Evidence for magnetic Weyl fermions in a correlated metal

Magnetostriction, piezomagnetism and domain nucleation in a Kagome antiferromagnet

Whenever the elastic energy of a solid depends on magnetic field, there is a magnetostrictive response. Field-linear magnetostriction implies piezomagnetism and vice versa. Here, we show that Mn3Sn, a non-collinear antiferromanget with Weyl nodes, hosts a large and almost perfectly linear magnetostriction even at room temperature. The longitudinal and transverse magnetostriction, with opposite signs and similar amplitude are restricted to the kagome planes and the out-of-plane response is negligibly small. By studying four different samples with different Mn:Sn ratios, we find a clear correlation between the linear magnetostriction, the spontaneous magnetization and the concentration of Sn vacancies. The recently reported piezomagnetic data fits in our picture. We show that linear magnetostriction and piezomagnetism are both driven by the field-induced in-plane twist of spins. A quantitative account of the experimental data requires the distortion of the spin texture by Sn vacancies. We find that the field-induced domain nucleation within the hysteresis loop corresponds to a phase transition. Within the hysteresis loop, a concomitant mesoscopic modulation of local strain and spin twist angles, leading to twisto-magnetic stripes, arises as a result of the competition between elastic and magnetic energies.

Recent progress of MnBi2Te4 epitaxial thin films as a platform for realising the quantum anomalous Hall effect

Since the first realisation of the quantum anomalous Hall effect (QAHE) in a dilute magnetic-doped topological insulator thin film in 2013, the quantisation temperature has been limited to less than 1 K due to magnetic disorder in dilute magnetic systems. With magnetic moments ordered into the crystal lattice, the intrinsic magnetic topological insulator MnBi2Te4 has the potential to eliminate or significantly reduce magnetic disorder and improve the quantisation temperature. Surprisingly, to date, the QAHE has yet to be observed in molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films at zero magnetic field, and what leads to the difficulty in quantisation is still an active research area. Although bulk MnBi2Te4 and exfoliated flakes have been well studied, revealing both the QAHE and axion insulator phases, experimental progress on MBE thin films has been slower. Understanding how the breakdown of the QAHE occurs in MnBi2Te4 thin films and finding solutions that will enable mass-produced millimetre-size QAHE devices operating at elevated temperatures are required. In this mini-review, we will summarise recent studies on the electronic and magnetic properties of MBE MnBi2Te4 thin films and discuss mechanisms that could explain the failure of the QAHE from the aspects of defects, electronic structure, magnetic order, and consequences of their delicate interplay. Finally, we propose several strategies for realising the QAHE at elevated temperatures in MnBi2Te4 thin films.

Nanoscale Visualization of Symmetry-Breaking Electronic Orders and Magnetic Anisotropy in a Kagome Magnet YMn6Sn6

A kagome lattice hosts a plethora of quantum states arising from the interplay between nontrivial topology and electron correlations. The recently discovered kagome magnet RMn6Sn6 (R represents a rare-earth element) is believed to showcase a kagome band closely resembling textbook characteristics. Here, we report the characterization of local electronic states and their magnetization response in YMn6Sn6 via scanning tunneling microscopy measurements under vector magnetic fields. Our spectroscopic maps reveal a spontaneously trimerized kagome electronic order in YMn6Sn6, where the 6-fold rotational symmetry is disrupted while translational symmetry is maintained. Further application of an external magnetic field demonstrates a strong coupling of the YMn6Sn6 kagome band to the field, which exhibits an energy shift discrepancy under different field directions, implying the existence of magnetization-response anisotropy and anomalous g factors. Our findings establish YMn6Sn6 as an ideal platform for investigating kagome-derived orbital magnetic moment and correlated magnetic topological states.

Tunable hybrid-order Weyl semimetal via staggered magnetic flux

We investigate a hybrid-order Weyl semimetal (HOWS) constructed by stacking the two-dimensional kagome lattice with staggered magnetic flux. By adjusting the magnitude of flux, higher-order topological phases are tunably intertwined with the first-order topological Chern insulators, which is governed by the evolution of Weyl points. Meanwhile the surface Fermi arcs undergo topological Lifshitz transition. Notably, due to the breaking of time-reversal symmetry (TRS), a novel split of a quadratic double Weyl point occurs, giving rise to additional three type-II Weyl points hybridizing with one type-I node. This phenomenon plays a crucial role in realizing high-Chern-number phases withC=±2and reveals a new mechanism for the emergence of type-II Weyl fermions in topological kagome semimetals. We anticipate that this study will stimulate further investigation into the unique physics of kagome materials and Weyl semimetals.

Observation of Omnidirectional Exchange Bias at All-Antiferromagnetic Polycrystalline Heterointerface

Due to promising functionalities that may dramatically enhance spintronics performance, antiferromagnets are the subject of intensive research for developing the next-generation active elements to replace ferromagnets. In particular, the recent experimental demonstration of tunneling magnetoresistance and electrical switching using chiral antiferromagnets has sparked expectations for the practical integration of antiferromagnetic materials into device architectures. To further develop the technology to manipulate the magnetic anisotropies in all-antiferromagnetic devices, it is essential to realize exchange bias through the interface between antiferromagnetic multilayers. Here, the first observation on the omnidirectional exchange bias at an all-antiferromagnetic polycrystalline heterointerface is reported. This experiment demonstrates that the interfacial energy causing the exchange bias between the chiral-antiferromagnet Mn3Sn/collinear-antiferromagnet MnN layers is comparable to those found at the conventional ferromagnet/antiferromagnet interface at room temperature. In sharp contrast with previous reports using ferromagnets, the magnetic field control of the unidirectional anisotropy is found to be omnidirectional due to the absence of the shape anisotropy in the antiferromagnetic multilayer. The realization of the omnidirectional exchange bias at the interface between polycrystalline antiferromagnets on amorphous templates, highly compatible with existing Si-based devices, paves the way for developing ultra-low power and ultra-high speed memory devices based on antiferromagnets.

Two-Dimensional Ultrathin Fe3Sn2 Kagome Metal with Defect-Dependent Magnetic Property

Two-dimensional (2D) Fe3Sn2, which is a room-temperature ferromagnetic kagome metal, has potential applications in spintronic devices. However, the systematic synthesis and magnetic study of 2D Fe3Sn2 single crystals have rarely been reported. Here we have synthesized 2D hexagonal and triangular Fe3Sn2 nanosheets by controlling the amount of FeCl2 precursors in the chemical vapor deposition (CVD) method. It is found that the hexagonal Fe3Sn2 nanosheets exist with Fe vacancy defects and show no obvious coercivity. While the triangular Fe3Sn2 nanosheet has obvious hysteresis loops at room temperature, its coercivity first increases and then remains stable with an increase in temperature, which should result from the competition of the thermal activation mechanism and spin direction rotation mechanism. A first-principles calculation study shows that the Fe vacancy defects in Fe3Sn2 can increase the distances between Fe atoms and weaken the ferromagnetism of Fe3Sn2. The resulting 2D Fe3Sn2 nanosheets provide a new choice for spintronic devices.

Fermi Surface Spin Texture and Topological Superconductivity in Spin-Orbit Free Noncollinear Antiferromagnets

We explore the relationship among the magnetic ordering in real space, the resulting spin texture on the Fermi surface, and the related superconducting gap structure in noncollinear antiferromagnetic metals without spin-orbit coupling. Via a perturbative approach, we show that noncollinear magnetic ordering in a metal can generate momentum-dependent spin texture on its Fermi surface, even in the absence of spin-orbit coupling, if the metal has more than three sublattices in its magnetic unit cell. Thus, our theory naturally extends the idea of altermagnetism to noncollinear spin structures. When superconductivity is developed in a magnetic metal, as the gap-opening condition is strongly constrained by the spin texture, the nodal structure of the superconducting state is also enforced by the magnetism-induced spin texture. Taking the noncollinear antiferromagnet on the kagome lattice as a representative example, we demonstrate how the Fermi surface spin texture induced by noncollinear antiferromagnetism naturally leads to odd-parity spin-triplet superconductivity with nontrivial topological properties.

Universal scaling law for chiral antiferromagnetism

The chiral antiferromagnetic (AFM) materials, which have been widely investigated due to their rich physics, such as non-zero Berry phase and topology, provide a platform for the development of antiferromagnetic spintronics. Here, we find two distinctive anomalous Hall effect (AHE) contributions in the chiral AFM Mn3Pt, originating from a time-reversal symmetry breaking induced intrinsic mechanism and a skew scattering induced topological AHE due to an out-of-plane spin canting with respect to the Kagome plane. We propose a universal AHE scaling law to explain the AHE resistivity (ρ A H ) in this chiral magnet, with both a scalar spin chirality (SSC)-induced skew scattering topological AHE term,a s k and non-collinear spin-texture induced intrinsic anomalous Hall term,b i n . We found thata s k andb i n can be effectively modulated by the interfacial electron scattering, exhibiting a linear relation with the inverse film thickness. Moreover, the scaling law can explain the anomalous Hall effect in various chiral magnets and has far-reaching implications for chiral-based spintronics devices.

Emerging Antiferromagnets for Spintronics

Antiferromagnets constitute promising contender materials for next-generation spintronic devices with superior stability, scalability, and dynamics. Nevertheless, the perception of well-established ferromagnetic spintronics underpinned by spontaneous magnetization seemed to indicate the inadequacy of antiferromagnets for spintronics-their compensated magnetization has been perceived to result in uncontrollable antiferromagnetic order and subtle magnetoelectronic responses. However, remarkable advancements have been achieved in antiferromagnetic spintronics in recent years, with consecutive unanticipated discoveries substantiating the feasibility of antiferromagnet-centered spintronic devices. It is emphasized that, distinct from ferromagnets, the richness in complex antiferromagnetic crystal structures is the unique and essential virtue of antiferromagnets that can open up their endless possibilities of novel phenomena and functionality for spintronics. In this Perspective, the recent progress in antiferromagnetic spintronics is reviewed, with a particular focus on that based on several kinds of antiferromagnets with special antiferromagnetic crystal structures. The latest developments in efficiently manipulating antiferromagnetic order, exploring novel antiferromagnetic physical responses, and demonstrating prototype antiferromagnetic spintronic devices are discussed. An outlook on future research directions is also provided. It is hoped that this Perspective can serve as guidance for readers who are interested in this field and encourage unprecedented studies on antiferromagnetic spintronic materials, phenomena, and devices.

Unusual multiple magnetic transitions and anomalous Hall effect observed in antiferromagnetic Weyl semimetal, Mn2.94Ge (Ge-rich)

We report on the magnetic and Hall effect measurements of the magnetic Weyl semimetal, Mn2.94Ge (Ge-rich) single crystal. From the magnetic properties study, we identify unusual multiple magnetic transitions below the Ne'el temperature of 353 K, such as the spin-reorientation (TSR) and ferromagnetic-like transitions. Consistent with the magnetic properties, the Hall effect study shows unusual behavior around the spin-reorientation transition. Specifically, the anomalous Hall conductivity increases with increasing temperature, reaching a maximum atTSR, which then gradually decreases with increasing temperature. This observation is quite in contrast to the Mn3+δGe (Mn-rich) system, though both compositions share the same hexagonal crystal symmetry. This study unravels the sensitivity of magnetic and topological properties on the Mn concentration.

Tunable Spin Textures in a Kagome Antiferromagnetic Semimetal via Symmetry Design

Kagome antiferromagnetic semimetals such as Mn3Sn have attracted extensive attention for their potential application in antiferromagnetic spintronics. Realizing high manipulation of kagome antiferromagnetic spin states at room temperature can reveal rich emergent phenomena resulting from the quantum interactions between topology, spin, and correlation. Here, we achieved tunable spin textures of Mn3Sn through symmetry design by controlling alternate Mn3Sn and heavy-metal Pt thicknesses. The various topological spin textures were predicted with theoretical simulations, and the skyrmion-induced topological Hall effect, strong spin-dependent scattering, and vertical gradient of spin states were obtained by magnetotransport and magnetic circular dichroism (MCD) spectroscopy measurements in Mn3Sn/Pt heterostructures. Our work provides an effective strategy for the innovative design of topological antiferromagnetic spintronic devices.

IrGe4: A Predicted Weyl-Metal with a Chiral Crystal Structure

Polycrystalline IrGe4 was synthesized by annealing elements at 800 °C for 240 h, and the composition was confirmed by energy-dispersive X-ray spectroscopy. IrGe4 adopts a chiral crystal structure (space group P3121) instead of a polar crystal structure (P31), which was corroborated by the convergent-beam electron diffraction and Rietveld refinements using synchrotron powder X-ray diffraction data. The crystal structure features layers of IrGe8 polyhedra along the b axis, and the layers are connected by edge- and corner-sharing. Each layer consists of corner-shared [Ir3Ge20] trimers, which are formed by three IrGe8 polyhedra connected by edge-sharing. Temperature-dependent resistivity indicates metallic behavior. The magnetoresistance increases with increasing applied magnetic field, and the nonsaturating magnetoresistance reaches 11.5% at 9 T and 10 K. The Hall resistivity suggests that holes are the majority carrier type, with a carrier concentration of 4.02 × 1021 cm-3 at 300 K. Electronic band structures calculated by density functional theory reveal a Weyl point with a chiral charge of +3 above the Fermi level.

SdH Oscillations from the Dirac Surface State in the Fermi-Arc Antiferromagnet NdBi

The recent progress in CuMnAs and Mn3X (X = Sn, Ge, Pt) shows that antiferromagnets (AFMs) provide a promising platform for advanced spintronics device innovations. Most recently, a switchable Fermi-arc is discovered by the ARPES technique in antiferromagnet NdBi, but the knowledge about electron-transport property and the manipulability of the magnetic structure in NdBi is still vacant to date. In this study, SdH oscillations are successfully verified from the Dirac surface states (SSs) with 2-dimensionality and nonzero Berry phase. Particularly, it is observed that the spin-flop transition only appears when the external magnetical field is applied along [001] direction, and features obvious hysteresis for the first time in NdBi, which provides a powerful handle for adjusting the spin texture in NdBi. Crucially, the DFT shows the Dirac cone and the Fermi arc strongly depend on the high-order magnetic structure of NdBi and further reveals the orbital magnetic moment of Nd plays a crucial role in fostering the peculiar SSs, leading to unveil the mystery of the band-splitting effect and to manipulate the electronic transport, high-effectively, in the thin film works in NdBi. It is believed that this study provides important guidance for the development of new antiferromagnet-based spintronics devices based on cutting-edge rare-earth monopnictides.

Voltage-Controlled High-Bandwidth Terahertz Oscillators Based on Antiferromagnets

Producing compact voltage-controlled frequency generators and sensors operating in the terahertz (THz) regime represents a major technological challenge. Here, we show that noncollinear antiferromagnets (NCAFMs) with kagome structure host gapless self-oscillations whose frequencies are tunable from 0 Hz to the THz regime via electrically induced spin-orbit torques (SOTs). The auto-oscillations' initiation, bandwidth, and amplitude are investigated by deriving an effective theory, which captures the reactive and dissipative SOTs. We find that the dynamics strongly depends on the ground state's chirality, with one chirality having gapped excitations, whereas the opposite chirality provides gapless self-oscillations. Our results reveal that NCAFMs offer unique THz functional components, which could play a significant role in filling the THz technology gap.

Magnetic States and Electronic Properties of Manganese-Based Intermetallic Compounds Mn2YAl and Mn3Z (Y = V, Cr, Fe, Co, Ni; Z = Al, Ge, Sn, Si, Pt)

We present a brief review of experimental and theoretical papers on studies of electron transport and magnetic properties in manganese-based compounds Mn2YZ and Mn3Z (Y = V, Cr, Fe, Co, Ni, etc.; Z = Al, Ge, Sn, Si, Pt, etc.). It has been shown that in the electronic subsystem of Mn2YZ compounds, the states of a half-metallic ferromagnet and a spin gapless semiconductor can arise with the realization of various magnetic states, such as a ferromagnet, a compensated ferrimagnet, and a frustrated antiferromagnet. Binary compounds of Mn3Z have the properties of a half-metallic ferromagnet and a topological semimetal with a large anomalous Hall effect, spin Hall effect, spin Nernst effect, and thermal Hall effect. Their magnetic states are also very diverse: from a ferrimagnet and an antiferromagnet to a compensated ferrimagnet and a frustrated antiferromagnet, as well as an antiferromagnet with a kagome-type lattice. It has been demonstrated that the electronic and magnetic properties of such materials are very sensitive to external influences (temperature, magnetic field, external pressure), as well as the processing method (cast, rapidly quenched, nanostructured, etc.). Knowledge of the regularities in the behavior of the electronic and magnetic characteristics of Mn2YAl and Mn3Z compounds can be used for applications in micro- and nanoelectronics and spintronics.

Anomalous spin current anisotropy in a noncollinear antiferromagnet

Cubic materials host high crystal symmetry and hence are not expected to support anisotropy in transport phenomena. In contrast to this common expectation, here we report an anomalous anisotropy of spin current can emerge in the (001) film of Mn3Pt, a noncollinear antiferromagnetic spin source with face-centered cubic structure. Such spin current anisotropy originates from the intertwined time reversal-odd ([Formula: see text]-odd) and time reversal-even ([Formula: see text]-even) spin Hall effects. Based on symmetry analyses and experimental characterizations of the current-induced spin torques in Mn3Pt-based heterostructures, we find that the spin current generated by Mn3Pt (001) exhibits exotic dependences on the current direction for all the spin components, deviating from that in conventional cubic systems. We also demonstrate that such an anisotropic spin current can be used to realize low-power spintronic applications such as the efficient field-free switching of the perpendicular magnetizations.

Discovery and construction of surface kagome electronic states induced by p-d electronic hybridization in Co3Sn2S2

Kagome-lattice materials possess attractive properties for quantum computing applications, but their synthesis remains challenging. Herein, based on the compelling identification of the two cleavable surfaces of Co3Sn2S2, we show surface kagome electronic states (SKESs) on a Sn-terminated triangular Co3Sn2S2 surface. Such SKESs are imprinted by vertical p-d electronic hybridization between the surface Sn (subsurface S) atoms and the buried Co kagome-lattice network in the Co3Sn layer under the surface. Owing to the subsequent lateral hybridization of the Sn and S atoms in a corner-sharing manner, the kagome symmetry and topological electronic properties of the Co3Sn layer is proximate to the Sn surface. The SKESs and both hybridizations were verified via qPlus non-contact atomic force microscopy (nc-AFM) and density functional theory calculations. The construction of SKESs with tunable properties can be achieved by the atomic substitution of surface Sn (subsurface S) with other group III-V elements (Se or Te), which was demonstrated theoretically. This work exhibits the powerful capacity of nc-AFM in characterizing localized topological states and reveals the strategy for synthesis of large-area transition-metal-based kagome-lattice materials using conventional surface deposition techniques.

Magnetic Weyl Semimetal in BaCrSe2 with Long-Distance Distribution of Weyl Points

Weyl semimetals (WSMs) have attracted great attentions that provide intriguing platforms for exploring fundamental physical phenomena and future topotronics applications. Despite the fact that numerous WSMs are achieved, WSMs with long-distance distribution of Weyl points (WPs) in given material candidates remain elusive. Here, the emergence of intrinsic ferromagnetic WSMs in BaCrSe₂ with the nontrivial nature explicitly confirmed by the Chern number and Fermi arc surface states analysis is theoretically demonstrated. Remarkably, unlike previous WSMs for which opposite chirality WPs are located very close to each other, the WPs of BaCrSe₂ host a long-distance distribution, as much as half of the reciprocal space vector, suggesting that the WPs are highly robust and difficult to be annihilated by perturbations. The presented results not only advance the general understanding of magnetic WSMs but also put forward potential applications in topotronics.

Semiconducting Electronic Structure of the Ferromagnetic Spinel HgCr_{2}Se_{4} Revealed by Soft-X-Ray Angle-Resolved Photoemission Spectroscopy

We study the electronic structure of the ferromagnetic spinel HgCr_{2}Se_{4} by soft-x-ray angle-resolved photoemission spectroscopy (SX-ARPES) and first-principles calculations. While a theoretical study has predicted that this material is a magnetic Weyl semimetal, SX-ARPES measurements give direct evidence for a semiconducting state in the ferromagnetic phase. Band calculations based on the density functional theory with hybrid functionals reproduce the experimentally determined band gap value, and the calculated band dispersion matches well with ARPES experiments. We conclude that the theoretical prediction of a Weyl semimetal state in HgCr_{2}Se_{4} underestimates the band gap, and this material is a ferromagnetic semiconductor.

Discovery of Topological Magnetic Textures near Room Temperature in Quantum Magnet TbMn6 Sn6

The study of topology in quantum materials has fundamentally advanced the understanding in condensed matter physics and potential applications in next-generation quantum information technology. Recently, the discovery of a topological Chern phase in the spin-orbit-coupled Kagome lattice TbMn₆ Sn₆ has attracted considerable interest. Whereas these phenomena highlight the contribution of momentum space Berry curvature and Chern gap on the electronic transport properties, less is known about the intrinsic real space magnetic texture, which is crucial for understanding the electronic properties and further exploring the unique quantum behavior. Here, the stabilization of topological magnetic skyrmions in TbMn₆ Sn₆ using Lorentz transmission electron microscopy near room temperature, where the spins experience full spin reorientation transition between the a- and c-axes, is directly observed. An effective spin Hamiltonian based on the Ginzburg-Landau theory is constructed and micromagnetic simulation is performed to clarify the critical role of Ruderman-Kittel-Kasuya-Yosida interaction on the stabilization of skyrmion lattice. These results not only uncover nontrivial spin topological texture in TbMn₆ Sn₆ , but also provide a solid basis to study its interplay with electronic topology.

Ultrafast Dynamics of Intrinsic Anomalous Hall Effect in the Topological Antiferromagnet Mn_{3}Sn

We investigate ultrafast dynamics of the anomalous Hall effect (AHE) in the topological antiferromagnet Mn_{3}Sn with sub-100 fs time resolution. Optical pulse excitations largely elevate the electron temperature up to 700 K, and terahertz probe pulses clearly resolve ultrafast suppression of the AHE before demagnetization. The result is well reproduced by microscopic calculation of the intrinsic Berry-curvature mechanism while the extrinsic contribution is clearly excluded. Our work opens a new avenue for the study of nonequilibrium AHE to identify the microscopic origin by drastic control of the electron temperature by light.

Field-linear anomalous Hall effect and Berry curvature induced by spin chirality in the kagome antiferromagnet Mn3Sn

During the past two decades, it has been established that a non-trivial electron wave-function topology generates an anomalous Hall effect (AHE), which shows itself as a Hall conductivity non-linear in magnetic field. Here, we report on an unprecedented case of field-linear AHE. In Mn₃Sn, a kagome magnet, the out-of-plane Hall response, which shows an abrupt jump, was discovered to be a case of AHE. We find now that the in-plane Hall response, which is perfectly linear in magnetic field, is set by the Berry curvature of the wavefunction. The amplitude of the Hall response and its concomitant Nernst signal exceed by far what is expected in the semiclassical picture. We argue that magnetic field induces out-of-plane spin canting and thereafter gives rise to nontrivial spin chirality on the kagome lattice. In band structure, we find that the spin chirality modifies the topology by gapping out Weyl nodal lines unknown before, accounting for the AHE observed. Our work reveals intriguing unification of real-space Berry phase from spin chirality and momentum-space Berry curvature in a kagome material.

Widely Tunable Berry Curvature in the Magnetic Semimetal Cr1+ δ Te2

Magnetic semimetals have increasingly emerged as lucrative platforms hosting spin-based topological phenomena in real and momentum spaces. Cr_{1+ δ} Te₂ is a self-intercalated magnetic transition metal dichalcogenide (TMD), which exhibits topological magnetism and tunable electron filling. While recent studies have explored real-space Berry curvature effects, similar considerations of momentum-space Berry curvature are lacking. Here, the electronic structure and transport properties of epitaxial Cr_{1+ δ} Te₂ thin films are systematically investigated over a range of doping, δ (0.33 - 0.71). Spectroscopic experiments reveal the presence of a characteristic semi-metallic band region, which shows a rigid like energy shift with δ. Transport experiments show that the intrinsic component of the anomalous Hall effect (AHE) is sizable and undergoes a sign flip across δ. Finally, density functional theory calculations establish a link between the doping evolution of the band structure and AHE: the AHE sign flip is shown to emerge from the sign change of the Berry curvature, as the semi-metallic band region crosses the Fermi energy. These findings underscore the increasing relevance of momentum-space Berry curvature in magnetic TMDs and provide a unique platform for intertwining topological physics in real and momentum spaces.

Topological Hall Effect in Thin Films of an Antiferromagnetic Weyl Semimetal Integrated on Si

Since the large room-temperature anomalous Hall effect was discovered in noncollinear antiferromagnets, Mn₃Sn has received immense research interest as it exhibits abundant exotic physical properties including Weyl points and enormous potential for antiferromagnetic spintronic device applications. In this work, we report the emergence of the topological Hall effect in Mn₃Sn films grown on Si that is the workhorse for the modern highly integrated information technology. Importantly, through a series of systematic comparative experiments, the intriguing topological Hall effect phenomenon related to the appearance of the noncoplanar chiral spin structure is found to be induced by the Mn₃Sn/SiO₂ interface. Furthermore, it was found that the current injection to a Pt/Mn₃Sn bilayer Hall bar device can effectively manipulate the chiral spin structure of Mn₃Sn, which demonstrates the feasibility of Si-based noncollinear antiferromagnetic spintronics.

All-electrical switching of a topological non-collinear antiferromagnet at room temperature

Non-collinear antiferromagnetic Weyl semimetals, combining the advantages of a zero stray field and ultrafast spin dynamics, as well as a large anomalous Hall effect and the chiral anomaly of Weyl fermions, have attracted extensive interest. However, the all-electrical control of such systems at room temperature, a crucial step toward practical application, has not been reported. Here, using a small writing current density of around 5 × 10⁶ A·cm^-2, we realize the all-electrical current-induced deterministic switching of the non-collinear antiferromagnet Mn₃Sn, with a strong readout signal at room temperature in the Si/SiO₂/Mn₃Sn/AlO_x structure, and without external magnetic field or injected spin current. Our simulations reveal that the switching originates from the current-induced intrinsic non-collinear spin-orbit torques in Mn₃Sn itself. Our findings pave the way for the development of topological antiferromagnetic spintronics.

Visualization of Tunable Weyl Line in A-A Stacking Kagome Magnets

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin-orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle-resolved photoemission spectroscopy, the Weyl lines are directly visualized with strong out-of-plane dispersion in the A-A stacked kagome magnet GdMn₆ Sn₆ . Remarkably, the Weyl lines exhibit a strong magnetization-direction-tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn₆ Sn₆ (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.

Octupole-driven magnetoresistance in an antiferromagnetic tunnel junction

The tunnelling electric current passing through a magnetic tunnel junction (MTJ) is strongly dependent on the relative orientation of magnetizations in ferromagnetic electrodes sandwiching an insulating barrier, rendering efficient readout of spintronics devices^1-5. Thus, tunnelling magnetoresistance (TMR) is considered to be proportional to spin polarization at the interface¹ and, to date, has been studied primarily in ferromagnets. Here we report observation of TMR in an all-antiferromagnetic tunnel junction consisting of Mn₃Sn/MgO/Mn₃Sn (ref. ⁶). We measured a TMR ratio of around 2% at room temperature, which arises between the parallel and antiparallel configurations of the cluster magnetic octupoles in the chiral antiferromagnetic state. Moreover, we carried out measurements using a Fe/MgO/Mn₃Sn MTJ and show that the sign and direction of anisotropic longitudinal spin-polarized current in the antiferromagnet⁷ can be controlled by octupole direction. Strikingly, the TMR ratio (about 2%) of the all-antiferromagnetic MTJ is much larger than that estimated using the observed spin polarization. Theoretically, we found that the chiral antiferromagnetic MTJ may produce a substantially large TMR ratio as a result of the time-reversal, symmetry-breaking polarization characteristic of cluster magnetic octupoles. Our work lays the foundation for the development of ultrafast and efficient spintronic devices using antiferromagnets^8-10.

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.

Topological kagome magnets and superconductors

A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin and correlation. Here we review these key developments in this field, starting from the fundamental concepts of a kagome lattice, to the realizations of Chern and Weyl topological magnetism, to various flat-band many-body correlations, and then to the puzzles of unconventional charge-density waves and superconductivity. We highlight the connection between theoretical ideas and experimental observations, and the bond between quantum interactions within kagome magnets and kagome superconductors, as well as their relation to the concepts in topological insulators, topological superconductors, Weyl semimetals and high-temperature superconductors. These developments broadly bridge topological quantum physics and correlated many-body physics in a wide range of bulk materials and substantially advance the frontier of topological quantum matter.

Fermiology and Origin of T_{c} Enhancement in a Kagome Superconductor Cs(V_{1-x}Nb_{x})_{3}Sb_{5}

Kagome metals AV_{3}Sb_{5} (A=K, Rb, and Cs) exhibit a characteristic superconducting ground state coexisting with a charge density wave (CDW), whereas the mechanisms of the superconductivity and CDW have yet to be clarified. Here we report a systematic angle-resolved photoemission spectroscopy (ARPES) study of Cs(V_{1-x}Nb_{x})_{3}Sb_{5} as a function of Nb content x, where isovalent Nb substitution causes an enhancement of superconducting transition temperature (T_{c}) and the reduction of CDW temperature (T_{CDW}). We found that the Nb substitution shifts the Sb-derived electron band at the Γ point downward and simultaneously moves the V-derived band around the M point upward to lift up the saddle point (SP) away from the Fermi level, leading to the reduction of the CDW-gap magnitude and T_{CDW}. This indicates a primary role of the SP density of states to stabilize the CDW. The present result also suggests that the enhancement of superconductivity by Nb substitution is caused by the cooperation between the expansion of the Sb-derived electron pocket and the recovery of the V-derived density of states at the Fermi level.

Higher harmonics in planar Hall effect induced by cluster magnetic multipoles

Antiferromagnetic (AFM) materials are attracting tremendous attention due to their spintronic applications and associated novel topological phenomena. However, detecting and identifying the spin configurations in AFM materials are quite challenging due to the absence of net magnetization. Herein, we report the practicality of utilizing the planar Hall effect (PHE) to detect and distinguish “cluster magnetic multipoles” in AFM Nd₂Ir₂O₇ (NIO-227) fully strained films. By imposing compressive strain on the spin structure of NIO-227, we artificially induced cluster magnetic multipoles, namely dipoles and A₂- and T₁-octupoles. Importantly, under magnetic field rotation, each magnetic multipole exhibits distinctive harmonics of the PHE oscillation. Moreover, the planar Hall conductivity has a nonlinear magnetic field dependence, which can be attributed to the magnetic response of the cluster magnetic octupoles. Our work provides a strategy for identifying cluster magnetic multipoles in AFM systems and would promote octupole-based AFM spintronics.

The lack of net magnetization in antiferromagnets makes them technologically promising, but it also makes detecting the spin orders challenging. Here, using electrical transport measurement, Song et al show how the planar Hall effect can detect different cluster magnetic multipoles in antiferromagnetic Nd₂Ir₂O₇ film.

Shubnikov-de Haas oscillations and nontrivial topological states in Weyl semimetal candidate SmAlSi

The RAlX (R = Light rare earth; X = Ge, Si) compounds, as a family of magnetic Weyl semimetal, have recently attracted growing attention due to the tunability of Weyl nodes and its interactions with diverse magnetism by rare-earth atoms. Here, we report the magnetotransport evidence and electronic structure calculations on nontrivial band topology of SmAlSi, a new member of this family. At low temperatures, SmAlSi exhibits large non-saturated magnetoresistance (MR) (as large as ∼5500% at 2 K and 48 T) and distinct Shubnikov-de Haas (SdH) oscillations. The field dependent MRs at 2 K deviate from the semiclassical (μ₀H)²variation but follow the power-law relation MR∝(μ₀H)^mwith a crossover fromm∼ 1.52 at low fields (μ₀H< 15 T) tom∼ 1 under high fields (μ₀H> 18 T), which is attributed to the existence of Weyl points and electron-hole compensated characteristics with high mobility. From the analysis of SdH oscillations, two fundamental frequencies originating from the Fermi surface pockets with non-trivialπBerry phases and small cyclotron mass can be identified, this feature is supported by the calculated electronic band structures with two Weyl pockets near the Fermi level. Our study establishes SmAlSi as a paradigm for researching the novel topological states of RAlX family.

A 2D heavy fermion CePb3 kagome material on silicon: emergence of unique spin polarized states for spintronics

We report on the successful synthesis of a 2D atomically thin heavy-fermion CePb₃ kagome compound on a Si(111) surface. Growth and morphology were controlled and characterized through scanning tunneling microscopy observations revealing the high crystalline quality of the sample. Angle-resolved photoelectron spectroscopy measurements revealed the giant highly-anisotropic Rashba-like spin splitting of the surface states and semi-metallic character of the spectrum. According to the DFT calculations, the occupied hole and unoccupied electron states with huge spin-orbit splitting and out-of-plane spin polarization reside at the M̄ points near the Fermi level E_F, which is ≈100 meV above the experimental one. The out-of-plane FM magnetization was found to be preferred with Ce spin and orbital magnetic momenta values of 0.895μ_B and -0.840μ_B, respectively. The spin-split states near E_F are primarily formed by Pb p_xy orbitals with the admixing of Ce d and f electrons due to the Ce f-d hybridization acquired asymmetry with respect to the sign of k_∥. The observed electronic structure of the CePb₃/Si(111)√3 × √3 system is rather unique and in the hole-doped state, like in our experiment, can be enabled in the tunable spin current regime, which makes it a prospective 2D material for spintronic applications.

Magnetization switching in polycrystalline Mn3Sn thin film induced by self-generated spin-polarized current

Electrical manipulation of spins is essential to design state-of-the-art spintronic devices and commonly relies on the spin current injected from a second heavy-metal material. The fact that chiral antiferromagnets produce spin current inspires us to explore the magnetization switching of chiral spins using self-generated spin torque. Here, we demonstrate the electric switching of noncollinear antiferromagnetic state in Mn₃Sn by observing a crossover from conventional spin-orbit torque to the self-generated spin torque when increasing the MgO thickness in Ta/MgO/Mn₃Sn polycrystalline films. The spin current injection from the Ta layer can be controlled and even blocked by varying the MgO thickness, but the switching sustains even at a large MgO thickness. Furthermore, the switching polarity reverses when the MgO thickness exceeds around 3 nm, which cannot be explained by the spin-orbit torque scenario due to spin current injection from the Ta layer. Evident current-induced switching is also observed in MgO/Mn₃Sn and Ti/Mn₃Sn bilayers, where external injection of spin Hall current to Mn₃Sn is negligible. The inter-grain spin-transfer torque induced by spin-polarized current explains the experimental observations. Our findings provide an alternative pathway for electrical manipulation of non-collinear antiferromagnetic state without resorting to the conventional bilayer structure.

Under an applied current, chiral antiferromagnets, such as Mn₃Sn, can produce a spin-polarized current. Here, by varying the thickness of a buffering layer, the authors show that this spin-polarized current can drive self-induced switching in polycrystalline Mn₃Sn.

Disorder- and Topology-Enhanced Fully Spin-Polarized Currents in Nodal Chain Spin-Gapless Semimetals

Recently discovered high-quality nodal chain spin-gapless semimetals MF_{3} (M=Pd, Mn) feature an ultraclean nodal chain in the spin up channel residing right at the Fermi level and displaying a large spin gap leading to a 100% spin polarization of transport properties. Here, we investigate both intrinsic and extrinsic contributions to anomalous and spin transport in this class of materials. The dominant intrinsic origin is found to originate entirely from the gapped nodal chains without the entanglement of any other trivial bands. The side-jump mechanism is predicted to be negligibly small, but intrinsic skew scattering enhances the intrinsic Hall and Nernst signals significantly, leading to large values of respective conductivities. Our findings open a new material platform for exploring strong anomalous and spin transport properties in magnetic topological semimetals.

Noncollinear Spin Current for Switching of Chiral Magnetic Textures

We propose a concept of noncollinear spin current, whose spin polarization varies in space even in nonmagnetic crystals. While it is commonly assumed that the spin polarization of the spin Hall current is uniform, asymmetric local crystal potential generally allows the spin polarization to be noncollinear in space. Based on microscopic considerations, we demonstrate that such noncollinear spin Hall currents can be observed, for example, in layered Kagome Mn_{3}X (X=Ge, Sn) compounds. Moreover, by referring to atomistic spin dynamics simulations we show that noncollinear spin currents can be used to switch the chiral spin texture of Mn_{3}X in a deterministic way even in the absence of an external magnetic field. Our theoretical prediction can be readily tested in experiments, which will open a novel route toward electric control of complex spin structures in noncollinear antiferromagnets.

Efficient perpendicular magnetization switching by a magnetic spin Hall effect in a noncollinear antiferromagnet

Current induced spin-orbit torques driven by the conventional spin Hall effect are widely used to manipulate the magnetization. This approach, however, is nondeterministic and inefficient for the switching of magnets with perpendicular magnetic anisotropy that are demanded by the high-density magnetic storage and memory devices. Here, we demonstrate that this limitation can be overcome by exploiting a magnetic spin Hall effect in noncollinear antiferromagnets, such as Mn₃Sn. The magnetic group symmetry of Mn₃Sn allows generation of the out-of-plane spin current carrying spin polarization collinear to its direction induced by an in-plane charge current. This spin current drives an out-of-plane anti-damping torque providing the deterministic switching of the perpendicular magnetization of an adjacent Ni/Co multilayer. Due to being odd with respect to time reversal symmetry, the observed magnetic spin Hall effect and the resulting spin-orbit torque can be reversed with reversal of the antiferromagnetic order. Contrary to the conventional spin-orbit torque devices, the demonstrated magnetization switching does not need an external magnetic field and requires much lower current density which is useful for low-power spintronics.

Spin-orbit torques driven by the conventional spin Hall effect are widely used to switch magnetization, but this approach is nondeterministic and inefficient for magnets with perpendicular magnetic anisotropy. Here, the authors demonstrate deterministic, field-free switching in a Ni/Co multilayer by exploiting the magnetic spin Hall effect in adjacent Mn₃Sn.

Perpendicular full switching of chiral antiferromagnetic order by current

Electrical control of a magnetic state of matter lays the foundation for information technologies and for understanding of spintronic phenomena. Spin-orbit torque provides an efficient mechanism for the electrical manipulation of magnetic orders^1-11. In particular, spin-orbit torque switching of perpendicular magnetization in nanoscale ferromagnetic bits has enabled the development of stable, reliable and low-power memories and computation^12-14. Likewise, for antiferromagnetic spintronics, electrical bidirectional switching of an antiferromagnetic order in a perpendicular geometry may have huge impacts, given its potential advantage for high-density integration and ultrafast operation^15,16. Here we report the experimental realization of perpendicular and full spin-orbit torque switching of an antiferromagnetic binary state. We use the chiral antiferromagnet Mn₃Sn (ref. ¹⁷), which exhibits the magnetization-free anomalous Hall effect owing to a ferroic order of a cluster magnetic octupole hosted in its chiral antiferromagnetic state¹⁸. We fabricate heavy-metal/Mn₃Sn heterostructures by molecular beam epitaxy and introduce perpendicular magnetic anisotropy of the octupole using an epitaxial in-plane tensile strain. By using the anomalous Hall effect as the readout, we demonstrate 100 per cent switching of the perpendicular octupole polarization in a 30-nanometre-thick Mn₃Sn film with a small critical current density of less than 15 megaamperes per square centimetre. Our theory reveals that the perpendicular geometry between the polarization directions of current-induced spin accumulation and of the octupole persistently maximizes the spin-orbit torque efficiency during the deterministic bidirectional switching process. Our work provides a significant basis for antiferromagnetic spintronics.

Quantum Sensing and Imaging of Spin-Orbit-Torque-Driven Spin Dynamics in the Non-Collinear Antiferromagnet Mn3 Sn

Novel non-collinear antiferromagnets with spontaneous time-reversal symmetry breaking, non-trivial band topology, and unconventional transport properties have received immense research interest over the past decade due to their rich physics and enormous promise in technological applications. One of the central focuses in this emerging field is exploring the relationship between the microscopic magnetic structure and exotic material properties. Here, nanoscale imaging of both spin-orbit-torque-induced deterministic magnetic switching and chiral spin rotation in non-collinear antiferromagnet Mn₃ Sn films using nitrogen-vacancy (NV) centers are reported. Direct evidence of the off-resonance dipole-dipole coupling between the spin dynamics in Mn₃ Sn and proximate NV centers is also demonstrated by NV relaxometry measurements. These results demonstrate the unique capabilities of NV centers in accessing the local information of the magnetic order and dynamics in these emergent quantum materials and suggest new opportunities for investigating the interplay between topology and magnetism in a broad range of topological magnets.

Chemical Potential Switching of the Anomalous Hall Effect in an Ultrathin Noncollinear Antiferromagnetic Metal

The discovery of the anomalous Hall effect in noncollinear antiferromagnetic metals represents one of the most important breakthroughs for the emergent antiferromagnetic spintronics. The tuning of chemical potential has been an important theoretical approach to varying the anomalous Hall conductivity, but the direct experimental demonstration has been challenging owing to the large carrier density of metals. In this work, an ultrathin noncollinear antiferromagnetic Mn₃ Ge film is fabricated and its carrier density is modulated by ionic liquid gating. Via a small voltage of ≈3 V, its carrier density is altered by ≈90% and, accordingly, the anomalous Hall effect is completely switched off. This work thus creates an attractive new way to steering the anomalous Hall effect in noncollinear antiferromagnets.

A new class of bilayer kagome lattice compounds with Dirac nodal lines and pressure-induced superconductivity

Kagome lattice composed of transition-metal ions provides a great opportunity to explore the intertwining between geometry, electronic orders and band topology. The discovery of multiple competing orders that connect intimately with the underlying topological band structure in nonmagnetic kagome metals AV₃Sb₅ (A = K, Rb, Cs) further pushes this topic to the quantum frontier. Here we report a new class of vanadium-based compounds with kagome bilayers, namely AV₆Sb₆ (A = K, Rb, Cs) and V₆Sb₄, which, together with AV₃Sb₅, compose a series of kagome compounds with a generic chemical formula (A_m-1Sb_2m)(V₃Sb)_n (m = 1, 2; n = 1, 2). Theoretical calculations combined with angle-resolved photoemission measurements reveal that these compounds feature Dirac nodal lines in close vicinity to the Fermi level. Pressure-induced superconductivity in AV₆Sb₆ further suggests promising emergent phenomena in these materials. The establishment of a new family of layered kagome materials paves the way for designer of fascinating kagome systems with diverse topological nontrivialities and collective ground states.

Progress and prospects in magnetic topological materials

Magnetic topological materials represent a class of compounds with properties that are strongly influenced by the topology of their electronic wavefunctions coupled with the magnetic spin configuration. Such materials can support chiral electronic channels of perfect conduction, and can be used for an array of applications, from information storage and control to dissipationless spin and charge transport. Here we review the theoretical and experimental progress achieved in the field of magnetic topological materials, beginning with the theoretical prediction of the quantum anomalous Hall effect without Landau levels, and leading to the recent discoveries of magnetic Weyl semimetals and antiferromagnetic topological insulators. We outline recent theoretical progress that has resulted in the tabulation of, for the first time, all magnetic symmetry group representations and topology. We describe several experiments realizing Chern insulators, Weyl and Dirac magnetic semimetals, and an array of axionic and higher-order topological phases of matter, and we survey future perspectives.

Evolution of Electronic Structure in Pristine and Rb-Reconstructed Surfaces of Kagome Metal RbV3Sb5

We report on in situ low-temperature (4 K) scanning tunneling microscope measurements of atomic and electronic structures of the cleaved surfaces of an alkali-based kagome metal RbV₃Sb₅ single crystals. We find that the dominant pristine surface exhibits Rb-1×1 structure, in which a unique unidirectional √3a₀ charge order is discovered. As the sample temperature slightly rises, Rb-√3×1 and Rb-√3×√3 reconstructions form due to desorption of surface Rb atoms. Our conductance mapping results demonstrate that Rb desorption not only gives rise to hole doping but also reconstructs the electronic band structures. Surprisingly, we find a ubiquitous gap opening near the Fermi level in tunneling spectra on all the surfaces despite their large differences of hole-carrier concentration, indicating an orbital-selective band reconstruction in RbV₃Sb₅. The Rb desorption induced electronic reconstructions are further confirmed by our density functional theory calculations.

Mid-infrared broadband circular polarizer based on Weyl semimetals

As a three-dimensional topological phase of matter, Weyl semimetals possess extremely large gyrotropic optical response in the mid-infrared region, leading to the strong chiral anomaly. This study proposes a circular polarizer design with a double-WSM-layer structure. It is theoretically shown that the proposed polarizer possesses a high circular polarization efficiency and high average transmittance in the wavelength region from 9 µm to 15 µm at incidence angles up to 50°. The modified 4 × 4 matrix method is used to calculate the circularly polarized transmittance of Weyl semimetals in thin-film or multilayer structures. The temperature dependence on the transmittance is also examined to demonstrate the flexibility of the proposed polarizer in a varying temperature environment. This study reveals the technological prospect that Weyl semimetals are promising candidates for high-performance circular polarizers in infrared spectroscopy and polarimetry.

Topological spintronics and magnetoelectronics

Topological electronic materials, such as topological insulators, are distinct from trivial materials in the topology of their electronic band structures that lead to robust, unconventional topological states, which could bring revolutionary developments in electronics. This Perspective summarizes developments of topological insulators in various electronic applications including spintronics and magnetoelectronics. We group and analyse several important phenomena in spintronics using topological insulators, including spin-orbit torque, the magnetic proximity effect, interplay between antiferromagnetism and topology, and the formation of topological spin textures. We also outline recent developments in magnetoelectronics such as the axion insulator and the topological magnetoelectric effect observed using different topological insulators.

Magnetic Weyl Semimetallic Phase in Thin Films of Eu_{2}Ir_{2}O_{7}

The interplay between electronic interactions and strong spin-orbit coupling is expected to create a plethora of fascinating correlated topological states of quantum matter. Of particular interest are magnetic Weyl semimetals originally proposed in the pyrochlore iridates, which are only expected to reveal their topological nature in thin film form. To date, however, direct experimental demonstrations of these exotic phases remain elusive, due to the lack of usable single crystals and the insufficient quality of available films. Here, we report on the discovery of signatures for the long-sought magnetic Weyl semimetallic phase in (111)-oriented Eu_{2}Ir_{2}O_{7} high-quality epitaxial thin films. We observed an intrinsic anomalous Hall effect with colossal coercivity but vanishing net magnetization, which emerges right below the onset of a peculiar magnetic phase with all-in-all-out (AIAO) antiferromagnetic ordering. The anomalous Hall conductivity obtained experimentally is consistent with the theoretical prediction, likely arising from the nonzero Berry curvature emanated by Weyl node pairs near the Fermi level that act as sources and sinks of Berry flux, activated by broken cubic crystal symmetry at the top and bottom terminations of the thin film.

Signatures of Weyl Fermion Annihilation in a Correlated Kagome Magnet

The manipulation of topological states in quantum matter is an essential pursuit of fundamental physics and next-generation quantum technology. Here we report the magnetic manipulation of Weyl fermions in the kagome spin-orbit semimetal Co_{3}Sn_{2}S_{2}, observed by high-resolution photoemission spectroscopy. We demonstrate the exchange collapse of spin-orbit-gapped ferromagnetic Weyl loops into paramagnetic Dirac loops under suppression of the magnetic order. We further observe that topological Fermi arcs disappear in the paramagnetic phase, suggesting the annihilation of exchange-split Weyl points. Our findings indicate that magnetic exchange collapse naturally drives Weyl fermion annihilation, opening new opportunities for engineering topology under correlated order parameters.

Topology and geometry under the nonlinear electromagnetic spotlight

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this Review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. We give an overview of the field by discussing theoretical ideas, experiments and the materials that drive them. We conclude by discussing how these techniques can be combined with device architectures to uncover, probe and ultimately control quantum phases with emergent topological and correlated properties.

Magnetism-induced topological transition in EuAs3

The nature of the interaction between magnetism and topology in magnetic topological semimetals remains mysterious, but may be expected to lead to a variety of novel physics. We systematically studied the magnetic semimetal EuAs3, demonstrating a magnetism-induced topological transition from a topological nodal-line semimetal in the paramagnetic or the spin-polarized state to a topological massive Dirac metal in the antiferromagnetic ground state at low temperature. The topological nature in the antiferromagnetic state and the spin-polarized state has been verified by electrical transport measurements. An unsaturated and extremely large magnetoresistance of ~2 × 105% at 1.8 K and 28.3 T is observed. In the paramagnetic states, the topological nodal-line structure at the Y point is proven by angle-resolved photoemission spectroscopy. Moreover, a temperature-induced Lifshitz transition accompanied by the emergence of a new band below 3 K is revealed. These results indicate that magnetic EuAs3 provides a rich platform to explore exotic physics arising from the interaction of magnetism with topology.