Observation of Long-Range Current-Induced Torque in Ni/Pt Bilayers.

The generation of current-induced torques through the spin Hall effect in Pt has been key to the development of spintronics. In prototypical ferromagnetic-metal/Pt devices, the characteristic length of the torque generation is known to be about 1 nm due to the short spin diffusion length of Pt. Here, we report the observation of a long-range current-induced torque in Ni/Pt bilayers. We demonstrate that when Ni is used as the ferromagnetic layer, the torque efficiency increases with the Pt thickness, even when it exceeds 10 nm. The torque efficiency is also enhanced by increasing the Ni thickness, providing evidence that the observed torque cannot be attributed to the spin Hall effect in the Pt layer. These findings, coupled with our semirealistic tight-binding calculations of the current-induced torque, suggest the possibility that the observed long-range torque is dominated by the orbital Hall effect in the Pt layer.

Topology-Engineered Orbital Hall Effect in Two-Dimensional Ferromagnets.

Recent advances in the manipulation of the orbital angular momentum (OAM) within the paradigm of orbitronics presents a promising avenue for the design of future electronic devices. In this context, the recently observed orbital Hall effect (OHE) occupies a special place. Here, focusing on both the second-order topological and quantum anomalous Hall insulators in two-dimensional ferromagnets, we demonstrate that topological phase transitions present an efficient and straightforward way to engineer the OHE, where the OAM distribution can be controlled by the nature of the band inversion. Using first-principles calculations, we identify Janus RuBrCl and three septuple layers of MnBi2Te4 as experimentally feasible examples of the proposed mechanism of OHE engineering by topology. With our work, we open up new possibilities for innovative applications in topological spintronics and orbitronics.

Electrostatic Gating of Spin Dynamics of a Quasi-2D Kagome Magnet.

Electrostatic gating has emerged as a powerful technique for tailoring the magnetic properties of two-dimensional (2D) magnets, offering exciting prospects including enhancement of magnetic anisotropy, boosting Curie temperature, and strengthening exchange coupling effects. Here, we focus on electrical control of the ferromagnetic resonance of the quasi-2D Kagome magnet Cu(1,3-bdc). By harnessing an electrostatic field through ionic liquid gating, significant shifts are observed in the ferromagnetic resonance field in both out-of-plane and in-plane measurements. Moreover, the effective magnetization and gyromagnetic ratios display voltage-dependent variations. A closer examination reveals that the voltage-induced changes can modulate magnetocrystalline anisotropy by several hundred gauss, while the impact on orbital magnetization remains relatively subtle. Density functional theory (DFT) calculations reveal varying d-orbital hybridizations at different voltages. This research unveils intricate physics within the Kagome lattice magnet and further underscores the potential of electrostatic manipulation in steering magnetism with promising implications for the development of spintronic devices.

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.

Controlling the Interlayer Dzyaloshinskii-Moriya Interaction by Electrical Currents.

The recently discovered interlayer Dzyaloshinskii-Moriya interaction (IL-DMI) in multilayers with perpendicular magnetic anisotropy favors canting of spins in the in-plane direction. It could thus stabilize intriguing spin textures such as Hopfions. A key requirement for nucleation is to control the IL-DMI. Therefore, we investigate the influence of an electric current on a synthetic antiferromagnet with growth-induced IL-DMI. The IL-DMI is quantified by using out-of-plane hysteresis loops of the anomalous Hall effect while applying a static in-plane magnetic field at varied azimuthal angles. We observe a shift in the azimuthal dependence with an increasing current, which we conclude to originate from the additional in-plane symmetry breaking introduced by the current flow. Fitting the angular dependence, we demonstrate the presence of an additive current-induced term that linearly increases the IL-DMI in the direction of current flow. This opens the possibility of easily manipulating 3D spin textures by currents.

Long-Range Orbital Torque by Momentum-Space Hotspots.

While it is often assumed that the orbital response is suppressed and short ranged due to strong crystal field potential and orbital quenching, we show that the orbital response can be remarkably long ranged in ferromagnets. In a bilayer consisting of a nonmagnet and a ferromagnet, spin injection from the interface results in spin accumulation and torque in the ferromagnet, which rapidly oscillate and decay by spin dephasing. In contrast, even when an external electric field is applied only on the nonmagnet, we find substantially long-ranged induced orbital angular momentum in the ferromagnet, which can go far beyond the spin dephasing length. This unusual feature is attributed to nearly degenerate orbital characters imposed by the crystal symmetry, which form hotspots for the intrinsic orbital response. Because only the states near the hotspots contribute dominantly, the induced orbital angular momentum does not exhibit destructive interference among states with different momentum as in the case of the spin dephasing. This gives rise to a distinct type of orbital torque on the magnetization, increasing with the thickness of the ferromagnet. Such behavior may serve as critical long-sought evidence of orbital transport to be directly tested in experiments. Our findings open the possibility of using long-range orbital response in orbitronic device applications.

Evidence of Magnon-Mediated Orbital Magnetism in a Quasi-2D Topological Magnon Insulator.

We explore spin dynamics in Cu(1,3-bdc), a quasi-2D topological magnon insulator. The results show that the thermal evolution of the Landé g factor (g) is anisotropic: gin-plane decreases while gout-of-plane increases with increasing temperature T. Moreover, the anisotropy of the g factor (Δg) and the anisotropy of saturation magnetization (ΔMs) are correlated below 4 K, but they diverge above 4 K. We show that the electronic orbital moment contributes to the g anisotropy at lower T, while the topological orbital moment induced by thermally excited spin chirality dictates the g anisotropy at higher T. Our work suggests an interplay among topology, spin chirality, and orbital magnetism in Cu(1,3-bdc).

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.

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.

Observation of the Orbital Rashba-Edelstein Magnetoresistance.

We report the observation of magnetoresistance (MR) that could originate from the orbital angular momentum (OAM) transport in a permalloy (Py)/oxidized Cu (Cu^{*}) heterostructure: the orbital Rashba-Edelstein magnetoresistance. The angular dependence of the MR depends on the relative angle between the induced OAM and the magnetization in a similar fashion as the spin Hall magnetoresistance. Despite the absence of elements with large spin-orbit coupling, we find a sizable MR ratio, which is in contrast to the conventional spin Hall magnetoresistance which requires heavy elements. Through Py thickness-dependence studies, we conclude another mechanism beyond the conventional spin-based scenario is responsible for the MR observed in Py/Cu^{*} structures-originated in a sizable transport of OAM. Our findings not only suggest the current-induced torques without using any heavy elements via the OAM channel but also provide an important clue towards the microscopic understanding of the role that OAM transport can play for magnetization dynamics.

Roadmap of spin-orbit torques.

Spin-orbit torque (SOT) is an emerging technology that enables the efficient manipulation of spintronic devices. The initial processes of interest in SOTs involved electric fields, spin-orbit coupling, conduction electron spins and magnetization. More recently interest has grown to include a variety of other processes that include phonons, magnons, or heat. Over the past decade, many materials have been explored to achieve a larger SOT efficiency. Recently, holistic design to maximize the performance of SOT devices has extended material research from a nonmagnetic layer to a magnetic layer. The rapid development of SOT has spurred a variety of SOT-based applications. In this Roadmap paper, we first review the theories of SOTs by introducing the various mechanisms thought to generate or control SOTs, such as the spin Hall effect, the Rashba-Edelstein effect, the orbital Hall effect, thermal gradients, magnons, and strain effects. Then, we discuss the materials that enable these effects, including metals, metallic alloys, topological insulators, two-dimensional materials, and complex oxides. We also discuss the important roles in SOT devices of different types of magnetic layers, such as magnetic insulators, antiferromagnets, and ferrimagnets. Afterward, we discuss device applications utilizing SOTs. We discuss and compare three-terminal and two-terminal SOT-magnetoresistive random-access memories (MRAMs); we mention various schemes to eliminate the need for an external field. We provide technological application considerations for SOT-MRAM and give perspectives on SOT-based neuromorphic devices and circuits. In addition to SOT-MRAM, we present SOT-based spintronic terahertz generators, nano-oscillators, and domain wall and skyrmion racetrack memories. This paper aims to achieve a comprehensive review of SOT theory, materials, and applications, guiding future SOT development in both the academic and industrial sectors.

Long-range chiral exchange interaction in synthetic antiferromagnets.

The exchange interaction governs static and dynamic magnetism. This fundamental interaction comes in two flavours-symmetric and antisymmetric. The symmetric interaction leads to ferro- and antiferromagnetism, and the antisymmetric interaction has attracted significant interest owing to its major role in promoting topologically non-trivial spin textures that promise fast, energy-efficient devices. So far, the antisymmetric exchange interaction has been found to be rather short ranged and limited to a single magnetic layer. Here we report a long-range antisymmetric interlayer exchange interaction in perpendicularly magnetized synthetic antiferromagnets with parallel and antiparallel magnetization alignments. Asymmetric hysteresis loops under an in-plane field reveal a unidirectional and chiral nature of this interaction, which results in canted magnetic structures. We explain our results by considering spin-orbit coupling combined with reduced symmetry in multilayers. Our discovery of a long-range chiral interaction provides an additional handle to engineer magnetic structures and could enable three-dimensional topological structures.

Author Correction: Long-range chiral exchange interaction in synthetic antiferromagnets.

In the version of this Article originally published, the sentence 'D.-S.H. wrote the paper with K.L., J.H. and M.K.' in the author contributions was incorrect; it should have read 'D.-S.H. wrote the paper with K.L., J.H., M.-H.J. and M.K.' This has been corrected in the online versions of the Article.

Chiral Hall Effect in Noncollinear Magnets from a Cyclic Cohomology Approach.

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the reinterpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.

Antiferromagnetic Topological Insulator with Nonsymmorphic Protection in Two Dimensions.

The recent demonstration of topological states in antiferromagnets (AFMs) provides an exciting platform for exploring prominent physical phenomena and applications of antiferromagnetic spintronics. A famous example is the AFM topological insulator (TI) state, which, however, was still not observed in two dimensions. Using a tight-binding model and first-principles calculations, we show that, in contrast to previously observed AFM topological insulators in three dimensions, an AFM TI can emerge in two dimensions as a result of a nonsymmorphic symmetry that combines the twofold rotation symmetry and half-lattice translation. Based on the spin Chern number, Wannier charge centers, and gapless edge states analysis, we identify intrinsic AFM XMnY (X=Sr and Ba, Y=Sn and Pb) quintuple layers as experimentally feasible examples of predicted topological states with a stable crystal structure and giant magnitude of the nontrivial band gaps, reaching as much as 186 meV for SrMnPb, thereby promoting these systems as promising candidates for innovative spintronics applications.

Electric-Field Control of Spin-Orbit Torques in Perpendicularly Magnetized W/CoFeB/MgO Films.

Controlling magnetism by electric fields offers a highly attractive perspective for designing future generations of energy-efficient information technologies. Here, we demonstrate that the magnitude of current-induced spin-orbit torques in thin perpendicularly magnetized CoFeB films can be tuned and even increased by electric-field generated piezoelectric strain. Using theoretical calculations, we uncover that the subtle interplay of spin-orbit coupling, crystal symmetry, and orbital polarization is at the core of the observed strain dependence of spin-orbit torques. Our results open a path to integrating two energy efficient spin manipulation approaches, the electric-field-induced strain and the current-induced magnetization switching, thereby enabling novel device concepts.

Harnessing Orbital-to-Spin Conversion of Interfacial Orbital Currents for Efficient Spin-Orbit Torques.

Current-induced spin-orbit torques (SOTs) allow for the efficient electrical manipulation of magnetism in spintronic devices. Engineering the SOT efficiency is a key goal that is pursued by maximizing the active interfacial spin accumulation or modulating the nonequilibrium spin density that builds up through the spin Hall and inverse spin galvanic effects. Regardless of the origin, the fundamental requirement for the generation of the current-induced torques is a net spin accumulation. We report on the large enhancement of the SOT efficiency in thulium iron garnet (TmIG)/Pt by capping with a CuO_{x} layer. Considering the weak spin-orbit coupling (SOC) of CuO_{x}, these surprising findings likely result from an orbital current generated at the interface between CuO_{x} and Pt, which is injected into the Pt layer and converted into a spin current by strong SOC. The converted spin current decays across the Pt layer and exerts a "nonlocal" torque on TmIG. This additional torque leads to a maximum colossal enhancement of the SOT efficiency of a factor 16 for 1.5 nm of Pt at room temperature, thus opening a path to increase torques while at the same time offering insights into the underlying physics of orbital transport, which has so far been elusive.

Two-Dimensional Topological Crystalline Insulator and Topological Phase Transition in TlSe and TlS Monolayers.

The properties that distinguish topological crystalline insulator (TCI) and topological insulator (TI) rely on crystalline symmetry and time-reversal symmetry, respectively, which encodes different bulk and surface/edge properties. Here, we predict theoretically that electron-doped TlM (M = S and Se) (110) monolayers realize a family of two-dimensional (2D) TCIs characterized by mirror Chern number CM = -2. Remarkably, under uniaxial strain (≈ 1%), a topological phase transition between 2D TCI and 2D TI is revealed with the calculated spin Chern number CS = -1 for the 2D TI. Using spin-resolved edge states analysis, we show different edge-state behaviors, especially at the time reversal invariant points. Finally, a TlBiSe2/NaCl quantum well is proposed to realize an undoped 2D TCI with inverted gap as large as 0.37 eV, indicating the high possibility for room-temperature observation.

Spin Hall effects in metallic antiferromagnets.

We investigate four CuAu-I-type metallic antiferromagnets for their potential as spin current detectors using spin pumping and inverse spin Hall effect. Nontrivial spin Hall effects were observed for FeMn, PdMn, and IrMn while a much higher effect was obtained for PtMn. Using thickness-dependent measurements, we determined the spin diffusion lengths of these materials to be short, on the order of 1 nm. The estimated spin Hall angles of the four materials follow the relationship PtMn>IrMn>PdMn>FeMn, highlighting the correlation between the spin-orbit coupling of nonmagnetic species and the magnitude of the spin Hall effect in their antiferromagnetic alloys. These experiments are compared with first-principles calculations. Engineering the properties of the antiferromagnets as well as their interfaces can pave the way for manipulation of the spin dependent transport properties in antiferromagnet-based spintronics.

Time-domain observation of ballistic orbital-angular-momentum currents with giant relaxation length in tungsten.

The emerging field of orbitronics exploits the electron orbital momentum L. Compared to spin-polarized electrons, L may allow the transfer of magnetic information with considerably higher density over longer distances in more materials. However, direct experimental observation of L currents, their extended propagation lengths and their conversion into charge currents has remained challenging. Here, we optically trigger ultrafast angular-momentum transport in Ni|W|SiO2 thin-film stacks. The resulting terahertz charge-current bursts exhibit a marked delay and width that grow linearly with the W thickness. We consistently ascribe these observations to a ballistic L current from Ni through W with a giant decay length (~80 nm) and low velocity (~0.1 nm fs-1). At the W/SiO2 interface, the L flow is efficiently converted into a charge current by the inverse orbital Rashba-Edelstein effect, consistent with ab initio calculations. Our findings establish orbitronic materials with long-distance ballistic L transport as possible candidates for future ultrafast devices and an approach to discriminate Hall-like and Rashba-Edelstein-like conversion processes.