Large topological Hall effect in a short-period helimagnet MnGe

Probing the anomalous Hall transport and magnetic reversal of quasi-two-dimensional antiferromagnet Co1/3NbS2

The recent discovery of anomalous Hall effect (AHE) in non-collinear antiferromagnets offers a promising platform for developing ultra-compact, ultrafast, and low-power antiferromagnetic spintronics, as well as for the in-depth investigation of topological physics. One notable example is the quasi-two-dimensional antiferromagnet Co1/3NbS2, which exhibits a large spontaneous Hall effect with compensated magnetization. Here, we report the observation of a large spontaneous Nernst effect in exfoliated Co1/3NbS2 flakes. By analyzing the temperature- and field-dependent thermoelectric and transport phenomena, we confirm the intrinsic k-space Berry curvature as the origin of the spontaneous Hall effect. Reflective magnetic circular dichroism measurements further reveal the presence of non-collinear antiferromagnetic domains in Co1/3NbS2. Combined with electrical transport measurements, we elucidate the distinct magnetic reversal mechanisms between bulk and exfoliated samples. Our study provides a comprehensive phenomenological understanding of the magnetic and transport properties of Co1/3NbS2, laying the groundwork for further exploration of the underlying physics and potential applications of two-dimensional non-collinear magnets.

Anomalous Electrical Transport in the Kagome Magnet YbFe_{6}Ge_{6}

Two-dimensional (2D) kagome metals offer a unique platform for exploring electron correlation phenomena derived from quantum many-body effects. Here, we report a combined study of electrical magnetotransport and neutron scattering on YbFe_{6}Ge_{6}, where the Fe moments in the 2D kagome layers exhibit an A-type collinear antiferromagnetic order below T_{N}≈500  K. Interactions between the Fe ions in the layers and the localized Yb magnetic ions in between reorient the c-axis-aligned Fe moments to the kagome plane below T_{SR}≈63  K. Our magnetotransport measurements show an intriguing anomalous Hall effect (AHE) that emerges in the spin-reorientated collinear state, accompanied by the closing of the spin anisotropy gap as revealed from inelastic neutron scattering. The gapless spin excitations and the Yb-Fe interaction are able to support a dynamic scalar spin chirality, which explains the observed AHE. Therefore, our Letter demonstrates that spin fluctuations may provide an additional scattering channel for the conduction electrons and give rise to AHE even in a collinear antiferromagnet.

Fluctuation-driven topological Hall effect in room-temperature itinerant helimagnet Fe3Ga4

The topological Hall effect (THE) is a hallmark of a non-trivial geometric spin arrangement in a magnetic metal, originating from a finite scalar spin chirality (SSC). The associated Berry phase is often a consequence of non-coplanar magnetic structures identified by multiple k-vectors. For single - k magnetic structures however with zero SSC, the emergence of a finite topological Hall signal presents a conceptual challenge. Here, we report that a fluctuation-driven mechanism involving chiral magnons is responsible for the observed THE in a low-symmetry compound, monoclinic Fe3Ga4. Through neutron scattering experiments, we discovered several nontrivial magnetic phases in this system. In our focus is the helical spiral phase at room temperature, which transforms into a transverse conical state in applied magnetic field, supporting a significant THE signal up to and above room temperature. Our work offers a fresh perspective in the search for novel materials with intertwined topological magnetic and transport properties.

Emergent Magnetic Skyrmions in a Topological Weyl Nodal Ring Semimetal

Topological magnetic materials are expected to show multiple transport responses because of their unusual bulk electronic topology in momentum space and their topological spin texture in real space. However, such multiple topological properties-hosting materials are rare in nature. In this work, we unambiguously reveal the emergence of magnetic skyrmions in Mn5Ge3 single crystal through detailed electrical transport and Lorentz transmission electron microscopy (L-TEM) combined with ab initio calculations. We demonstrate that Mn5Ge3 is a topological ferromagnet with multiple nodal rings in its electronic structure. Importantly, L-TEM experiments further reveal that the magnetic skyrmions appear in the (001) plane when an appropriate magnetic field is applied along the [001] direction. Skyrmion-induced topological Hall resistivity as large as ∼972 nΩ cm is also observed over a wide temperature-magnetic field region. These prove Mn5Ge3 as a rare magnetic topological nodal-ring semimetal with great significance to explore novel topological multifunctionality, which facilitate the development of spintronics.

In-Situ Monitoring the Magnetotransport Signature of Topological Transitions in a Chiral Magnet

Emerging magnetic fields related to the presence of topologically protected spin textures such as skyrmions are expected to give rise to additional, topology-related contributions to the Hall effect. In order to doubtlessly identify this so-called topological Hall effect, it is crucial to disentangle such contributions from the anomalous Hall effect. This necessitates a direct correlation of the transversal Hall voltage with the underlying magnetic textures. A novel measurement platform is developed that allows to acquire high-resolution Lorentz transmission electron microscopy images of magnetic textures as a function of an external magnetic field and to concurrently measure the (anomalous) Hall voltage in-situ in the microscope on one and the same specimen. This approach is used to investigate the transport signatures of the chiral soliton lattice and antiskyrmions in Mn1.4PtSn. Notably, the observed textures allow to fully understand the measured Hall voltage without the need of any additional contributions due to a topological Hall effect, and the field-controlled formation and annihilation of anstiskyrmions are found to have no effect on the measured Hall voltage.

Observation of magnetic skyrmion lattice in Cr0.82Mn0.18Ge by small-angle neutron scattering

Incommensurate magnetic phases in chiral cubic crystals are an established source of topological spin textures such as skyrmion and hedgehog lattices, with potential applications in spintronics and information storage. We report a comprehensive small-angle neutron scattering (SANS) study on the B20-type chiral magnet Cr[Formula: see text]Mn[Formula: see text]Ge, exploring its magnetic phase diagram and confirming the stabilization of a skyrmion lattice under low magnetic fields. Our results reveal a helical ground state with a decreasing pitch from 40 to 35 nm upon cooling, and a skyrmion phase stable in applied magnetic fields of 10-30 mT, and over an unusually wide temperature range for chiral magnets of 6 K ([Formula: see text], [Formula: see text] K). The skyrmion lattice forms a standard two-dimensional hexagonal coordination that can be trained into a single domain, distinguishing it from the three-dimensional hedgehog lattice observed in MnGe-based systems. Additionally, we demonstrate the persistence of a metastable SkL at 2 K, even at zero field. These findings advance our understanding of magnetic textures in Cr-based B20 compounds, highlighting Cr0.82Mn0.18Ge as a promising material for further exploration in topological magnetism.

Research on the Structural and Magnetic Phase Transitions of CeMn2Ge2 Alloy

Magnetic phase transitions play crucial roles in various material applications, including sensors, actuators, information storage, magnetic refrigeration, and so on. Typically, these magnetic phase transitions exhibit discontinuous first-order phase transitions. When a material undergoes a magnetic phase transition, it often exhibits simultaneous changes in both its crystal and electronic structures. However, the coupling relationship between the crystal structure and electronic structure during these phase transitions has not been well studied. This lack of understanding hinders our ability to integrate macroscopic physical phenomena with microscopic crystal and electronic structures. In this paper, we prepared single crystal and polycrystalline CeMn2Ge2 alloy, which has been extensively studied in recent years as a material of skyrmions. The relationships between the magnetic phase transition and the crystal structure of CeMn2Ge2 were investigated through magnetic measurements, variable-temperature X-ray diffraction (XRD), and experimental electron density analysis via the maximum entropy method (MEM). The results indicate that the antiferromagnetic phase transition at TN = 415 K is characterized by an increase in the intralayer Mn-Mn bond and a decrease in the Ge-Ge bond. More importantly, the ferromagnetic transition at TC = 315 K can be divided into two stages: the first stage involves the anisotropic transformation of Mn, and the second stage involves the electron enhancement of Mn. The combination of phase transition features and transport properties indicates strong anisotropy in CeMn2Ge2. Notably, our work reveals a coupling between a material's physical properties, crystal structure, and electronic structure. Our study offers a new approach for determining the origin of magnetic phase transitions and the causes of their physical properties in materials at the electronic level.

Effects of nonmagnetic Cr substitution for Mn on kagome magnet DyMn6Sn6

RMn6Sn6(R= rare-earth) kagome magnets have been one of the research focuses in condensed matter physics, primarily due to their exotic physical properties rooted in the interplay between magnetism and nontrivial topological band structures. We reported herein the crystal growth of Cr substituted DyMn4Cr2Sn6and investigations on their magnetotransport properties. It is unveiled that the Mn kagome layer is destroyed and the in-plane ferromagnetic exchange is consequently weakened by the substituted nonmagnetic Cr. Furthermore, the substitution apparently benefits reorientations of the Mn spins under external magnetic field. Besides, the Cr substitution results in a significantly enhanced large intrinsic anomalous Hall conductivity, reaching 600 S cm-1at 240 K. The anomaly observed in the anomalous Hall conductivity as well as in the Hall coefficient might indicate a topological magnetic structure formed during the spin reorientation process. These findings pave the way for manipulating magnetism and electronic structures in magnetic kagome topological phases and offer a fertile ground for discovering exotic topological properties.

Giant Domain Wall Anomalous Hall Effect in a Layered Antiferromagnet EuAl_{2}Si_{2}

Generally, the dissipationless Hall effect in solids requires time-reversal symmetry breaking (TRSB), where TRSB induced by external magnetic field results in the ordinary Hall effect, while TRSB caused by spontaneous magnetization gives rise to the anomalous Hall effect (AHE) which scales with the net magnetization. The AHE is therefore not expected in antiferromagnets with vanishing small magnetization. However, large AHE was recently observed in certain antiferromagnets with noncollinear spin structure and nonvanishing Berry curvature. Here, we report another origin of AHE in a layered antiferromagnet EuAl_{2}Si_{2}, namely, the domain wall (DW) skew scattering with Weyl points near the Fermi level, in experiments for the first time. Interestingly, the DWs form a unique periodic stripe structure with controllable periodicity by external magnetic field, which decreases nearly monotonically from 975 nm at 0 T to 232 nm at 4 T. Electrons incident on DW with topological bound states experience strong asymmetric scattering, leading to a giant AHE, with the DW Hall conductivity (DWHC) at 2 K and 1.2 T reaching a record value of ∼1.51×10^{4}  Scm^{-1} among bulk systems and being 2 orders of magnitude larger than the intrinsic anomalous Hall conductivity. The observation not only sets a new paradigm for exploration of large anomalous Hall effect, but also provides potential applications in spintronic devices.

Designing giant Hall response in layered topological semimetals

Noncoplanar magnets are excellent candidates for spintronics. However, such materials are difficult to find, and even more so to intentionally design. Here, we report a chemical design strategy that allows us to find a series of noncoplanar magnets-Ln3Sn7 (Ln = Dy, Tb)-by targeting layered materials that have decoupled magnetic sublattices with dissimilar single-ion anisotropies and combining those with a square-net topological semimetal sublattice. Ln3Sn7 shows high carrier mobilities upwards of 17,000 cm2 ⋅ V-1 ⋅ s-1, and hosts noncoplanar magnetic order. This results in a giant Hall response with an anomalous Hall angle of 0.17 and Hall conductivity of over 42,000 Ω-1 ⋅ cm-1-a value over an order of magnitude larger than the established benchmarks in Co3Sn2S2 and Fe thin films.

Topological Hall effect instigated in kagome Mn3-xSn due to Mn-deficit induced noncoplanar spin structure

Magnetic topological semimetals are manifestations of the interplay between electronic and magnetic phases of matter, leading to peculiar characteristics such as the anomalous Hall effect (AHE) and the topological Hall effect (THE). Mn3Sn is a time-reversal symmetry-broken magnetic Weyl semimetal showing topological characteristics within the Kagome lattice network. This study reveals a large THE in Mn2.8Sn (6% Mn deficit Mn3Sn) at room temperature in thexy-plane, despite being an antiferromagnet. We argue that the magnetocrystalline anisotropy induced noncoplanar spin structure is responsible for the observed THE in these systems. Further, the topological properties of these systems are highly anisotropic, as we observe a large AHE in thezx-plane. We find that Fe doping at the Mn site, Mn3-xFexSn (x= 0.2, 0.25, & 0.35), tunes the topological properties of these systems. These findings promise the realization of potential topotronic applications at room temperature.

Experimental progress in Eu(Al,Ga)4topological antiferromagnets

The non-trivial magnetic and electronic phases occurring in topological magnets are often entangled, thus leading to a variety of exotic physical properties. Recently, the BaAl4-type compounds have been extensively investigated to elucidate the topological features appearing in their real- and momentum spaces. In particular, the topological Hall effect and the spin textures, typical of the centrosymmetric Eu(Al,Ga)4family, have stimulated extensive experimental and theoretical research. In this topical review, we discuss the latest findings on the Eu(Al,Ga)4topological antiferromagnets and related materials, arising from a wide range of experimental techniques. We show that Eu(Al,Ga)4represents a suitable platform to explore the interplay between lattice-, charge-, and spin degrees of freedom, and associated emergent phenomena. Finally, we address some key questions open to future investigation.

Extremely Large Anomalous Hall Conductivity and Unusual Axial Diamagnetism in a Quasi-1D Dirac Material La3MgBi5

Anomalous Hall effect (AHE), one of the most important electronic transport phenomena, generally appears in ferromagnetic materials but is rare in materials without magnetic elements. Here, a study of La3MgBi5 is presented, whose band structure carries multitype Dirac fermions. Although magnetic elements are absent in La3MgBi5, the signals of AHE can be observed. In particular, the anomalous Hall conductivity is extremely large, reaching 42,356 Ω-1 cm-1 with an anomalous Hall angle of 8.8%, the largest one that has been observed in the current AHE systems. The AHE is suggested to originate from the combination of skew scattering and Berry curvature. Another unique property discovered in La3MgBi5 is the axial diamagnetism. The diamagnetism is significantly enhanced and dominates the magnetization in the axial directions, which is the result of the restricted motion of the Dirac fermion at the Fermi level. These findings not only establish La3MgBi5 as a suitable platform to study AHE and quantum transport but also indicate the great potential of 315-type Bi-based materials for exploring novel physical properties.

Observation of Topological Hall Effect in a Chemically Complex Alloy

The topological Hall effect (THE) is the transport response of chiral spin textures and thus can serve as a powerful probe for detecting and understanding these unconventional magnetic orders. So far, the THE is only observed in either noncentrosymmetric systems where spin chirality is stabilized by Dzyaloshinskii-Moriya interactions, or triangular-lattice magnets with Ruderman-Kittel-Kasuya-Yosida-type interactions. Here, a pronounced THE is observed in a Fe-Co-Ni-Mn chemically complex alloy with a simple face-centered cubic (fcc) structure across a wide range of temperatures and magnetic fields. The alloy is shown to have a strong magnetic frustration owing to the random occupation of magnetic atoms on the close-packed fcc lattice and the direct Heisenberg exchange interaction among atoms, as evidenced by the appearance of a reentrant spin glass state in the low-temperature regime and the first principles calculations. Consequently, THE is attributed to the nonvanishing spin chirality created by strong spin frustration under the external magnetic field, which is distinct from the mechanism responsible for the skyrmion systems, as well as geometrically frustrated magnets.

Electrical Detection and Nucleation of a Magnetic Skyrmion in a Magnetic Tunnel Junction Observed via Operando Magnetic Microscopy

Magnetic skyrmions are topological spin textures which are envisioned as nanometer scale information carriers in magnetic memory and logic devices. The recent demonstrations of room temperature skyrmions and their current induced manipulation in ultrathin films were first steps toward the realization of such devices. However, important challenges remain regarding the electrical detection and the low-power nucleation of skyrmions, which are required for the read and write operations. Here, we demonstrate, using operando magnetic microscopy experiments, the electrical detection of a single magnetic skyrmion in a magnetic tunnel junction (MTJ) and its nucleation and annihilation by gate voltage via voltage control of magnetic anisotropy. The nucleated skyrmion can be manipulated by both gate voltages and external magnetic fields, leading to tunable intermediate resistance states. Our results unambiguously demonstrate the readout and voltage controlled write operations in a single MTJ device, which is a major milestone for low power skyrmion based technologies.

Tunable positions of Weyl nodes via magnetism and pressure in the ferromagnetic Weyl semimetal CeAlSi

The noncentrosymmetric ferromagnetic Weyl semimetal CeAlSi with simultaneous space-inversion and time-reversal symmetry breaking provides a unique platform for exploring novel topological states. Here, by employing multiple experimental techniques, we demonstrate that ferromagnetism and pressure can serve as efficient parameters to tune the positions of Weyl nodes in CeAlSi. At ambient pressure, a magnetism-facilitated anomalous Hall/Nernst effect (AHE/ANE) is uncovered. Angle-resolved photoemission spectroscopy (ARPES) measurements demonstrated that the Weyl nodes with opposite chirality are moving away from each other upon entering the ferromagnetic phase. Under pressure, by tracing the pressure evolution of AHE and band structure, we demonstrate that pressure could also serve as a pivotal knob to tune the positions of Weyl nodes. Moreover, multiple pressure-induced phase transitions are also revealed. These findings indicate that CeAlSi provides a unique and tunable platform for exploring exotic topological physics and electron correlations, as well as catering to potential applications, such as spintronics.

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.

High-density, spontaneous magnetic biskyrmions induced by negative thermal expansion in ferrimagnets

Magnetic skyrmions are topologically protected quasiparticles that are promising for applications in spintronics. However, the low stability of most magnetic skyrmions leads to either a narrow temperature range in which they can exist, a low density of skyrmions, or the need for an external magnetic field, which greatly limits their wide application. In this study, high-density, spontaneous magnetic biskyrmions existing within a wide temperature range and without the need for a magnetic field were formed in ferrimagnets owing to the existence of a negative thermal expansion of the lattice. Moreover, a strong connection between the atomic-scale ferrimagnetic structure and nanoscale magnetic domains in Ho(Co,Fe)3 was revealed via in situ neutron powder diffraction and Lorentz transmission electron microscopy measurements. The critical role of the negative thermal expansion in generating biskyrmions in HoCo3 based on the magnetoelastic coupling effect is further demonstrated by comparing the behavior of HoCo2.8Fe0.2 with a positive thermal expansion.

Tuning of electrical, magnetic, and topological properties of magnetic Weyl semimetal Mn3+xGe by Fe doping

We report on the tuning of electrical, magnetic, and topological properties of the magnetic Weyl semimetal (Mn3+xGe) by Fe doping at the Mn site, Mn(3+x)-δFeδGe (δ= 0, 0.30, and 0.62). Fe doping significantly changes the electrical and magnetic properties of Mn3+xGe. The resistivity of the parent compound displays metallic behavior, the system withδ= 0.30 of Fe doping exhibits semiconducting or bad-metallic behavior, and the system withδ= 0.62 of Fe doping demonstrates a metal-insulator transition at around 100 K. Further, we observe that the Fe doping increases in-plane ferromagnetism, magnetocrystalline anisotropy, and induces a spin-glass state at low temperatures. Surprisingly, topological Hall state has been noticed at a Fe doping ofδ= 0.30 that is not found in the parent compound or withδ= 0.62 of Fe doping. In addition, spontaneous anomalous Hall effect observed in the parent system is significantly reduced with increasing Fe doping concentration.

Ordering of room-temperature magnetic skyrmions in a polar van der Waals magnet

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications.

Magnetic-field modulation of topological electronic state and emergent magneto-transport in a magnetic Weyl semimetal

The modulation of topological electronic state by an external magnetic field is highly desired for condensed-matter physics. Schemes to achieve this have been proposed theoretically, but few can be realized experimentally. Here, combining transverse transport, theoretical calculations, and scanning tunneling microscopy/spectroscopy (STM/S) investigations, we provide an observation that the topological electronic state, accompanied by an emergent magneto-transport phenomenon, was modulated by applying magnetic field through induced non-collinear magnetism in the magnetic Weyl semimetal EuB₆. A giant unconventional anomalous Hall effect (UAHE) is found during the magnetization re-orientation from easy axes to hard ones in magnetic field, with a UAHE peak around the low field of 5 kOe. Under the reasonable spin-canting effect, the folding of the topological anti-crossing bands occurs, generating a strong Berry curvature that accounts for the observed UAHE. Field-dependent STM/S reveals a highly synchronous evolution of electronic density of states, with a dI/dV peak around the same field of 5 kOe, which provides evidence to the folded bands and excited UAHE by external magnetic fields. This finding elucidates the connection between the real-space non-collinear magnetism and the k-space topological electronic state and establishes a novel manner to engineer the magneto-transport behaviors of correlated electrons for future topological spintronics.

Room-Temperature Magnetic Skyrmions and Large Topological Hall Effect in Chromium Telluride Engineered by Self-Intercalation

Room-temperature magnetic skyrmion materials exhibiting robust topological Hall effect (THE) are crucial for novel nano-spintronic devices. However, such skyrmion-hosting materials are rare in nature. In this study, a self-intercalated transition metal dichalcogenide Cr_{1+ x} Te₂ with a layered crystal structure that hosts room-temperature skyrmions and exhibits large THE is reported. By tuning the self-intercalate concentration, a monotonic control of Curie temperature from 169 to 333 K and a magnetic anisotropy transition from out-of-plane to the in-plane configuration are achieved. Based on the intercalation engineering, room-temperature skyrmions are successfully created in Cr_1.53 Te₂ with a Curie temperature of 295 K and a relatively weak perpendicular magnetic anisotropy. Remarkably, a skyrmion-induced topological Hall resistivity as large as ≈106 nΩ cm is observed at 290 K. Moreover, a sign reversal of THE is also found at low temperatures, which can be ascribed to other topological spin textures having an opposite topological charge to that of the skyrmions. Therefore, chromium telluride can be a new paradigm of the skyrmion material family with promising prospects for future device applications.

Topological Hall Effect Anisotropy in Kagome Bilayer Metal Fe_{3}Sn_{2}

Kagome lattice materials have attracted growing interest for their topological properties and flatbands in electronic structure. We present a comprehensive study on the anisotropy and out-of-plane electric transport in Fe_{3}Sn_{2}, a metal with bilayer of Fe kagome planes and with massive Dirac fermions that features high-temperature noncollinear magnetic structure and magnetic skyrmions. For the electrical current path along the c axis, in micron-size crystals, we found a large topological Hall effect over a wide temperature range down to spin-glass state. Twofold and fourfold angular magnetoresistance are observed for different magnetic phases, reflecting the competition of magnetic interactions and magnetic anisotropy in kagome lattice that preserve robust topological Hall effect for inter-kagome bilayer currents. This provides new insight into the anisotropy in Fe_{3}Sn_{2}, of interest in skyrmionic-bubble application-related micron-size devices.

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.

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.

Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers

We investigate an instability toward a square-lattice formation of magnetic skyrmions in centrosymmetric layered systems. By focusing on a bilayer square-lattice structure with the inversion center at the interlayer bond instead of the atomic site, we numerically examine the stability of the square skyrmion crystal (SkX) based on an effective spin model with the momentum-resolved interaction in the ground state through the simulated annealing. As a result, we find that a layer-dependent staggered Dzyaloshinskii-Moriya (DM) interaction built in the lattice structure becomes the origin of the square SkX in an external magnetic field irrespective of the sign of the interlayer exchange interaction. The obtained square SkX is constituted of the SkXs with different helicities in each layer due to the staggered DM interaction. Furthermore, we show that the interplay between the staggered DM interaction and the interlayer exchange interaction gives rise to a double-Qstate with a uniform component of the scalar chirality in the low-field region. The present results provide another way of stabilizing the square SkX in centrosymmetric magnets, which will be useful to explore further exotic topological spin textures.

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.

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.

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.

Spin and Orbital Effects on Asymmetric Exchange Interaction in Polar Magnets: M(IO3)2 (M = Cu and Mn)

Magnetic polar materials feature an astonishing range of physical properties, such as magnetoelectric coupling, chiral spin textures, and related new spin topology physics. This is primarily attributable to their lack of space inversion symmetry in conjunction with unpaired electrons, potentially facilitating an asymmetric Dzyaloshinskii-Moriya (DM) exchange interaction supported by spin-orbital and electron-lattice coupling. However, engineering the appropriate ensemble of coupled degrees of freedom necessary for enhanced DM exchange has remained elusive for polar magnets. Here, we study how spin and orbital components influence the capability of promoting the magnetic interaction by studying two magnetic polar materials, α-Cu(IO₃)₂ (²D) and Mn(IO₃)₂ (⁶S), and connecting their electronic and magnetic properties with their structures. The chemically controlled low-temperature synthesis of these complexes resulted in pure polycrystalline samples, providing a viable pathway to prepare bulk forms of transition-metal iodates. Rietveld refinements of the powder synchrotron X-ray diffraction data reveal that these materials exhibit different crystal structures but crystallize in the same polar and chiral P2₁ space group, giving rise to an electric polarization along the b-axis direction. The presence and absence of an evident phase transition to a possible topologically distinct state observed in α-Cu(IO₃)₂ and Mn(IO₃)₂, respectively, imply the important role of spin-orbit coupling. Neutron diffraction experiments reveal helpful insights into the magnetic ground state of these materials. While the long-wavelength incommensurability of α-Cu(IO₃)₂ is in harmony with sizable asymmetric DM interaction and low dimensionality of the electronic structure, the commensurate stripe AFM ground state of Mn(IO₃)₂ is attributed to negligible DM exchange and isotropic orbital overlapping. The work demonstrates connections between combined spin and orbital effects, magnetic coupling dimensionality, and DM exchange, providing a worthwhile approach for tuning asymmetric interaction, which promotes evolution of topologically distinct spin phases.

Giant Topological Hall Effect in van der Waals Heterostructures of CrTe2/Bi2Te3

Discoveries of the interfacial topological Hall effect (THE) provide an ideal platform for exploring the physics arising from the interplay between topology and magnetism. The interfacial topological Hall effect is closely related to the Dzyaloshinskii-Moriya interaction (DMI) at an interface and topological spin textures. However, it is difficult to achieve a sizable THE in heterostructures due to the stringent constraints on the constituents of THE heterostructures, such as strong spin-orbit coupling (SOC). Here, we report the observation of a giant THE signal of 1.39 μΩ·cm in the van der Waals heterostructures of CrTe₂/Bi₂Te₃ fabricated by molecular beam epitaxy, a prototype of two-dimensional (2D) ferromagnet (FM)/topological insulator (TI). This large magnitude of THE is attributed to an optimized combination of 2D ferromagnetism in CrTe₂, strong SOC in Bi₂Te₃, and an atomically sharp interface. Our work reveals CrTe₂/Bi₂Te₃ as a convenient platform for achieving large interfacial THE in hybrid systems, which could be utilized to develop quantum science and high-density information storage devices.

Magneto-optical spectroscopy on Weyl nodes for anomalous and topological Hall effects in chiral MnGe

Physics of Weyl electrons has been attracting considerable interests and further accelerated by recent discoveries of giant anomalous Hall effect (AHE) and topological Hall effect (THE) in several magnetic systems including non-coplanar magnets with spin chirality or small-size skyrmions. These AHEs/THEs are often attributed to the intense Berry curvature generated around the Weyl nodes accompanied by band anti-crossings, yet the direct experimental evidence still remains elusive. Here, we demonstrate an essential role of the band anti-crossing for the giant AHE and THE in MnGe thin film by using the terahertz magneto-optical spectroscopy. The low-energy resonance structures around ~ 1.2 meV in the optical Hall conductivity show the enhanced AHE and THE, indicating the emergence of at least two distinct anti-crossings near the Fermi level. The theoretical analysis demonstrates that the competition of these resonances with opposite signs is a cause of the strong temperature and magnetic-field dependences of observed DC Hall conductivity. These results lead to the comprehensive understanding of the interplay among the transport phenomena, optical responses and electronic/spin structures.

Previous work has proposed that the anomalous and topological Hall effects, associated with Weyl nodes, should have a signature in optical conductivity. Here, using THz optical spectroscopy, the authors assign these two effects to optical conductivity resonances, arising near band anti-crossings, in thin films of MnGe.

Topological spin crystals by itinerant frustration

Spin textures with nontrivial topology, such as vortices and skyrmions, have attracted attention as a source of unconventional magnetic, transport, and optical phenomena. Recently, a new generation of topological spin textures has been extensively studied in itinerant magnets; in contrast to the conventional ones induced, e.g., by the Dzyaloshinskii-Moriya interaction in noncentrosymmetric systems, they are characterized by extremely short magnetic periods and stable even in centrosymmetric systems. Here we review such new types of topological spin textures with particular emphasis on their stabilization mechanism. Focusing on the interplay between charge and spin degrees of freedom in itinerant electron systems, we show that itinerant frustration, which is the competition among electron-mediated interactions, plays a central role in stabilizing a variety of topological spin crystals including a skyrmion crystal with unconventional high skyrmion number, meron crystals, and hedgehog crystals. We also show that the essential ingredients in the itinerant frustration are represented by bilinear and biquadratic spin interactions in momentum space. This perspective not only provides a unified understanding of the unconventional topological spin crystals but also stimulates further exploration of exotic topological phenomena in itinerant magnets.

Characterization of a Disordered above Room Temperature Skyrmion Material Co8Zn8Mn4

Topologically nontrivial spin textures host great promise for future spintronic applications. Skyrmions in particular are of burgeoning interest owing to their nanometric size, topological protection, and high mobility via ultra-low current densities. It has been previously reported through magnetic susceptibility, microscopy, and scattering techniques that Co8Zn8Mn4 forms an above room temperature triangular skyrmion lattice. Here, we report the synthesis procedure and characterization of a polycrystalline Co8Zn8Mn4 disordered bulk sample. We employ powder X-ray diffraction and backscatter Laue diffraction as characterization tools of the crystallinity of the samples, while magnetic susceptibility and Small Angle Neutron Scattering (SANS) measurements are performed to study the skyrmion phase. Magnetic susceptibility measurements show a dip anomaly in the magnetization curves, which persists over a range of approximately 305 K-315 K. SANS measurements reveal a rotationally disordered polydomain skyrmion lattice. Applying a symmetry-breaking magnetic field sequence, we were able to orient and order the previously jammed state to yield the prototypical hexagonal diffraction patterns with secondary diffraction rings. This emergence of the skyrmion order serves as a unique demonstration of the fundamental interplay of structural disorder and anisotropy in stabilizing the thermal equilibrium phase.

Recent Progress in Proximity Coupling of Magnetism to Topological Insulators

Inducing long-range magnetic order in 3D topological insulators can gap the Dirac-like metallic surface states, leading to exotic new phases such as the quantum anomalous Hall effect or the axion insulator state. These magnetic topological phases can host robust, dissipationless charge and spin currents or unique magnetoelectric behavior, which can be exploited in low-energy electronics and spintronics applications. Although several different strategies have been successfully implemented to realize these states, to date these phenomena have been confined to temperatures below a few Kelvin. This review focuses on one strategy: inducing magnetic order in topological insulators by proximity of magnetic materials, which has the capability for room temperature operation, unlocking the potential of magnetic topological phases for applications. The unique advantages of this strategy, the important physical mechanisms facilitating magnetic proximity effect, and the recent progress to achieve, understand, and harness proximity-coupled magnetic order in topological insulators are discussed. Some emerging new phenomena and applications enabled by proximity coupling of magnetism and topological materials, such as skyrmions and the topological Hall effect, are also highlighted, and the authors conclude with an outlook on remaining challenges and opportunities in the field.

Unconventional Hall effect and its variation with Co-doping in van der Waals Fe3GeTe2

Two-dimensional (2D) van der Waals (vdW) magnetic materials have attracted a lot of attention owing to the stabilization of long range magnetic order down to atomic dimensions, and the prospect of novel spintronic devices with unique functionalities. The clarification of the magnetoresistive properties and its correlation to the underlying magnetic configurations is essential for 2D vdW-based spintronic devices. Here, the effect of Co-doping on the magnetic and magnetotransport properties of Fe₃GeTe₂ have been investigated. Magnetotransport measurements reveal an unusual Hall effect behavior whose strength was considerably modified by Co-doping and attributed to arise from the underlying complicated spin textures. The present results provide a clue to tailoring of the underlying interactions necessary for the realization of a variety of unconventional spin textures for 2D vdW FM-based spintronics.

Emergence of Room Temperature Magnetotransport Anomaly in Epitaxial Pt/γ'-Fe4N/MgO Heterostructures toward Noncollinear Spintronics

Noncollinear spin textures have attracted much attention due to their novel physical behaviors in heavy/ferromagnetic metal (HM/FM) systems. The transport anomaly, appearing as contrast humps in Hall resistivity curves, is the mark of noncollinear spin textures. Here, the epitaxial Pt/γ'-Fe₄N bilayers with noncollinear spin textures were obtained by facing target sputtering. Large micromagnetic Dzyaloshinskii-Moriya interaction coefficient D of 2.90 mJ/m² appears in Pt/γ'-Fe₄N/MgO systems, which is larger than 2.05 mJ/m² of Pt/Co/MgO systems with skyrmionic states. Moreover, at 300 K, magnetic bubble-like domains appear in Pt/γ'-Fe₄N bilayers that just possess a 3 nm thick ferromagnetic layer instead of [HM/FM]_n or [HM₁/FM/HM₂]_n multilayers. Additionally, a room-temperature transport anomaly appears in Pt/γ'-Fe₄N/MgO systems. The contrast humps of Pt(3 nm)/γ'-Fe₄N(t_Fe4N ≤ 4 nm)/MgO heterostructures are not sharp due to the nonuniform distributions of the magnetic bubble-like domains with various sizes and irregular shapes, as observed by the magnetic force microscopy. The discovery of epitaxial Pt/γ'-Fe₄N bilayers with noncollinear spin states is more crucial than that of polycrystalline or amorphous HM/FM systems for reducing ohmic heating, which provides a candidate for noncollinear spintronic applications.

Absence of Hall effect due to Berry curvature in phase space

Transverse current due to Berry curvature in phase space is formulated based on the Boltzmann equations with the semiclassical equations of motion for an electron wave packet. It is shown that the Hall effect due to the phase space Berry curvature is absent because the contributions from “anomalous velocity” and “effective Lorentz force” are completely cancelled out.

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.

Giant c-axis nonlinear anomalous Hall effect in Td-MoTe2 and WTe2

While the anomalous Hall effect can manifest even without an external magnetic field, time reversal symmetry is nonetheless still broken by the internal magnetization of the sample. Recently, it has been shown that certain materials without an inversion center allow for a nonlinear type of anomalous Hall effect whilst retaining time reversal symmetry. The effect may arise from either Berry curvature or through various asymmetric scattering mechanisms. Here, we report the observation of an extremely large c-axis nonlinear anomalous Hall effect in the non-centrosymmetric Td phase of MoTe2 and WTe2 without intrinsic magnetic order. We find that the effect is dominated by skew-scattering at higher temperatures combined with another scattering process active at low temperatures. Application of higher bias yields an extremely large Hall ratio of E⊥/E|| = 2.47 and corresponding anomalous Hall conductivity of order 8 × 107 S/m.

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.

Emulating spin transport with nonlinear optics, from high-order skyrmions to the topological Hall effect

Exploring material magnetization led to countless fundamental discoveries and applications, culminating in the field of spintronics. Recently, research effort in this field focused on magnetic skyrmions – topologically robust chiral magnetization textures, capable of storing information and routing spin currents via the topological Hall effect. In this article, we propose an optical system emulating any 2D spin transport phenomena with unprecedented controllability, by employing three-wave mixing in 3D nonlinear photonic crystals. Precise photonic crystal engineering, as well as active all-optical control, enable the realization of effective magnetization textures beyond the limits of thermodynamic stability in current materials. As a proof-of-concept, we theoretically design skyrmionic nonlinear photonic crystals with arbitrary topologies and propose an optical system exhibiting the topological Hall effect. Our work paves the way towards quantum spintronics simulations and novel optoelectronic applications inspired by spintronics, for both classical and quantum optical information processing.

Control of effective magnetization textures like skyrmions is limited by the thermodynamic stability in current materials. Here, the authors propose a 3D nonlinear photonic crystal to emulate 2D spin transport phenomena with excellent controllability.

Recent Progress on Topological Structures in Ferroic Thin Films and Heterostructures

Topological spin/polarization structures in ferroic materials continue to draw great attention as a result of their fascinating physical behaviors and promising applications in the field of high-density nonvolatile memories as well as future energy-efficient nanoelectronic and spintronic devices. Such developments have been made, in part, based on recent advances in theoretical calculations, the synthesis of high-quality thin films, and the characterization of their emergent phenomena and exotic phases. Herein, progress over the last decade in the study of topological structures in ferroic thin films and heterostructures is explored, including the observation of topological structures and control of their structures and emergent physical phenomena through epitaxial strain, layer thickness, electric, magnetic fields, etc. First, the evolution of topological spin structures (e.g., magnetic skyrmions) and associated functionalities (e.g., topological Hall effect) in magnetic thin films and heterostructures is discussed. Then, the exotic polar topologies (e.g., domain walls, closure domains, polar vortices, bubble domains, and polar skyrmions) and their emergent physical properties in ferroelectric oxide films and heterostructures are explored. Finally, a brief overview and prospectus of how the field may evolve in the coming years is provided.

Chiral-Bubble-Induced Topological Hall Effect in Ferromagnetic Topological Insulator Heterostructures

We report compelling evidence of an emergent topological Hall effect (THE) from chiral bubbles in a two-dimensional uniaxial ferromagnet, V-doped Sb₂Te₃ heterostructure. The sign of THE signal is determined by the net curvature of domain walls in different domain configurations, and the strength of THE signal is correlated with the density of nucleation or pinned bubble domains. The experimental results are in good agreement with the integrated linear transport and Monte Carlo simulations, corroborating the emergent gauge field at chiral magnetic bubbles. Our findings not only reveal a general mechanism of THE in two-dimensional ferromagnets but also pave the way for the creation and manipulation of topological spin textures for spintronic applications.

Anomalous transport due to Weyl fermions in the chiral antiferromagnets Mn3X, X = Sn, Ge

The recent discoveries of strikingly large zero-field Hall and Nernst effects in antiferromagnets Mn₃X (X = Sn, Ge) have brought the study of magnetic topological states to the forefront of condensed matter research and technological innovation. These effects are considered fingerprints of Weyl nodes residing near the Fermi energy, promoting Mn₃X (X = Sn, Ge) as a fascinating platform to explore the elusive magnetic Weyl fermions. In this review, we provide recent updates on the insights drawn from experimental and theoretical studies of Mn₃X (X = Sn, Ge) by combining previous reports with our new, comprehensive set of transport measurements of high-quality Mn₃Sn and Mn₃Ge single crystals. In particular, we report magnetotransport signatures specific to chiral anomalies in Mn₃Ge and planar Hall effect in Mn₃Sn, which have not yet been found in earlier studies. The results summarized here indicate the essential role of magnetic Weyl fermions in producing the large transverse responses in the absence of magnetization.

The large anomalous Hall (AHE) and anomalous Nernst effects (ANE) in antiferromagnets Mn₃Sn/Mn₃Ge are considered fingerprints of Weyl nodes residing near the Fermi energy. Here, the authors review the results from previous studies combining with new transport measurements on Mn₃Sn/Mn₃Ge single crystals, suggesting the essential role of magnetic Weyl fermions in explaining the AHE and ANE.