pressure-controlled materials suggests a new route for direct manipulation of the spin-texture topology by facile mechanical methods.

Anomalous Nonreciprocal Electrical Transport on Chiral Magnetic Order

Nonreciprocal flow of conduction electrons is systematically investigated in a monoaxial chiral helimagnet CrNb_{3}S_{6}. We found that such directional dichroism of the electrical transport phenomena, called the electrical magnetochiral (EMC) effect, occurs in a wide range of magnetic fields and temperatures. The EMC signal turns out to be considerably enhanced below the magnetic ordering temperature, suggesting a strong influence of the chiral magnetic order on this anomalous EMC transport property. The EMC coefficients are separately evaluated in terms of crystalline and magnetic contributions in the magnetic phase diagram.

Discrete Hall resistivity contribution from Néel skyrmions in multilayer nanodiscs

Magnetic skyrmions are knot-like quasiparticles. They are candidates for non-volatile data storage in which information is moved between fixed read and write terminals. The read-out operation of skyrmion-based spintronic devices will rely on the electrical detection of a single magnetic skyrmion within a nanostructure. Here we present Pt/Co/Ir nanodiscs that support skyrmions at room temperature. We measured the Hall resistivity and simultaneously imaged the spin texture using magnetic scanning transmission X-ray microscopy. The Hall resistivity is correlated to both the presence and size of the skyrmion. The size-dependent part matches the expected anomalous Hall signal when averaging the magnetization over the entire disc. We observed a resistivity contribution that only depends on the number and sign of skyrmion-like objects present in the disc. Each skyrmion gives rise to 22 ± 2 nΩ cm irrespective of its size. This contribution needs to be considered in all-electrical detection schemes applied to skyrmion-based devices. Not only the area of Néel skyrmions but also their number and sign contribute to their Hall resistivity.

Large anomalous Hall effect in the chiral-lattice antiferromagnet CoNb3S6

An ordinary Hall effect in a conductor arises due to the Lorentz force acting on the charge carriers. In ferromagnets, an additional contribution to the Hall effect, the anomalous Hall effect (AHE), appears proportional to the magnetization. While the AHE is not seen in a collinear antiferromagnet, with zero net magnetization, recently it has been shown that an intrinsic AHE can be non-zero in non-collinear antiferromagnets as well as in topological materials hosting Weyl nodes near the Fermi energy. Here we report a large anomalous Hall effect with Hall conductivity of 27 Ω⁻¹ cm⁻¹ in a chiral-lattice antiferromagnet, CoNb₃S₆ consisting of a small intrinsic ferromagnetic component (≈0.0013 μ_B per Co) along c-axis. This small moment alone cannot explain the observed size of the AHE. We attribute the AHE to either formation of a complex magnetic texture or the combined effect of the small intrinsic moment on the electronic band structure.

Anomalous Hall effect (AHE) in antiferromagnets is intriguing and requires further understanding. Here the authors report large AHE in a chiral-lattice antiferromagnet CoNb₃S₆ of which the origin can be due to complex magnetic texture or broken time-reversal symmetry on the electronic band structure.

Exchange-biasing topological charges by antiferromagnetism

Geometric Hall effect is induced by the emergent gauge field experienced by the carriers adiabatically passing through certain real-space topological spin textures, which is a probe to non-trivial spin textures, such as magnetic skyrmions. We report experimental indications of spin-texture topological charges induced in heterostructures of a topological insulator (Bi,Sb)2Te3 coupled to an antiferromagnet MnTe. Through a seeding effect, the pinned spins at the interface leads to a tunable modification of the averaged real-space topological charge. This effect experimentally manifests as a modification of the field-dependent geometric Hall effect when the system is field-cooled along different directions. This heterostructure represents a platform for manipulating magnetic topological transitions using antiferromagnetic order.

Anomalous Hall effect derived from multiple Weyl nodes in high-mobility EuTiO3 films

EuTiO₃, a magnetic semiconductor with a simple band structure, is one of the ideal systems to control the anomalous Hall effect (AHE) by tuning the Fermi level. The electrons in the conduction bands of La-doped EuTiO₃ are subject to the spin-orbit interaction and Zeeman field from the spontaneous magnetization, which generates rich structures in the electron band such as Weyl nodes. This unique property makes EuTiO₃ a relatively simple multiband system with its Berry curvature being controlled by electron doping and magnetic field. We report a nonmonotonic magnetic field dependence of the anomalous Hall resistivity, which is ascribed to the change of electronic bands induced by the Zeeman splitting during the magnetization process. The anomalous Hall resistivity measurement in high-mobility films grown by gas source molecular beam epitaxy shows additional terms in the AHE during the magnetization process, which is not proportional to the magnetization. Our theoretical calculation indicates that the change of Zeeman field in the process of canting the magnetic moments causes the type II Weyl nodes in the conduction band to move, resulting in a peculiar magnetic field dependence of the AHE; this is revealed by the high-quality films with a long scattering lifetime of conduction electrons.

Electrical detection of single magnetic skyrmions in metallic multilayers at room temperature

Magnetic skyrmions are topologically protected whirling spin textures that can be stabilized in magnetic materials by an asymmetric exchange interaction between neighbouring spins that imposes a fixed chirality. Their small size, together with the robustness against external perturbations, make magnetic skyrmions potential storage bits in a novel generation of memory and logic devices. To this aim, their contribution to the electrical transport properties of a device must be characterized-however, the existing demonstrations are limited to low temperatures and mainly in magnetic materials with a B20 crystal structure. Here we combine concomitant magnetic force microscopy and Hall resistivity measurements to demonstrate the electrical detection of sub-100 nm skyrmions in a multilayered thin film at room temperature. Furthermore, we detect and analyse the Hall signal of a single skyrmion, which indicates that it arises from the anomalous Hall effect with a negligible contribution from the topological Hall effect.

Multiplet of Skyrmion States on a Curvilinear Defect: Reconfigurable Skyrmion Lattices

Typically, the chiral magnetic Skyrmion is a single-state excitation. Here we propose a system, where multiplet of Skyrmion states appears and one of these states can be the ground one. We show that the presence of a localized curvilinear defect drastically changes the magnetic properties of a thin perpendicularly magnetized ferromagnetic film. For a large enough defect amplitude a discrete set of equilibrium magnetization states appears forming a ladder of energy levels. Each equilibrium state has either a zero or a unit topological charge; i.e., topologically trivial and Skyrmion multiplets generally appear. Transitions between the levels with the same topological charge are allowed and can be utilized to encode and switch a bit of information. There is a wide range of geometrical and material parameters, where the Skyrmion level has the lowest energy. Thus, periodically arranged curvilinear defects can result in a Skyrmion lattice as the ground state.

Spin chirality induced skew scattering and anomalous Hall effect in chiral magnets

Noncoplanar magnetic orders in magnetic metals give rise to an anomalous Hall effect of unconventional origin, which, by the spin Berry phase effect, is known as the topological Hall effect. This effect is pronounced in the low-temperature limit, where the fluctuation of spins is suppressed. In contrast, we here discuss that the fluctuating but locally correlated spins close to the phase boundary give rise to another anomalous Hall effect, that with the opposite sign to the topological Hall effect. Using the Born approximation, we show that the anomalous Hall effect is attributed to the skew scattering induced by the local correlation of spins. The relation of the scalar spin chirality to the skew scattering amplitude is given, and the explicit formula for the Hall conductivity is derived using a semiclassical Boltzmann transport theory. Our theory potentially accounts for the sign change of the anomalous Hall effect observed in chiral magnets in the vicinity of the phase boundary.

Large magneto-thermopower in MnGe with topological spin texture

Quantum states characterized by nontrivial topology produce interesting electrodynamics and versatile electronic functionalities. One source for such remarkable phenomena is emergent electromagnetic field, which is the outcome of interplay between topological spin structures with scalar spin chirality and conduction electrons. However, it has scarcely been exploited for emergent function related to heat-electricity conversion. Here we report an unusually enhanced thermopower by application of magnetic field in MnGe hosting topological spin textures. By considering all conceivable origins through quantitative investigations of electronic structures and properties, a possible origin of large magneto-thermopower is assigned to the strong energy dependence of charge-transport lifetime caused by unconventional carrier scattering via the dynamics of emergent magnetic field. Furthermore, high-magnetic-field measurements corroborate the presence of residual magnetic fluctuations even in the nominally ferromagnetic region, leading to a subsisting behavior of field-enhanced thermopower. The present finding may pave a way for thermoelectric function of topological magnets.

Mixed Weyl semimetals and low-dissipation magnetization control in insulators by spin-orbit torques

Reliable and energy-efficient magnetization switching by electrically induced spin–orbit torques is of crucial technological relevance for spintronic devices implementing memory and logic functionality. Here we predict that the strength of spin–orbit torques and the Dzyaloshinskii-Moriya interaction in topologically nontrivial magnetic insulators can exceed by far that of conventional metals. In analogy to the quantum anomalous Hall effect, we explain this extraordinary response in the absence of longitudinal currents as hallmark of monopoles in the electronic structure of systems that are interpreted most naturally within the framework of mixed Weyl semimetals. We thereby launch the effect of spin–orbit torque into the field of topology and reveal its crucial role in mediating the topological phase transitions arising from the complex interplay between magnetization direction and momentum-space topology. The presented concepts may be exploited to understand and utilize magnetoelectric coupling phenomena in insulating ferromagnets and antiferromagnets.

Electric-field control of magnetization switching is highly promising for low-dissipation spintronics. Here, the authors propose an electrically induced topological phase transition mediated by spin orbit torques as attractive way to control magnetization in absence of longitudinal charge currents.

Nucleation and annihilation of skyrmions in Mn2CoAl observed through the topological Hall effect

Magnetic skyrmions are topologically protected spin textures with great technological potential. These topologically non-trivial non-coplanar spin textures give rise to a topological Hall effect, enabling the purely electronic detection of magnetic skyrmions. We report a clear topological Hall effect in thin films of the the Heusler alloy Mn₂CoAl, a ferromagnetic spin-gapless semiconductor, capped by a thin layer of Pd. We exploit the strong thickness- and temperature-dependence of the anomalous Hall effect in this system, tuning it to zero to enable the unambiguous measurement of the topological Hall effect, which is observed for temperatures between 3 K and 280 K. The topological Hall effect is evidence of skyrmions, and we demonstrate the simultaneous coexistence of opposite polarity skyrmions using a novel method involving minor field loops of the Hall effect.

Noncentrosymmetric Magnets Hosting Magnetic Skyrmions

The concept of a skyrmion, which was first introduced by Tony Skyrme in the field of particle physics, has become widespread in condensed matter physics to describe various topological orders. Skyrmions in magnetic materials have recently received particular attention; they represent vortex-like spin structures with the character of nanometric particles and produce fascinating physical properties rooted in their topological nature. Here, a series of noncentrosymmetric ferromagnets hosting skyrmions is reviewed: B20 metals, Cu₂ OSeO₃ , Co-Zn-Mn alloys, and GaV₄ S₈ , where Dzyaloshinskii-Moriya interaction plays a key role in the stabilization of skyrmion spin texture. Their topological spin arrangements and consequent emergent electromagnetic fields give rise to striking features in transport and magnetoelectric properties in metals and insulators, such as the topological Hall effect, efficient electric-drive of skyrmions, and multiferroic behavior. Such electric controllability and nanometric particle natures highlight magnetic skyrmions as a potential information carrier for high-density magnetic storage devices with excellent energy efficiency.

Transition from Anomalous Hall Effect to Topological Hall Effect in Hexagonal Non-Collinear Magnet Mn3Ga

We report experimental observation of large anomalous Hall effect exhibited in non-collinear triangular antiferromagnet D0₁₉-type Mn₃Ga with coplanar spin structure at temperatures higher than 100 K. The value of anomalous Hall resistivity increases with increasing temperature, which reaches 1.25 μΩ · cm at a low field of ~300 Oe at room temperature. The corresponding room-temperature anomalous Hall conductivity is about 17 (Ω · cm)⁻¹. Most interestingly, as temperature falls below 100 K, a temperature-independent topological-like Hall effect was observed. The maximum peak value of topological Hall resistivity is about 0.255 μΩ · cm. The appearance of the topological Hall effect is attributed to the change of spin texture as a result of weak structural distortion from hexagonal to orthorhombic symmetry in Mn₃Ga. Present study suggests that Mn₃Ga shows promising possibility to be antiferromagnetic spintronics or topological Hall effect-based data storage devices.

Room-temperature helimagnetism in FeGe thin films

Chiral magnets are promising materials for the realisation of high-density and low-power spintronic memory devices. For these future applications, a key requirement is the synthesis of appropriate materials in the form of thin films ordering well above room temperature. Driven by the Dzyaloshinskii-Moriya interaction, the cubic compound FeGe exhibits helimagnetism with a relatively high transition temperature of 278 K in bulk crystals. We demonstrate that this temperature can be enhanced significantly in thin films. Using x-ray scattering and ferromagnetic resonance techniques, we provide unambiguous experimental evidence for long-wavelength helimagnetic order at room temperature and magnetic properties similar to the bulk material. We obtain α_intr = 0.0036 ± 0.0003 at 310 K for the intrinsic damping parameter. We probe the dynamics of the system by means of muon-spin rotation, indicating that the ground state is reached via a freezing out of slow dynamics. Our work paves the way towards the fabrication of thin films of chiral magnets that host certain spin whirls, so-called skyrmions, at room temperature and potentially offer integrability into modern electronics.

Prototypical topological orbital ferromagnet γ-FeMn

We predict from first principles an entirely topological orbital magnetization in the noncoplanar bulk antiferromagnet γ-FeMn originating in the nontrivial topology of the underlying spin structure, without any reference to spin-orbit interaction. Studying the influence of strain, composition ratio, and spin texture on the topological orbital magnetization and the accompanying topological Hall effect, we promote the scalar spin chirality as key mechanism lifting the orbital degeneracy. The system is thus a prototypical topological orbital ferromagnet, the macroscopic orbital magnetization of which is prominent even without spin-orbit coupling. One of the remarkable features of γ-FeMn is the possibility for pronounced orbital magnetostriction mediated by the complex spin topology in real space.

Robust Zero-Field Skyrmion Formation in FeGe Epitaxial Thin Films

B20 phase magnetic materials have been of significant interest because they enable magnetic Skyrmions. One major effort in this emerging field is the stabilization of Skyrmions at room temperature and zero magnetic field. We grow phase-pure, high crystalline quality FeGe epitaxial films on Si(111). Hall effect measurements reveal a strong topological Hall effect after subtracting the ordinary and anomalous Hall effects, demonstrating the formation of high density Skyrmions in FeGe films between 5 and 275 K. In particular, a substantial topological Hall effect was observed at a zero magnetic field, showing a robust Skyrmion phase without the need of an external magnetic field.

Selective Chemical Vapor Deposition Growth of Cubic FeGe Nanowires That Support Stabilized Magnetic Skyrmions

Magnetic skyrmions are topologically stable vortex-like spin structures that are promising for next generation information storage applications. Materials that host magnetic skyrmions, such as MnSi and FeGe with the noncentrosymmetric cubic B20 crystal structure, have been shown to stabilize skyrmions upon nanostructuring. Here, we report a chemical vapor deposition method to selectively grow nanowires (NWs) of cubic FeGe out of three possible FeGe polymorphs for the first time using finely ground particles of cubic FeGe as seeds. X-ray diffraction and transmission electron microscopy (TEM) confirm that these micron-length NWs with ∼100 nm to 1 μm diameters have the cubic B20 crystal structure. Although Fe₁₃Ge₈ NWs are also formed, the two types of NWs can be readily differentiated by their faceting. Lorentz TEM imaging of the cubic FeGe NWs reveals a skyrmion lattice phase under small applied magnetic fields (∼0.1 T) at 233 K, a skyrmion chain state at lower temperatures (95 K) and under high magnetic fields (∼0.4 T), and a larger skyrmion stability window than bulk FeGe. This synthetic approach to cubic FeGe NWs that support stabilized skyrmions opens a route toward the exploration of new skyrmion physics and devices based on similar nanostructures.

High-pressure single-crystal synchrotron diffraction study of MnGe and related compounds

Single crystal synchrotron diffraction for pressures up to 50 GPa has revealed an essential difference in structural properties and compressibility of MnGe compared with Mn1-x Co x Ge and Mn1-x Fe x Ge solid solutions. A negative thermal expansion has been observed for MnGe at low-temperatures and high-pressures. The single crystal refinement has shown a discontinuous change of the atomic coordinates and Mn-Ge interatomic distances of MnGe in contrast to Mn0.1Co0.9Ge. These peculiarities of MnGe are likely to be associated with high-spin-low-spin transition. The relation between anisotropy of the coordination of Mn-atom and its magnetic moment is discussed.

Skyrmions and Hall Transport

We derive a generalized set of Ward identities that captures the effects of topological charge on Hall transport. The Ward identities follow from the (2+1)-dimensional momentum algebra, which includes a central extension proportional to the topological charge density. In the presence of topological objects like Skyrmions, we observe that the central term leads to a direct relation between the thermal Hall conductivity and the topological charge density. We extend this relation to incorporate the effects of a magnetic field and an electric current. The topological charge density produces a distinct signature in the electric Hall conductivity, which is identified in existing experimental data and yields further novel predictions. For insulating materials with translation invariance, the Hall viscosity can be directly determined from the Skyrmion density and the thermal Hall conductivity to be measured as a function of momentum.

A Centrosymmetric Hexagonal Magnet with Superstable Biskyrmion Magnetic Nanodomains in a Wide Temperature Range of 100-340 K

Superstable biskyrmion magnetic nanodomains are experimentally observed for the first time in a hexagonal MnNiGa, a common and easily produced centrosymmetric material. The biskyrmion states in MnNiGa thin plates, as determined by the combination of in situ Lorentz transmission electron microscopy images, magnetoresistivity, and topological Hall effect measurements, are surprisingly stable over a broad temperature range of 100-340 K.

Exotic skyrmion crystals in chiral magnets with compass anisotropy

The compass-type anisotropy appears naturally in diverse physical contexts with strong spin-orbit coupling (SOC) such as transition metal oxides and cold atomic gases etc, and it has been receiving substantial attention. Motivated by recent studies and particularly recent experimental observations on helimagnet MnGe, we investigate the critical roles of this compass-type anisotropy in modulating various spin textures of chiral magnets with strong SOC, by Monte Carlo simulations based on a classical Heisenberg spin model with Dzyaloshinsky-Moriya interaction and compass anisotropy. A phase diagram with emergent spin orders in the space of compass anisotropy and out-of-plane magnetic field is presented. In this phase diagram, we propose that a hybrid super-crystal structure consisting of alternating half-skyrmion and half-anti-skyrmion is the possible zero-field ground state of MnGe. The simulated evolution of the spin structure driven by magnetic field is in good accordance with experimental observations on MnGe. Therefore, this Heisenberg spin model successfully captures the main physics responsible for the magnetic structures in MnGe, and the present work may also be instructive to research on the magnetic states in other systems with strong SOC.

Interface-driven topological Hall effect in SrRuO3-SrIrO3 bilayer

Electron transport coupled with magnetism has attracted attention over the years. Among them, recently discovered is topological Hall effect (THE), originating from scalar spin chirality, that is, the solid angle subtended by the spins. THE is found to be a promising tool for probing the Dzyaloshinskii-Moriya (DM) interaction and consequent magnetic skyrmions. This interaction arises from broken inversion symmetry and hence can be artificially introduced at interface; this concept is lately verified in metal multilayers. However, there are few attempts to investigate such DM interaction at interface through electron transport. We clarified how the transport properties couple with interface DM interaction by fabricating the epitaxial oxide interface. We observed THE in epitaxial bilayers consisting of ferromagnetic SrRuO3 and paramagnetic SrIrO3 over a wide region of both temperature and magnetic field. The magnitude of THE rapidly decreases with the thickness of SrRuO3, suggesting that the interface DM interaction plays a significant role. Such interaction is expected to realize a 10-nm-sized Néel-type magnetic skyrmion. The present results established that the high-quality oxide interface enables us to tune the effective DM interaction; this can be a step toward future topological electronics.

Large anomalous Nernst effect in a skyrmion crystal

Thermoelectric properties of a model skyrmion crystal were theoretically investigated, and it was found that its large anomalous Hall conductivity, corresponding to large Chern numbers induced by its peculiar spin structure leads to a large transverse thermoelectric voltage through the anomalous Nernst effect. This implies the possibility of finding good thermoelectric materials among skyrmion systems, and thus motivates our quests for them by means of the first-principles calculations as were employed in this study.

Critical phenomena of emergent magnetic monopoles in a chiral magnet

Second-order continuous phase transitions are characterized by symmetry breaking with order parameters. Topological orders of electrons, characterized by the topological index defined in momentum space, provide a distinct perspective for phase transitions, which are categorized as quantum phase transitions not being accompanied by symmetry breaking. However, there are still limited observations of counterparts in real space. Here we show a real-space topological phase transition in a chiral magnet MnGe, hosting a periodic array of hedgehog and antihedgehog topological spin singularities. This transition is driven by the pair annihilation of the hedgehogs and antihedgehogs acting as monopoles and antimonopoles of the emergent electromagnetic field. Observed anomalies in the magnetoresistivity and phonon softening are consistent with the theoretical prediction of critical phenomena associated with enhanced fluctuations of emergent field near the transition. This finding reveals a vital role of topology of the spins in strongly correlated systems.

Phase transitions in topologically non-trivial systems are characterized by changes of topological invariants, rather than conventional order parameters. Here, the authors propose a real-space topological phase transition upon pair annihilation of emergent monopoles inherent in chiral magnet MnGe.

On the possibility of using X-ray Compton scattering to study magnetoelectrical properties of crystals

The possibility of using X-ray Compton scattering to reveal antisymmetric components of the electron momentum density, as a fingerprint of magnetoelectric sample properties, is investigated experimentally and theoretically by studying the polar ferromagnet GaFeO₃.

This paper discusses the possibility of using Compton scattering – an inelastic X-ray scattering process that yields a projection of the electron momentum density – to probe magnetoelectrical properties. It is shown that an antisymmetric component of the momentum density is a unique fingerprint of such time- and parity-odd physics. It is argued that polar ferromagnets are ideal candidates to demonstrate this phenomenon and the first experimental results are shown, on a single-domain crystal of GaFeO₃. The measured antisymmetric Compton profile is very small (≃ 10⁻⁵ of the symmetric part) and of the same order of magnitude as the statistical errors. Relativistic first-principles simulations of the antisymmetric Compton profile are presented and it is shown that, while the effect is indeed predicted by theory, and scales with the size of the valence spin–orbit interaction, its magnitude is significantly overestimated. The paper outlines some important constraints on the properties of the antisymmetric Compton profile arising from the underlying crystallographic symmetry of the sample.