Observation of Spin-Splitter Torque in Collinear Antiferromagnetic RuO_{2}

Enhanced Field-Like Torque Generated from the Anisotropic Spin-Split Effect in Triple-Domain RuO2 for Energy-Efficient Spin-Orbit Torque Magnetic Random-Access Memory

Spin-current generation via the anisotropic spin-split effect has been predicted in antiferromagnetic RuO2, where the symmetry of RuO2 plays a critical role in spin-orbit torque (SOT). This phenomenon has garnered attention for its potential to enable energy-efficient spintronic devices, such as SOT magnetic random-access memory. In this study, a high-quality RuO2 (100) epitaxial film with a well-controlled triple-domain-structure is analyzed, and it is confirmed that out-of-plane spin-current generation is independent of the Néel vector (N ⃗ $\vec N$ ). ThisN ⃗ $\vec N$ independence of the out-of-plane spin current leads to equal SOT values for the two orthogonal currents. The spin-split effect-induced SOT demonstrates a field-like (FL) torque efficiency (-0.066 ± 0.001) that is six times higher than that of the Slonczewski-like torque efficiency (-0.011 ± 0.001). Furthermore, micromagnetic simulations show that this high FL torque reduces the critical switching voltage by a factor of 2.6 in the sub-nanosecond regime in an SOT device. These findings contribute to advancing research and the development of highly energy-efficient antiferromagnetic-based SOT magnetic random-access memory.

Fully Field-Free Spin-Orbit Torque Switching Induced by Spin Splitting Effect in Altermagnetic RuO2

Altermagnetism, a newly identified class of magnetism blending characteristics of both ferromagnetism and antiferromagnetism, is emerging as a compelling frontier in spintronics. This study reports a groundbreaking discovery of robust, 100% field-free spin-orbit torque (SOT) switching in a RuO2(101)/[Co/Pt]2/Ta structure. The experimental results reveal that the spin currents, induced by the in-plane charge current, flow along the [100] axis, with the spin polarization direction aligned parallel to the Néel vector. These z-polarized spins generate an out-of-plane anti-damping torque, enabling deterministic switching of the Co/Pt layer without the necessity of an external magnetic field. The altermagnetic spin splitting effect (ASSE) in RuO2 promotes the generation of spin currents with pronounced anisotropic behavior, maximized when the charge current flows along the [010] direction. This unique capability yields the highest field-free switching ratio, maintaining stable SOT switching even under a wide range of external magnetic fields, demonstrating exceptional resistance to magnetic interference. Notably, the ASSE-dominated spin current is found to be most effective when the current is aligned with the [010] direction. The study highlights the potential of RuO2 as a powerful spin current generator, opening new avenues for advancing spin-torque switching technologies and other cutting-edge spintronic devices.

Giant Strain-Induced Spin Splitting Effect in MnTe, a g-Wave Altermagnetic Semiconductor

Hexagonal MnTe is an altermagnetic semiconductor with g-wave symmetry of spin polarization in momentum space. In the nonrelativistic limit, this symmetry mandates that electric current flowing in any crystallographic direction is unpolarized. However, here I show that elastic strain is effective in inducing the spin splitting effect in MnTe. For this analysis, a spin-orbit-coupled k·p Hamiltonian for the valence band maximum at the A point is derived and fitted to eigenvalues calculated from first principles. The spin splitting angle is calculated using the Boltzmann approach in the relaxation-time approximation. The spin splitting gauge factor exceeds 30 near the valence band maximum. Thus, with suitable substrate engineering, MnTe can be used as an efficient source and detector of spin current in spintronic devices. Proper inclusion of the Rashba-Dresselhaus spin-orbit coupling is crucial for the correct description of the transport properties of MnTe.

Three-dimensional mapping of the altermagnetic spin splitting in CrSb

Altermagnetism, a kind of collinear magnetism that is characterized by a momentum-dependent band and spin splitting without net magnetization, has recently attracted considerable interest. Finding altermagnetic materials with large splitting near the Fermi level necessarily requires three-dimensional k-space mapping. While this is crucial for spintronic applications and emergent phenomena, it remains challenging. Here, using synchrotron-based angle-resolved photoemission spectroscopy (ARPES), spin-resolved ARPES and model calculations, we uncover a large altermagnetic splitting, up to  ~1.0 eV, near the Fermi level in CrSb. We verify its bulk-type g-wave altermagnetism through systematic three-dimensional k-space mapping, which unambiguously reveals the altermagnetic symmetry and associated nodal planes. Spin-resolved ARPES measurements further verify the spin polarizations of the split bands near Fermi level. Tight-binding model analysis indicates that the large altermagnetic splitting arises from strong third-nearest-neighbor hopping mediated by Sb ions. The large band/spin splitting near Fermi level in metallic CrSb, together with its high TN (up to 705 K) and simple spin configuration, paves the way for exploring emergent phenomena and spintronic applications based on altermagnets.

Manipulation of the altermagnetic order in CrSb via crystal symmetry

Crystal symmetry guides the development of condensed matter. The unique crystal symmetry connecting magnetic sublattices not only distinguishes altermagnetism1-6 from ferromagnetism and conventional antiferromagnetism but also enables it to combine the advantages of ferromagnetism and antiferromagnetism4,5. Altermagnetic order is essentially a magnetic crystal order7, determined by the magnetic-order (Néel) vector and crystal symmetry. Previous experimental studies have concentrated on manipulating the altermagnetic symmetry by tuning the Néel vector orientations8-12. However, manipulation of the crystal symmetry, which holds great promise for manipulating the altermagnetic order, remains challenging. Here we realize the manipulation of altermagnetic order in chromium antimonide (CrSb) films via crystal symmetry. The locking between the Dzyaloshinskii-Moriya vector and the magnetic space symmetry helps to reconstruct the altermagnetic order, from a collinear Néel vector to a canted one. It generates a room-temperature spontaneous anomalous Hall effect in an altermagnet. The relative direction between the current-induced spin polarization and the Dzyaloshinskii-Moriya vector determines the switching modes of altermagnetic order, that is, parallel for the field-assisted mode in CrSb ( 1 1 ¯ 00 ) /Pt and non-parallel for the field-free mode in W/CrSb ( 11 2 ¯ 0 ) . The Dzyaloshinskii-Moriya vector induces an asymmetric energy barrier in the field-assisted mode and generates an asymmetric driving force in the field-free mode. In particular, the latter is guaranteed by the emerging Dzyaloshinskii-Moriya torque in altermagnets. Reconstructing crystal symmetry adds a new twist to the manipulation of altermagnetic order. It not only underpins the magnetic-memory and nano-oscillator technology4,5 but also inspires crossover studies between altermagnetism and other research topics.

Controllable z-Polarized Spin Current in Artificially Structured Ferromagnetic Oxide with Strong Spin-Orbit Coupling

Realizing field-free switching of perpendicular magnetization by spin-orbit torques is crucial for developing advanced magnetic memory and logic devices. However, existing methods often involve complex designs or hybrid approaches, which complicate fabrication and affect device stability and scalability. Here, we propose a novel approach using z-polarized spin currents for deterministic switching of perpendicular magnetization through interfacial engineering. We fabricate La0.67Sr0.33MnO3-SrIrO3 (LSIMO) thin films with robust spin-orbit coupling and ferromagnetic order through orbital and lattice reconstruction, integrating SrIrO3 and La0.67Sr0.33MnO3 materials. Our investigation reveals that y- and z-polarized spin currents, driven by the spin Hall and spin-orbit precession effects, enable field-free switching of perpendicular magnetization. Notably, the z-polarized spin currents are tunable via the in-plane magnetization of LSIMO. These findings present a promising pathway for the development of energy-efficient spintronic devices, offering improved performance and scalability.

Altermagnetism: A Chemical Perspective

Altermagnets have been recently introduced as a classification of collinear, spin compensated magnetic materials that host net-zero magnetization yet display some electronic behaviors typically associated with noncompensated magnetic materials like ferromagnets. The emergence of such properties are a consequence of spin-split bands that arise under specific symmetry conditions in the limit of zero spin-orbit coupling. In this Perspective, we summarize the fundamental criteria for realizing an altermagnetic phase and present a qualitative electronic band structure derivation and symmetry analysis through chemical principles. We then discuss the properties that make altermagnets distinctive candidates for charge-to-spin conversion elements in spintronic devices and provide a brief review of some altermagnetic candidate materials. Finally, we discuss future directions for altermagnetism and highlight opportunities for chemists to advance this emerging field.

Electric-Field-Induced Switchable Two-Dimensional Altermagnets

Altermagnetism, as a recently discovered unconventional antiferromagnetism, allows the lifting of spin degeneracy without net magnetization. The spin splitting of the intrinsic altermagnets is protected by the spin space group symmetry and is therefore difficult to control externally. Here, we propose an extrinsic altermagnet as a complement to the intrinsic altermagnet, whose spin splitting is induced by and can be significantly modulated by the electric field. We then screened intrinsic and extrinsic altermagnets by combining symmetry analysis and high-throughput calculations, identifying 16 intrinsic altermagnets and 24 extrinsic altermagnets. We demonstrate that the spin splitting of extrinsic altermagnets is proportional to the electric field strength, and its sign can be switched by reversing the electric field. Some extrinsic altermagnets exhibit considerable spin splitting, such as CaMnSi with 398 meV under an electric field of 0.1 V/Å. This work provides a realistic material platform for the potential application of 2D altermagnets.

Spin-Orbit Coupling Driven Magnetic Response in Altermagnetic RuO2

The recent prediction of the new magnetic class, altermagnetism, has drawn considerable interest, fueled by its potential to host novel phenomena and to be utilized in next-generation spintronics devices. Among many promising candidates, rutile RuO2 is a prototypical candidate for realizing the prospects of altermagnetism. However, the experimental studies on RuO2 are still in the early stages. In this study, the magnetic responses in RuO2 film are investigated by the Planar Hall effect (PHE). By rotating the external field (Hext), the PHE exhibits twofold behaviors. Moreover, the planar Hall conductivity shows a nonlinear response to the Hext. These observed features in PHE resemble those in ferromagnet and topologically nontrivial systems, suggesting the field-induced magnetic response in rutile antiferromagnet. The work provides a strategy for detecting intriguing magnetic responses in altermagnetic materials, promoting further research in altermagnet-based spintronics and novel phenomena.

Spontaneous Hall effect induced by collinear antiferromagnetic order at room temperature

Magnetic information is usually stored in ferromagnets, where the ↑ and ↓ spin states are distinguishable due to time-reversal symmetry breaking. These states induce opposite signs of the Hall effect proportional to magnetization, which is widely used for their electrical read-out. By contrast, conventional antiferromagnets with a collinear antiparallel spin configuration cannot host such functions, because of T t symmetry (time-reversal T followed by translation t symmetry) and lack of macroscopic magnetization. Here we report the experimental observation of a spontaneous Hall effect in the collinear antiferromagnet FeS at room temperature. In this compound, the ↑↓ and ↓↑ spin states induce opposite signs of the spontaneous Hall effect. Our analysis suggests that this does not reflect magnetization, but rather originates from a fictitious magnetic field associated with the T t -symmetry-broken antiferromagnetic order. The present results pave the way for electrical reading and writing of the ↑↓ and ↓↑ spin states in conductive systems at room temperature, and suggest that T t -symmetry-broken collinear antiferromagnets can serve as an information medium with vanishingly small magnetization.

Confined Magnetization at the Sublattice-Matched Ruthenium Oxide Heterointerface

Creating a heterostructure by combining two magnetically and structurally distinct ruthenium oxides is a crucial approach for investigating their emergent magnetic states and interactions. Previously, research has predominantly concentrated on the intrinsic properties of the ferromagnet SrRuO3 and recently discovered altermagnet RuO2 solely. Here, the study engineers an ultrasharp sublattice-matched heterointerface using pseudo-cubic SrRuO3 and rutile RuO2, conducting an in-depth analysis of their spin interactions. Structurally, to accommodate the lattice symmetry mismatch, the inverted RuO2 layer undergoes an in-plane rotation of 18 degrees during epitaxial growth on SrRuO3 layer, resulting in an interesting and rotational interface with perfect crystallinity and negligible chemical intermixing. Performance-wise, the interfacial layer of 6 nm in RuO2 adjacent to SrRuO3 exhibits a nonzero magnetic moment, contributing to an enhanced anomalous Hall effect (AHE) at low temperatures. Furthermore, the observations indicate that in contrast to SrRuO3 single layers, the AHE of [(RuO2)15/(SrRuO3)n] heterostructures show nonlinear behavior and reaches its maximum when the SrRuO3 thickness reaches tens of nm. These results suggest that the interfacial magnetic interaction surpasses that of all-perovskite oxides (≈5-unit cells). This study underscores the significance and potential applications of magnetic interactions based on the crystallographic asymmetric interfaces in the design of spintronic devices.

Minimal Models and Transport Properties of Unconventional p-Wave Magnets

New unconventional compensated magnets with a p-wave spin polarization protected by a composite time-reversal translation symmetry have been proposed in the wake of altermagnets. To facilitate the experimental discovery and applications of these unconventional magnets, we construct an effective analytical model. The effective model is based on a minimal tight-binding model for unconventional p-wave magnets that clarifies the relation to other magnets with p-wave spin-polarized bands. One of the most prominent advantages of our analytical model is the possibility to employ various analytical approaches while capturing essential features of p-wave magnets. We illustrate the effective model by evaluating the tunneling conductance in junctions with p-wave magnets, revealing a large magnetoresistance, spin filtering, and anisotropic bulk spin conductivity beyond linear response despite the absence of a net magnetization. These results show that unconventional p-wave magnets offer several useful functionalities, broadening the material selection for spintronics devices.

Crystal Chemistry and Design Principles of Altermagnets

Altermagnetism was very recently identified as a new type of magnetic phase beyond the conventional dichotomy of ferromagnetism (FM) and antiferromagnetism (AFM). Its globally compensated magnetization and directional spin polarization promise new properties such as spin-polarized conductivity, spin-transfer torque, anomalous Hall effect, tunneling, and giant magnetoresistance that are highly useful for the next-generation memory devices, magnetic detectors, and energy conversion. Though this area has been historically led by the thin-film community, the identification of altermagnetism ultimately relies on precise magnetic structure determination, which can be most efficiently done in bulk materials. Our review, written from a materials chemistry perspective, intends to encourage materials and solid-state chemists to make contributions to this emerging topic through new materials discovery by leveraging neutron diffraction to determine the magnetic structures as well as bulk crystal growth for exploring exotic properties. We first review the symmetric classification for the identification of altermagnets with a summary of chemical principles and design rules, followed by a discussion of the unique physical properties in relation to crystal and magnetic structural symmetry. Several major families of compounds in which altermagnets have been identified are then reviewed. We conclude by giving an outlook for future directions.

Observation of Spin Splitting in Room-Temperature Metallic Antiferromagnet CrSb

Recently, unconventional antiferromagnets that enable the spin splitting (SS) of electronic states have been theoretically proposed and experimentally realized, where the magnetic sublattices containing moments pointing at different directions are connected by a novel set of symmetries. Such SS is substantial, k-dependent, and independent of the spin-orbit coupling (SOC) strength, making these magnets promising materials for antiferromagnetic spintronics. Here, combined with angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations, a systematic study on CrSb, a metallic spin-split antiferromagnet candidate with Néel temperature TN = 703 K, is conducted. The data reveal the electronic structure of CrSb along both out-of-plane and in-plane momentum directions, rendering an anisotropic k-dependent SS that agrees well with the calculational results. The magnitude of such SS reaches up to at least 0.8 eV at non-high-symmetry momentum points, which is significantly higher than the largest known SOC-induced SS. This compound expands the choice of materials in the field of antiferromagnetic spintronics and is likely to stimulate subsequent investigations of high-efficiency spintronic devices that are functional at room temperature.

Absence of Altermagnetic Spin Splitting Character in Rutile Oxide RuO_{2}

Rutile RuO_{2} has been posited as a potential d-wave altermagnetism candidate, with a predicted significant spin splitting up to 1.4 eV. Despite accumulating theoretical predictions and transport measurements, direct spectroscopic observation of spin splitting has remained elusive. Here, we employ spin- and angle-resolved photoemission spectroscopy to investigate the band structures and spin polarization of thin-film and single-crystal RuO_{2}. Contrary to expectations of altermagnetism, our analysis indicates that RuO_{2}'s electronic structure aligns with those predicted under nonmagnetic conditions, exhibiting no evidence of the hypothesized spin splitting. Additionally, we observe significant in-plane spin polarization of the low-lying bulk bands, which is antisymmetric about the high-symmetry plane and contrary to the d-wave spin texture due to time-reversal symmetry breaking in altermagnetism. These findings definitively challenge the altermagnetic order previously proposed for rutile RuO_{2}, prompting a reevaluation of its magnetic properties.

Chiral Split Magnon in Altermagnetic MnTe

Altermagnetism is a newly recognized magnetic class named after the alternating spin polarizations in both real and reciprocal spaces. Like the spin splitting of electronic bands, the magnon bands in altermagnets are predicted to exhibit alternating chiral splitting. In this work, by performing inelastic neutron scattering on α-MnTe, we directly observed the altermagnetic magnon splitting. The lifted degeneracy of magnons is well explained by a symmetric-exchange origin. Further calculation based on the obtained spin-wave model demonstrates the magnons are chiral split as well. In addition, the g-wave magnetism was experimentally identified in MnTe.

Efficient Generation of Out-of-Plane Polarized Spin Current in Polycrystalline Heavy Metal Devices with Broken Electric Symmetries

Spin currents of perpendicularly polarized spins (z spins) have received blooming interest for the potential in energy-efficient spin-orbit torque switching of perpendicular magnetization in the absence of a magnetic field. However, generation of z spins is limited mainly to magnetically or crystallographically low-symmetry single crystals that are hardly compatible with the integration to semiconductor circuits. This work reports efficient generation of z spins in sputter-deposited polycrystalline heavy metal devices via a new mechanism of broken electric symmetries in both the transverse and perpendicular directions. Both the damping-like and field-like spin-orbit torques of z spins can be tuned significantly by varying the degree of the electric asymmetries via the length, width, and thickness of devices as well as by varying the type of the heavy metals. The presence of z spins also enables deterministic, nearly-full, external-magnetic-field-free switching of a uniform perpendicularly magnetized FeCoB layer, the core structure of magnetic tunnel junctions, with high coercivity at a low current density. These results establish the first universal, energy-efficient, integration-friendly approach to generate z-spin current by electric asymmetry design for dense and low-power spin-torque memory and computing technologies and will stimulate investigation of z-spin currents in various polycrystalline materials.

Signatures of magnetism control by flow of angular momentum

Exploring new strategies to manipulate the order parameter of magnetic materials by electrical means is of great importance not only for advancing our understanding of fundamental magnetism but also for unlocking potential applications. A well-established concept uses gate voltages to control magnetic properties by modulating the carrier population in a capacitor structure1-5. Here we show that, in Pt/Al/Fe/GaAs(001) multilayers, the application of an in-plane charge current in Pt leads to a shift in the ferromagnetic resonance field depending on the microwave frequency when the Fe film is sufficiently thin. The experimental observation is interpreted as a current-induced modification of the magnetocrystalline anisotropy ΔHA of Fe. We show that (1) ΔHA decreases with increasing Fe film thickness and is connected to the damping-like torque; and (2) ΔHA depends not only on the polarity of charge current but also on the magnetization direction, that is, ΔHA has an opposite sign when the magnetization direction is reversed. The symmetry of the modification is consistent with a current-induced spin6-8 and/or orbit9-13 accumulation, which, respectively, act on the spin and/or orbit component of the magnetization. In this study, as Pt is regarded as a typical spin current source6,14, the spin current can play a dominant part. The control of magnetism by a spin current results from the modified exchange splitting of the majority and minority spin bands, providing functionality that was previously unknown and could be useful in advanced spintronic devices.

Generation of out-of-plane polarized spin current by non-uniform oxygen octahedral tilt/rotation

The free-field switching of the perpendicular magnetization by the out-of-plane polarized spin current induced spin-orbit torque makes it a promising technology for developing high-density memory and logic devices. The materials intrinsically with low symmetry are generally utilized to generate the spin current with out-of-plane spin polarization. However, the generation of the out-of-plane polarized spin current by engineering the symmetry of materials has not yet been reported. Here, we demonstrate that paramagnetic CaRuO3 films are able to generate out-of-plane polarized spin current by engineering the crystal symmetry. The non-uniform oxygen octahedral tilt/rotation along film's normal direction induced by oxygen octahedral coupling near interface breaks the screw-axis and glide-plane symmetries, which gives rise to a significant out-of-plane polarized spin current. This spin current can drive field-free spin-orbit torque switching of perpendicular magnetization with high efficiency. Our results offer a promising strategy based on crystal symmetry design to manipulate spin current and could have potential applications in advanced spintronic devices.

Antisymmetric planar Hall effect in rutile oxide films induced by the Lorentz force

The conventional Hall effect is linearly proportional to the field component or magnetization component perpendicular to a film. Despite the increasing theoretical proposals on the Hall effect to the in-plane field or magnetization in various special systems induced by the Berry curvature, such an unconventional Hall effect has only been experimentally reported in Weyl semimetals and in a heterodimensional superlattice. Here, we report an unambiguous experimental observation of the antisymmetric planar Hall effect (APHE) with respect to the in-plane magnetic field in centrosymmetric rutile RuO2 and IrO2 single-crystal films. The measured Hall resistivity is found to be linearly proportional to the component of the applied in-plane magnetic field along a particular crystal axis and to be independent of the current direction or temperature. Both the experimental observations and theoretical calculations confirm that the APHE in rutile oxide films is induced by the Lorentz force. Our findings can be generalized to ferromagnetic materials for the discovery of anomalous Hall effects and quantum anomalous Hall effects induced by in-plane magnetization. In addition to significantly expanding knowledge of the Hall effect, this work opens the door to explore new members in the Hall effect family.

Separation of Inverse Altermagnetic Spin-Splitting Effect from Inverse Spin Hall Effect in RuO_{2}

Recently, a significant amount of attention has been attracted toward a third classification of magnetism, altermagnetism, due to the unique physical properties of altermagnetic materials, which are compensated collinear antiferromagnets that host time-reversal symmetry-breaking phenomena like a ferromagnet. In an altermagnetic material, through the nonrelativistic altermagnetic spin-splitting effect (ASSE), a transverse spin current is generated upon charge current injection. However, it is very challenging to experimentally establish the ASSE since it is inevitably mixed with the spin Hall effect due to the relativistic spin-orbit coupling of the material. Additionally, the dependence on the hard-to-probe and hard-to-control Néel vectors makes it even more difficult to observe and establish the ASSE. In this Letter, we utilize the thermal spin injection from the ferrimagnetic insulator yttrium iron garnet and detect an inverse altermagnetic spin-splitting effect (IASSE) in the high-quality epitaxial altermagnetic RuO_{2} thin films. We observe an opposite sign for the spin-to-charge conversion through the IASSE compared to the inverse spin Hall effect (ISHE). The efficiency of the IASSE is approximately 70% of the ISHE in RuO_{2}. Moreover, we demonstrate that the ASSE or IASSE effect is observable only when the Néel vectors are well aligned. By modifying the Néel vector domains via RuO_{2} crystallinity, we study the ASSE or IASSE unequivocally and quantitatively. Our Letter provides significant insight into the spin-splitting effect in altermagnetic materials.

Realizing altermagnetism in two-dimensional metal-organic framework semiconductors with electric-field-controlled anisotropic spin current

Altermagnets exhibit momentum-dependent spin-splitting in a collinear antiferromagnetic order due to their peculiar crystallographic and magnetic symmetry, resulting in the creation of spin currents with light elements. Here, we report two two-dimensional (2D) metal-organic framework (MOF) semiconductors, M(pyz)2 (M = Ca and Sr, pyz = pyrazine), which exhibit both altermagnetism and topological nodal point and line by using first-principles calculations and group theory. The altermagnetic 2D MOFs exhibit unconventional spin-splitting and macroscopic zero magnetization caused by 4-fold rotation in crystalline real space and 2-fold rotation in spin space, leading to the generation and control of anisotropic spin currents when an in-plane electric field ( E ) is applied. In particular, pure spin current with the spin Hall effect occurs when E is applied along the angular bisector of the two spin arrangements. Our work indicates the existence of altermagnetic MOF systems and a universal approach to generate electric-field-controlled spin currents for potential applications in antiferromagnetic spintronics.

Inverse Spin Hall Effect Dominated Spin-Charge Conversion in (101) and (110)-Oriented RuO_{2} Films

Utilizing spin pumping, we present a comparative study of the spin-charge conversion in RuO_{2}(101) and RuO_{2}(110) films. RuO_{2}(101) shows a robust in-plane crystal-axis dependence, whereas RuO_{2}(110) exhibits an isotropic but stronger one. Symmetry-based analysis and first-principles calculations reveal that the spin-charge conversion in RuO_{2}(110) originates from the inverse spin Hall effect (ISHE) due to nodal lines splitting. In RuO_{2}(101), the ISHE also dominates although the inverse spin splitting effect (ISSE) may coexist. These findings, in sharp contrast to previously attributed ISSE, are further corroborated by the reciprocal relation between the spin pumping and the spin-torque ferromagnetic resonance measurements.

Direct and Inverse Spin Splitting Effects in Altermagnetic RuO2

Recently, the altermagnetic materials with spin splitting effect (SSE), have drawn significant attention due to their potential to the flexible control of the spin polarization by the Néel vector. Here, the direct and inverse altermagnetic SSE (ASSE) in the (101)-oriented RuO2 film with the tilted Néel vector are reported. First, the spin torque along the x-, y-, and z-axis is detected from the spin torque-induced ferromagnetic resonance (ST-FMR), and the z-spin torque emerges when the electric current is along the [010] direction, showing the anisotropic spin splitting of RuO2. Further, the current-induced modulation of damping is used to quantify the damping-like torque efficiency (ξDL) in RuO2/Py, and an anisotropic ξDL is obtained and maximized for the current along the [010] direction, which increases with the reduction of the temperature, indicating the present of ASSE. Next, by way of spin pumping measurement, the inverse altermagnetic spin splitting effect (IASSE) is studied, which also shows a crystal direction-dependent anisotropic behavior and temperature-dependent behavior. This work gives a comprehensive study of the direct and inverse ASSE effects in the altermagnetic RuO2, inspiring future altermagnetic materials and devices with flexible control of spin polarization.

Observation of a spontaneous anomalous Hall response in the Mn5Si3 d-wave altermagnet candidate

Phases with spontaneous time-reversal ( T ) symmetry breaking are sought after for their anomalous physical properties, low-dissipation electronic and spin responses, and information-technology applications. Recently predicted altermagnetic phase features an unconventional and attractive combination of a strong T -symmetry breaking in the electronic structure and a zero or only weak-relativistic magnetization. In this work, we experimentally observe the anomalous Hall effect, a prominent representative of the T -symmetry breaking responses, in the absence of an external magnetic field in epitaxial thin-film Mn5Si3 with a vanishingly small net magnetic moment. By symmetry analysis and first-principles calculations we demonstrate that the unconventional d-wave altermagnetic phase is consistent with the experimental structural and magnetic characterization of the Mn5Si3 epilayers, and that the theoretical anomalous Hall conductivity generated by the phase is sizable, in agreement with experiment. An analogy with unconventional d-wave superconductivity suggests that our identification of a candidate of unconventional d-wave altermagnetism points towards a new chapter of research and applications of magnetic phases.

X-Ray Magnetic Circular Dichroism in Altermagnetic α-MnTe

Altermagnetism is a recently identified magnetic symmetry class combining characteristics of conventional collinear ferromagnets and antiferromagnets, that were regarded as mutually exclusive, and enabling phenomena and functionalities unparalleled in either of the two traditional elementary magnetic classes. In this work we use symmetry, ab initio theory, and experiments to explore x-ray magnetic circular dichroism (XMCD) in the altermagnetic class. As a representative material for our XMCD study we choose α-MnTe with compensated antiparallel magnetic order in which an anomalous Hall effect has been already demonstrated. We predict and experimentally confirm a characteristic XMCD line shape for compensated moments lying in a plane perpendicular to the light propagation vector. Our results highlight the distinct phenomenology in altermagnets of this time-reversal symmetry breaking response, and its potential utility for element-specific spectroscopy and microscopy.

Landau Theory of Altermagnetism

We formulate a Landau theory for altermagnets, a class of collinear compensated magnets with spin-split bands. Starting from the nonrelativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space symmetries, providing a simple framework for understanding the key features of this family of materials. We find a set of multipolar secondary order parameters connecting existing ideas about the spin symmetries of these systems, their order parameters, and the effect of nonzero spin-orbit coupling. We account for several features of canonical altermagnets such as RuO_{2}, MnTe, and CuF_{2} that go beyond symmetry alone, relating the order parameter to key observables such as magnetization, anomalous Hall conductivity, and magnetoelastic and magneto-optical probes. Finally, we comment on generalizations of our framework to a wider family of exotic magnetic systems derived from the zero spin-orbit coupled limit.

Nonmagnetic Ground State in RuO_{2} Revealed by Muon Spin Rotation

The magnetic ground state of single crystalline RuO_{2} was investigated by the muon spin rotation and relaxation (μSR) experiment. The spin precession signal due to the spontaneous internal magnetic field B_{loc}, which is expected in the magnetically ordered phase, was not observed in the temperature range 5-400 K. Muon sites were evaluated by first-principles calculations using dilute hydrogen simulating muon as pseudohydrogen, and B_{loc} was simulated for the antiferromagnetic structures with a Ru magnetic moment |m_{Ru}|≈0.05μ_{B} suggested from diffraction experiments. As a result, the possibility was ruled out that muons are localized at sites where B_{loc} accidentally cancels. Conversely, assuming that the slow relaxation observed in μSR spectra was part of the precession signal, the upper limit for the magnitude of |m_{Ru}| was estimated to be 4.8(2)×10^{-4}μ_{B}, which is significantly less than 0.05μ_{B}. These results indicate that the antiferromagnetic order, as reported, is unlikely to exist in the bulk crystal.

Highly efficient field-free switching of perpendicular yttrium iron garnet with collinear spin current

Yttrium iron garnet, a material possessing ultralow magnetic damping and extraordinarily long magnon diffusion length, is the most widely studied magnetic insulator in spintronics and magnonics. Field-free electrical control of perpendicular yttrium iron garnet magnetization with considerable efficiency is highly desired for excellent device performance. Here, we demonstrate such an accomplishment with a collinear spin current, whose spin polarization and propagation direction are both perpendicular to the interface. Remarkably, the field-free magnetization switching is achieved not only with a heavy-metal-free material, Permalloy, but also with a higher efficiency as compared with a typical heavy metal, Pt. Combined with the direct and inverse effect measurements, we ascribe the collinear spin current to the anomalous spin Hall effect in Permalloy. Our findings provide a new insight into spin current generation in Permalloy and open an avenue in spintronic devices.

Electrical-Controllable Antiferromagnet-Based Tunnel Junction

An electrical-controllable antiferromagnet tunnel junction is a key goal in spintronics, holding immense promise for ultradense and ultrastable antiferromagnetic memory with high processing speed for modern information technology. Here, we have advanced toward this goal by achieving an electrical-controllable antiferromagnet-based tunnel junction of Pt/Co/Pt/Co/IrMn/MgO/Pt. The exchange coupling between antiferromagnetic IrMn and Co/Pt perpendicular magnetic multilayers results in the formation of an interfacial exchange bias and exchange spring in IrMn. Encoding information states "0" and "1" is realized through the exchange spring in IrMn, which can be electrically written by spin-orbit torque switching with high cyclability and electrically read by antiferromagnetic tunneling anisotropic magnetoresistance. Combining spin-orbit torque switching of both exchange spring and exchange bias, a 16 Boolean logic operation is successfully demonstrated. With both memory and logic functionalities integrated into our electrically controllable antiferromagnetic-based tunnel junction, we chart the course toward high-performance antiferromagnetic logic-in-memory.

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.

Wurtzite vs. rock-salt MnSe epitaxy: electronic and altermagnetic properties

Newly discovered altermagnets are magnetic materials exhibiting both compensated magnetic order, similar to antiferromagnets, and simultaneous non-relativistic spin-splitting of the bands, akin to ferromagnets. This characteristic arises from specific symmetry operation that connects the spin sublattices. In this report, we show with ab initio calculations that semiconductive MnSe exhibits altermagnetic spin-splitting in the wurtzite phase as well as a critical temperature well above room temperature. It is the first material from such a space group identified to possess altermagnetic properties. Furthermore, we demonstrate experimentally through structural characterization techniques that it is possible to obtain thin films of both the intriguing wurtzite phase of MnSe and more common rock-salt MnSe using molecular beam epitaxy on GaAs substrates. The choice of buffer layers plays a crucial role in determining the resulting phase and consequently extends the array of materials available for the physics of altermagnetism.

Direct observation of altermagnetic band splitting in CrSb thin films

Altermagnetism represents an emergent collinear magnetic phase with compensated order and an unconventional alternating even-parity wave spin order in the non-relativistic band structure. We investigate directly this unconventional band splitting near the Fermi energy through spin-integrated soft X-ray angular resolved photoemission spectroscopy. The experimentally obtained angle-dependent photoemission intensity, acquired from epitaxial thin films of the predicted altermagnet CrSb, demonstrates robust agreement with the corresponding band structure calculations. In particular, we observe the distinctive splitting of an electronic band on a low-symmetry path in the Brilliouin zone that connects two points featuring symmetry-induced degeneracy. The measured large magnitude of the spin splitting of approximately 0.6 eV and the position of the band just below the Fermi energy underscores the significance of altermagnets for spintronics based on robust broken time reversal symmetry responses arising from exchange energy scales, akin to ferromagnets, while remaining insensitive to external magnetic fields and possessing THz dynamics, akin to antiferromagnets.

Incommensurate Spin Density Wave in Antiferromagnetic RuO_{2} Evinced by Abnormal Spin Splitting Torque

Since the discovery of antiferromagnetism, metallic oxide RuO_{2} has exhibited numerous intriguing spintronics properties such as the anomalous Hall effect and anisotropic spin splitting effect. However, the microscopic origin of its antiferromagnetism remains unclear. By investigating the spin splitting torque in RuO_{2}/Py, we found that metallic RuO_{2} exhibits a spatially periodic spin structure which interacts with the spin waves in Py through interfacial exchange coupling. The wavelength of such structure is evaluated within 14-20 nm depending on the temperature, which is evidence of an incommensurate spin density wave state in RuO_{2}. Our work not only provides a dynamics approach to characterize the antiferromagnetic ordering in RuO_{2}, but also offers fundamental insights into the spin current generation due to anisotropic spin splitting effect associated with spin density wave.

Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2

Altermagnets are an emerging elementary class of collinear magnets. Unlike ferromagnets, their distinct crystal symmetries inhibit magnetization while, unlike antiferromagnets, they promote strong spin polarization in the band structure. The corresponding unconventional mechanism of time-reversal symmetry breaking without magnetization in the electronic spectra has been regarded as a primary signature of altermagnetism but has not been experimentally visualized to date. We directly observe strong time-reversal symmetry breaking in the band structure of altermagnetic RuO2 by detecting magnetic circular dichroism in angle-resolved photoemission spectra. Our experimental results, supported by ab initio calculations, establish the microscopic electronic structure basis for a family of interesting phenomena and functionalities in fields ranging from topological matter to spintronics, which are based on the unconventional time-reversal symmetry breaking in altermagnets.

Crystal Thermal Transport in Altermagnetic RuO_{2}

We demonstrate the emergence of a pronounced thermal transport in the recently discovered class of magnetic materials-altermagnets. From symmetry arguments and first-principles calculations performed for the showcase altermagnet, RuO_{2}, we uncover that crystal Nernst and crystal thermal Hall effects in this material are very large and strongly anisotropic with respect to the Néel vector. We find the large crystal thermal transport to originate from three sources of Berry's curvature in momentum space: the Weyl fermions due to crossings between well-separated bands, the strong spin-flip pseudonodal surfaces, and the weak spin-flip ladder transitions, defined by transitions among very weakly spin-split states of similar dispersion crossing the Fermi surface. Moreover, we reveal that the anomalous thermal and electrical transport coefficients in RuO_{2} are linked by an extended Wiedemann-Franz law in a temperature range much wider than expected for conventional magnets. Our results suggest that altermagnets may assume a leading role in realizing concepts in spin caloritronics not achievable with ferromagnets or antiferromagnets.

Observation of plaid-like spin splitting in a noncoplanar antiferromagnet

Spatial, momentum and energy separation of electronic spins in condensed-matter systems guides the development of new devices in which spin-polarized current is generated and manipulated1-3. Recent attention on a set of previously overlooked symmetry operations in magnetic materials4 leads to the emergence of a new type of spin splitting, enabling giant and momentum-dependent spin polarization of energy bands on selected antiferromagnets5-10. Despite the ever-growing theoretical predictions, the direct spectroscopic proof of such spin splitting is still lacking. Here we provide solid spectroscopic and computational evidence for the existence of such materials. In the noncoplanar antiferromagnet manganese ditelluride (MnTe2), the in-plane components of spin are found to be antisymmetric about the high-symmetry planes of the Brillouin zone, comprising a plaid-like spin texture in the antiferromagnetic (AFM) ground state. Such an unconventional spin pattern, further found to diminish at the high-temperature paramagnetic state, originates from the intrinsic AFM order instead of spin-orbit coupling (SOC). Our finding demonstrates a new type of quadratic spin texture induced by time-reversal breaking, placing AFM spintronics on a firm basis and paving the way for studying exotic quantum phenomena in related materials.

Altermagnetic lifting of Kramers spin degeneracy

Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids1,2. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology3-7 to topological quantum matter8-14. Traditionally, LKSD has been considered to originate from two possible internal symmetry-breaking mechanisms. The first refers to time-reversal symmetry breaking by magnetization of ferromagnets and tends to be strong because of the non-relativistic exchange origin15. The second applies to crystals with broken inversion symmetry and tends to be comparatively weaker, as it originates from the relativistic spin-orbit coupling (SOC)16-19. A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic20,21, that allows for LKSD without net magnetization and inversion-symmetry breaking. Here we provide the confirmation using photoemission spectroscopy and ab initio calculations. We identify two distinct unconventional mechanisms of LKSD generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization20-23. Our observation of the altermagnetic LKSD can have broad consequences in magnetism. It motivates exploration and exploitation of the unconventional nature of this magnetic phase in an extended family of materials, ranging from insulators and semiconductors to metals and superconductors20,21, that have been either identified recently or perceived for many decades as conventional antiferromagnets21,24,25.

Electrical 180° switching of Néel vector in spin-splitting antiferromagnet

Antiferromagnetic spintronics have attracted wide attention due to its great potential in constructing ultradense and ultrafast antiferromagnetic memory that suits modern high-performance information technology. The electrical 180° switching of Néel vector is a long-term goal for developing electrical-controllable antiferromagnetic memory with opposite Néel vectors as binary "0" and "1." However, the state-of-art antiferromagnetic switching mechanisms have long been limited for 90° or 120° switching of Néel vector, which unavoidably require multiple writing channels that contradict ultradense integration. Here, we propose a deterministic switching mechanism based on spin-orbit torque with asymmetric energy barrier and experimentally achieve electrical 180° switching of spin-splitting antiferromagnet Mn5Si3. Such a 180° switching is read out by the Néel vector-induced anomalous Hall effect. On the basis of our writing and readout methods, we fabricate an antiferromagnet device with electrical-controllable high- and low-resistance states that accomplishes robust write and read cycles. Besides fundamental advance, our work promotes practical spin-splitting antiferromagnetic devices based on spin-splitting antiferromagnet.

Chiral Magnons in Altermagnetic RuO_{2}

Magnons in ferromagnets have one chirality, and typically are in the GHz range and have a quadratic dispersion near the zero wave vector. In contrast, magnons in antiferromagnets are commonly considered to have bands with both chiralities that are degenerate across the entire Brillouin zone, and to be in the THz range and to have a linear dispersion near the center of the Brillouin zone. Here we theoretically demonstrate a new class of magnons on a prototypical d-wave altermagnet RuO_{2} with the compensated antiparallel magnetic order in the ground state. Based on density-functional-theory calculations we observe that the THz-range magnon bands in RuO_{2} have an alternating chirality splitting, similar to the alternating spin splitting of the electronic bands, and a linear magnon dispersion near the zero wave vector. We also show that, overall, the Landau damping of this metallic altermagnet is suppressed due to the spin-split electronic structure, as compared to an artificial antiferromagnetic phase of the same RuO_{2} crystal with spin-degenerate electronic bands and chirality-degenerate magnon bands.

Magnetic topological materials in two-dimensional: theory, material realization and application prospects

Two-dimensional (2D) magnetism and nontrivial band topology are both areas of research that are currently receiving significant attention in the study of 2D materials. Recently, a novel class of materials has emerged, known as 2D magnetic topological materials, which elegantly combine 2D magnetism and nontrivial topology. This field has garnered increasing interest, especially due to the emergence of several novel magnetic topological states that have been generalized into the 2D scale. These states include antiferromagnetic topological insulators/semimetals, second-order topological insulators, and topological half-metals. Despite the rapid advancements in this emerging research field in recent years, there have been few comprehensive summaries of the state-of-the-art progress. Therefore, this review aims to provide a thorough analysis of current progress on 2D magnetic topological materials. We cover various 2D magnetic topological insulators, a range of 2D magnetic topological semimetals, and the novel 2D topological half-metals, systematically analyzing the basic topological theory, the course of development, the material realization, and potential applications. Finally, we discuss the challenges and prospects for 2D magnetic topological materials, highlighting the potential for future breakthroughs in this exciting field.

Switching of Perpendicular Magnetization by Spin-Orbit Torque

Magnetic materials with strong perpendicular magnetic anisotropy are of great interest for the development of nonvolatile magnetic memory and computing technologies due to their high stabilities at the nanoscale. However, electrical switching of such perpendicular magnetization in an energy-efficient, deterministic, scalable manner has remained a big challenge. This problem has recently attracted enormous efforts in the field of spintronics. Here, recent advances and challenges in the understanding of the electrical generation of spin currents, the switching mechanisms and the switching strategies of perpendicular magnetization, the switching current density by spin-orbit torque of transverse spins, the choice of perpendicular magnetic materials are reviewed, and the progress in prototype perpendicular SOT memory and logic devices toward the goal of energy-efficient, dense, fast perpendicular spin-orbit torque applications is summarized.

Absence of Spin-Orbit Torque and Discovery of Anisotropic Planar Nernst Effect in CoFe Single Crystal

Exploration of exotic spin polarizations in single crystals is of increasing interest. A current of longitudinal spins, the so-called "Dresselhaus-like" spin current, which is forbidden in materials lacking certain inversion asymmetries, is implied to be generated by a charge current at the interface of single-crystal CoFe. This work reports unambiguous evidence that there is no indication of spin current of any spin polarizations from the interface or bulk of single-crystalline CoFe and that the sin2φ second harmonic Hall voltage, which is previously assumed to signify Dresselhaus-like spin current, is not related to any spin currents but rather a planar Nernst voltage induced by a longitudinal temperature gradient within the sample. Such sin2φ signal is independent of large applied magnetic fields and interfacial spin-orbit coupling, inversely correlated to the heat capacity of the substrates and overlayers, quadratic in charge current, and appears also in polycrystalline ferromagnets. Strikingly, the planar Nernst effect (PNE) in the CoFe single crystal has a strong fourfold anisotropy and varies with the crystalline orientation. Such strong, anisotropic PNE has widespread impacts on the analyses of a variety of spintronic experiments and opens a new avenue for the development of PNE-based thermoelectric battery and sensor applications.

Néel Spin Currents in Antiferromagnets

Ferromagnets are known to support spin-polarized currents that control various spin-dependent transport phenomena useful for spintronics. On the contrary, fully compensated antiferromagnets are expected to support only globally spin-neutral currents. Here, we demonstrate that these globally spin-neutral currents can represent the Néel spin currents, i.e., staggered spin currents flowing through different magnetic sublattices. The Néel spin currents emerge in antiferromagnets with strong intrasublattice coupling (hopping) and drive the spin-dependent transport phenomena such as tunneling magnetoresistance (TMR) and spin-transfer torque (STT) in antiferromagnetic tunnel junctions (AFMTJs). Using RuO_{2} and Fe_{4}GeTe_{2} as representative antiferromagnets, we predict that the Néel spin currents with a strong staggered spin polarization produce a sizable fieldlike STT capable of the deterministic switching of the Néel vector in the associated AFMTJs. Our work uncovers the previously unexplored potential of fully compensated antiferromagnets and paves a new route to realize the efficient writing and reading of information for antiferromagnetic spintronics.

Efficient Spin-to-Charge Conversion via Altermagnetic Spin Splitting Effect in Antiferromagnet RuO_{2}

The relativistic spin Hall effect and inverse spin Hall effect enable the efficient generation and detection of spin current. Recently, a nonrelativistic altermagnetic spin splitting effect (ASSE) has been theoretically and experimentally reported to generate time-reversal-odd spin current with controllable spin polarization in antiferromagnet RuO_{2}. The inverse effect, electrical detection of spin current via ASSE, still remains elusive. Here we show the spin-to-charge conversion stemming from ASSE in RuO_{2} by the spin Seebeck effect measurements. Unconventionally, the spin Seebeck voltage can be detected even when the injected spin current is polarized along the directions of either the voltage channel or the thermal gradient, indicating the successful conversion of x- and z-spin polarizations into the charge current. The crystal axes-dependent conversion efficiency further demonstrates that the nontrivial spin-to-charge conversion in RuO_{2} is ascribed to ASSE, which is distinct from the magnetic or antiferromagnetic inverse spin Hall effects. Our finding not only advances the emerging research landscape of altermagnetism, but also provides a promising pathway for the spin detection.

Nonrelativistic Spin-Momentum Coupling in Antiferromagnetic Twisted Bilayers

Spin-momentum coupling, which depends strongly on the relativistic effect of heavy elements in solids, is the basis of many phenomena in spintronics. In this Letter, we theoretically predict nonrelativistic spin-momentum coupling in two-dimensional materials. By proposing magnetic symmetry requirements for spin splitting in two-dimensional systems, we find that a simple twisting operation can realize nonrelativistic spin splitting in antiferromagnetic bilayers. Through first-principles calculations, we demonstrate that momentum-dependent spin splitting exists extensively in antiferromagnetic twisted bilayers with different crystal structures and twist angles. The size of the spin splitting caused by twisting is of the same order of magnitude as that arising from spin-orbit coupling. In particular, a transverse spin current with an extremely high charge-spin conversion ratio can be generated in twisted structures under an external electric field. The findings demonstrate the potential for achieving electrically controlled magnetism in materials without spin-orbit coupling.

Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor

The anomalous Hall effect, commonly observed in metallic magnets, has been established to originate from the time-reversal symmetry breaking by an internal macroscopic magnetization in ferromagnets or by a noncollinear magnetic order. Here we observe a spontaneous anomalous Hall signal in the absence of an external magnetic field in an epitaxial film of MnTe, which is a semiconductor with a collinear antiparallel magnetic ordering of Mn moments and a vanishing net magnetization. The anomalous Hall effect arises from an unconventional phase with strong time-reversal symmetry breaking and alternating spin polarization in real-space crystal structure and momentum-space electronic structure. The anisotropic crystal environment of magnetic Mn atoms due to the nonmagnetic Te atoms is essential for establishing the unconventional phase and generating the anomalous Hall effect.