Intrinsic spin Hall effect in platinum: first-principles calculations

Control of Charge-Spin Interconversion in van der Waals Heterostructures with Chiral Charge Density Waves

A charge density wave (CDW) represents an exotic state in which electrons are arranged in a long-range ordered pattern in low-dimensional materials. Although the understanding of the fundamental character of CDW is enriched after extensive studies, its practical application remains limited. Here, an unprecedented demonstration of a tunable charge-spin interconversion (CSI) in graphene/1T-TaS2 van der Waals heterostructures is shown by manipulating the distinct CDW phases in 1T-TaS2. Whereas CSI from spins polarized in all three directions is observed in the heterostructure when the CDW phase does not show commensurability, the output of one of the components disappears, and the other two are enhanced when the CDW phase becomes commensurate. The experimental observation is supported by first-principles calculations, which evidence that chiral CDW multidomains in the heterostructure are at the origin of the switching of CSI. The results uncover a new approach for on-demand CSI in low-dimensional systems, paving the way for advanced spin-orbitronic devices.

Two-dimensional antiferromagnetic nodal-line semimetal and spin Hall effect in MnC4

Nodal-line semimetals, characterized by Dirac-like crossings along one dimensionalk-space lines, represent a unique class of topological materials. In this study, we investigate the intriguing properties of room-temperature antiferromagneticMnC4and its nodal-line features both with and without spin-orbit coupling (SOC). In the absence of SOC, we identify a doubly degenerate Dirac-nodal line, robustly protected by a combination of time-reversal, mirror, and partial-translation symmetries. Remarkably, this nodal line withstands various external perturbations, including isotropic and anisotropic strain, and torsional deformations, due to the ionic-like bonding between Mn atoms and C clusters. With the inclusion of SOC, we observe a distinctive quasi-Dirac-nodal line that emerges due to the interplay between antiferromagnetism and SOC-induced spin-rotation symmetry breaking. Finally, we observed a robust spin Hall conductivity that aligns with the energy range where the quasi-nodal line appears. This study presents a compelling example of a robust symmetry-protected Dirac-nodal line antiferromagnetic monolayer, which has potential for applications in next-generation spintronic devices.

Observation of the Fluctuation Spin Hall Effect in a Low-Resistivity Antiferromagnet

The spin Hall effect (SHE) can generate a pure spin current by an electric current, which is promisingly used to electrically control magnetization. To reduce the power consumption of this control, a giant spin Hall angle (SHA) in the SHE is desired in low-resistivity systems for practical applications. Here, critical spin fluctuation near the antiferromagnetic (AFM) phase transition in chromium (Cr) is proven to be an effective mechanism for creating an additional part of the SHE, named the fluctuation spin Hall effect. The SHA is significantly enhanced when the temperature approaches the Néel temperature (TN) of Cr and has a peak value of -0.36 near TN. This value is higher than the room-temperature value by 153% and leads to a low normalized power consumption among known spin-orbit torque materials. This study demonstrates the critical spin fluctuation as a prospective way to increase the SHA and enriches the AFM material candidates for spin-orbitronic devices.

Room-Temperature van der Waals Ferromagnet Switching by Spin-Orbit Torques

The emerging wide varieties of the van der Waals (vdW) magnets with atomically thin and smooth interfaces hold great promise for next-generation spintronic devices. However, due to the lower Curie temperature of the vdW ferromagnets than room temperature, electrically manipulating its magnetization at room temperature has not been realized. In this work, it is demonstrated that the perpendicular magnetization of the vdW ferromagnet Fe3 GaTe2 can be effectively switched at room temperature in the Fe3 GaTe2 /Pt bilayer by spin-orbit torques (SOTs) with a relatively low current density of 1.3 × 107 A cm-2 . Moreover, the high SOT efficiency of ξDL ≈ 0.28 is quantitatively determined by harmonic measurements, which is higher than those in Pt-based heavy metal/conventional ferromagnet devices. The findings of room-temperature vdW ferromagnet switching by SOTs provide a significant basis for the development of vdW-ferromagnet-based spintronic applications.

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.

Nonlinear Topological Magnon Spin Hall Effect

When a magnon passes through two-dimensional magnetic textures, it will experience a fictitious magnetic field originating from the 3×3 skew-symmetric gauge fields. To date, only one of the three independent components of the gauge fields has been found to play a role in generating the fictitious magnetic field, while the other two are perfectly hidden. In this Letter, we show that they are concealed in the nonlinear magnon transport in magnetic textures. Without loss of generality, we theoretically study the nonlinear magnon-skyrmion interaction in antiferromagnets. By analyzing the scattering features of three-magnon processes between the circularly polarized incident magnon and breathing skyrmion, we predict a giant Hall angle of both the confluence and splitting modes. Furthermore, we find that the Hall angle reverses its sign when one switches the handedness of the incident magnons. We dub this the nonlinear topological magnon spin Hall effect. Our findings are deeply rooted in the bosonic nature of magnons that the particle number is not conserved, which has no counterpart in low-energy fermionic systems and may open the door for probing gauge fields by nonlinear means.

Tuning Intrinsic Spin Hall Effect in Platinum/Ferrimagnetic Insulator Heterostructure in Moderately Dirty Regime

Studying the mechanisms of the spin Hall effect (SHE) is essential for the fundamental understanding of spintronic physics. By now, despite the intensive studies of SHE on heavy metal (HM)/metallic magnet heterostructures, the SHE on HM/ferrimagnetic insulator (FMI) heterostructures still remains elusive. Here, we study the mechanism of SHE in the Pt/Tm3Fe5O12 (TmIG) heterostructure. We first tune the crystallinity and resistivity of Pt by an annealing method, and then study the spin-orbit torque (SOT) in the tuned-Pt/TmIG devices. The SOT generation efficiency per unit electric field and spin Hall angle were obtained, which are insensitive to the annealing temperature. We further demonstrate that the intrinsic contribution in the moderately dirty regime is responsible for the SHE in our Pt/TmIG bilayer. Our study provides an important piece of information for the SHE in FMI-based spintronic physics.

Observation of anti-damping spin-orbit torques generated by in-plane and out-of-plane spin polarizations in MnPd3

Large spin-orbit torques (SOTs) generated by topological materials and heavy metals interfaced with ferromagnets are promising for next-generation magnetic memory and logic devices. SOTs generated from y spin originating from spin Hall and Edelstein effects can realize field-free magnetization switching only when the magnetization and spin are collinear. Here we circumvent the above limitation by utilizing unconventional spins generated in a MnPd₃ thin film grown on an oxidized silicon substrate. We observe conventional SOT due to y spin, and out-of-plane and in-plane anti-damping-like torques originated from z spin and x spin, respectively, in MnPd₃/CoFeB heterostructures. Notably, we have demonstrated complete field-free switching of perpendicular cobalt via out-of-plane anti-damping-like SOT. Density functional theory calculations show that the observed unconventional torques are due to the low symmetry of the (114)-oriented MnPd₃ films. Altogether our results provide a path toward realization of a practical spin channel in ultrafast magnetic memory and logic devices.

Electrical Control of Spin Hall Effect in Pt by Hydrogen Ion Adsorption and Desorption

The manipulation of charge-to-spin current conversion and spin-orbit torque (SOT) is of great interest due to its profound physics and potential applications. Controlling the spin current through the electric field provides a perspective for highly efficient SOT devices. Here, we use H₂O-doped ionic liquid gating to realize the reversible and nonvolatile manipulation of the spin Hall effect of Pt, and the spin Hall angle can be modulated by 48% within an accessible gate voltage range. The increase in the spin Hall angle is demonstrated to be caused by the adsorption of hydrogen ions on the Pt surface and the consequent enhancement of the spin Hall conductivity under positive voltage. Furthermore, the enhancement of the spin Hall angle is beneficial to reduce the critical current density for driving the domain wall motion. These results supply a method for the dynamic control of the charge-to-spin current conversion, which will promote the development of spintronic devices driven by electric fields.

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.

High-Efficiency Magnon-Mediated Magnetization Switching in All-Oxide Heterostructures with Perpendicular Magnetic Anisotropy

The search for efficient approaches to realize local switching of magnetic moments in spintronic devices has attracted extensive attention. One of the most promising approaches is the electrical manipulation of magnetization through electron-mediated spin torque. However, the Joule heat generated via electron motion unavoidably causes substantial energy dissipation and potential damage to spintronic devices. Here, all-oxide heterostructures of SrRuO₃ /NiO/SrIrO₃ are epitaxially grown on SrTiO₃ single-crystal substrates following the order of the ferromagnetic transition metal oxide SrRuO₃ with perpendicular magnetic anisotropy, insulating and antiferromagnetic NiO, and metallic transition metal oxide SrIrO₃ with strong spin-orbit coupling. It is demonstrated that instead of the electron spin torques, the magnon torques present in the antiferromagnetic NiO layer can directly manipulate the perpendicular magnetization of the ferromagnetic layer. This magnon mechanism may significantly reduce the electron motion-related energy dissipation from electron-mediated spin currents. Interestingly, the threshold current density to generate a sufficient magnon current to manipulate the magnetization is one order of magnitude smaller than that in conventional metallic systems. These findings suggest a route for developing highly efficient all-oxide spintronic devices operated by magnon current.

Spin Swapping Effect of Band Structure Origin in Centrosymmetric Ferromagnets

We theoretically demonstrate the spin swapping effect of band structure origin in centrosymmetric ferromagnets. It is mediated by an orbital degree of freedom but does not require inversion asymmetry or impurity spin-orbit scattering. Analytic and tight-binding models reveal that it originates mainly from k points where bands with different spins and different orbitals are nearly degenerate, and thus it has no counterpart in normal metals. First-principle calculations for centrosymmetric 3d transition-metal ferromagnets show that the spin swapping conductivity of band structure origin can be comparable in magnitude to the intrinsic spin Hall conductivity of Pt. Our theory generalizes transverse spin currents generated by ferromagnets and emphasizes the important role of the orbital degree of freedom in describing spin-orbit-coupled transport in centrosymmetric materials.

Quantifying Spin-Orbit Torques in Antiferromagnet-Heavy-Metal Heterostructures

The effect of spin currents on the magnetic order of insulating antiferromagnets (AFMs) is of fundamental interest and can enable new applications. Toward this goal, characterizing the spin-orbit torques (SOTs) associated with AFM-heavy-metal (HM) interfaces is important. Here we report the full angular dependence of the harmonic Hall voltages in a predominantly easy-plane AFM, epitaxial c-axis oriented α-Fe_{2}O_{3} films, with an interface to Pt. By modeling the harmonic Hall signals together with the α-Fe_{2}O_{3} magnetic parameters, we determine the amplitudes of fieldlike and dampinglike SOTs. Out-of-plane field scans are shown to be essential to determining the dampinglike component of the torques. In contrast to ferromagnetic-heavy-metal heterostructures, our results demonstrate that the fieldlike torques are significantly larger than the dampinglike torques, which we correlate with the presence of a large imaginary component of the interface spin-mixing conductance. Our work demonstrates a direct way of characterizing SOTs in AFM-HM heterostructures.

Elastodynamically Induced Spin and Charge Pumping in Bulk Heavy Metals

Analogous to the spin-Hall effect (SHE), ab initio electronic structure calculations reveal that acoustic phonons can induce charge (spin) current flowing along (normal to) its propagation direction. Using the Floquet approach we have calculated the elastodynamically induced charge and spin pumping in bulk Pt and demonstrate that (i) the longitudinal charge pumping originates from the Berry curvature, while the transverse pumped spin current is an odd function of the electronic relaxation time and diverges in the clean limit. (ii) The longitudinal charge current is of nonrelativstic origin, while the transverse spin current is a relativistic effect that to lowest order scales linearly with the spin-orbit coupling strength. (iii) Both charge and spin pumped currents have parabolic dependence on the amplitude of the elastic wave.

Momentum-Space Spin Antivortex and Spin Transport in Monolayer Pb

Nontrivial momentum-space spin texture of electrons can be induced by spin-orbit coupling and underpins various spin transport phenomena, such as current-induced spin polarization and the spin Hall effect. In this work, we find a nontrivial spin texture, spin antivortex, can appear at certain momenta on the Γ-K line in a 2D monolayer Pb on top of SiC. Different from spin vortex due to the band degeneracy in the Rashba model, the existence of this spin antivortex is guaranteed by the Poincaré-Hopf theorem and thus topologically stable. Accompanied with this spin antivortex, a Lifshitz transition of Fermi surfaces occurs at certain momenta on the K-M line, and both phenomena are originated from the anticrossing between the j=1/2 and j=3/2 bands. A rapid variation of the response coefficients for both the current-induced spin polarization and spin Hall conductivity is found when the Fermi energy is tuned around the spin antivortex. Our work demonstrates the monolayer Pb as a potentially appealing platform for spintronic applications.

Regulating Interfacial Spin Hall Conductivity with Ferroelectricity

We report a new physical phenomenon of active and enhanced control of the spin Hall conductivity (SHC) in a family of metal-ferroelectric multilayers. Rather than the direction of the built-in electric field, such ferroelectric regulation of SHC originates from the drastic change of the interfacial electronic state along with its intrinsic Berry phase near the Fermi level due to the distinct hybridization between the metal film and substrate when the ferroelectric polarization reverses. Using Pt/PbZrTiO₃ multilayers as a representative model, we demonstrate the controllability of a large magnitude and even the sign of SHC in the Pt film at the two interfaces with an antitype conducting carrier in a ferroelectric substrate. The interfacial Rashba effect plays a role in contributing to the change of SHC through spin-projected band analysis. The present work makes a fundamental theoretical discovery and opens up a new direction to manipulate spin-charge conversion of thin-film layered structures by ferroelectricity, which is crucial for designing future electric and spintronic devices.

Topological bands in PdSe2 pentagonal monolayer

The electronic structure of monolayer pentagonal palladium diselenide (PdSe2) is analyzed from the topological band theory perspective. Employing first-principles calculations, effective models and symmetry indicators we find that the low-lying...

Functionalized tellurene; a candidate large-gap 2D topological insulator

The discovery of group IV and V elemental xene's with topologically non-trivial characters in their honeycomb lattice structure (HLS) has led to extensive efforts in realising analogous behaviour in group VI elemental monolayers. Theoretically; it was concluded that, group VI elemental monolayers cannot exist in HLS. However, some recent experimental evidence suggests that group VI elemental monolayers can be realised in HLS. In this letter, we report HLS of group VI elemental monolayer (such as, tellurene) can be realised to be dynamically stable when functionzalised with oxygen. The functionalization leads to, peculiar orbital filtering effects and broken spatial inversion symmetry which gives rise to the non-trivial topological character. The exotic quantum behaviour of this system is characterized by, spin-orbit coupling induced large-gap (≈0.36 eV) with isolated Dirac cone along the edges indicating potential room temperature spin-transport applications. Further investigations of spin Hall conductivity and the Berry curvatures unravel high conductivity as compared to previously explored xene's alongside the potential valley Hall effects. The non-trivial topological character is quantified in terms of theZ2invariant asν= 1 and Chern numberC= 1. Also, for practical purposes, we report that,hBN/TeO/hBN quantum-wells can be strain engineered to realize a sizeable non-trivial gap (≈0.11 eV). We finally conclude that, functionalization of group VI elemental monolayer with oxygen gives rise to, exotic quantum properties which are robust against surface oxidation and degradations while providing viable electronic degrees of freedom for spintronic/valleytronic applications.

Orbital torque in magnetic bilayers

The orbital Hall effect describes the generation of the orbital current flowing in a perpendicular direction to an external electric field, analogous to the spin Hall effect. As the orbital current carries the angular momentum as the spin current does, injection of the orbital current into a ferromagnet can result in torque on the magnetization, which provides a way to detect the orbital Hall effect. With this motivation, we examine the current-induced spin-orbit torques in various ferromagnet/heavy metal bilayers by theory and experiment. Analysis of the magnetic torque reveals the presence of the contribution from the orbital Hall effect in the heavy metal, which competes with the contribution from the spin Hall effect. In particular, we find that the net torque in Ni/Ta bilayers is opposite in sign to the spin Hall theory prediction but instead consistent with the orbital Hall theory, which unambiguously confirms the orbital torque generated by the orbital Hall effect. Our finding opens a possibility of utilizing the orbital current for spintronic device applications, and it will invigorate researches on spin-orbit-coupled phenomena based on orbital engineering.

Modulation of spin-torque ferromagnetic resonance with a nanometer-thick platinum by ionic gating

The spin Hall effect (SHE) and inverse spin Hall effect (ISHE) have played central roles in modern condensed matter physics especially in spintronics and spin-orbitronics, and much effort has been paid to fundamental and application-oriented research towards the discovery of novel spin-orbit physics and the creation of novel spintronic devices. However, studies on gate-tunability of such spintronics devices have been limited, because most of them are made of metallic materials, where the high bulk carrier densities hinder the tuning of physical properties by gating. Here, we show an experimental demonstration of the gate-tunable spin-orbit torque in Pt/Ni80Fe20 (Py) devices by controlling the SHE using nanometer-thick Pt with low carrier densities and ionic gating. The Gilbert damping parameter of Py and the spin-memory loss at the Pt/Py interface were modulated by ionic gating to Pt, which are compelling results for the successful tuning of spin-orbit interaction in Pt.

Emergence of Nontrivial Spin Textures in Frustrated Van Der Waals Ferromagnets

In this work, first principles ground state calculations are combined with the dynamic evolution of a classical spin Hamiltonian to study the metamagnetic transitions associated with the field dependence of magnetic properties in frustrated van der Waals ferromagnets. Dynamically stabilized spin textures are obtained relative to the direction of spin quantization as stochastic solutions of the Landau-Lifshitz-Gilbert-Slonczewski equation under the flow of the spin current. By explicitly considering the spin signatures that arise from geometrical frustrations at interfaces, we may observe the emergence of a magnetic skyrmion spin texture and characterize the formation under competing internal fields. The analysis of coercivity and magnetic hysteresis reveals a dynamic switch from a soft to hard magnetic configuration when considering the spin Hall effect on the skyrmion. It is found that heavy metals in capped multilayer heterostructure stacks host field-tunable spiral skyrmions that could serve as unique channels for carrier transport. The results are discussed to show the possibility of using dynamically switchable magnetic bits to read and write data without the need for a spin transfer torque. These results offer insight to the spin transport signatures that dynamically arise from metamagnetic transitions in spintronic devices.

Strain-Mediated Spin-Orbit Torque Enhancement in Pt/Co on Flexible Substrate

Current-induced magnetization switching by spin-orbit torque generated in heavy metals offers an enticing realm for energy-efficient memory and logic devices. The spin Hall efficiency is a key parameter in describing the generation of spin current. Recent findings have reported enhancement of spin Hall efficiency by mechanical strain, but its origin remains elusive. Here, we demonstrate a 45% increase in spin Hall efficiency in the platinum/cobalt (Pt/Co) bilayer, of which 78% of the enhancement was preserved even after the strain was removed. Spin transparency and X-ray magnetic circular dichroism revealed that the enhancement was attributed to a bulk effect in the Pt layer. This was further confirmed by the linear relationship between the spin Hall efficiency and resistivity, which indicates an increase in skew-scattering. These findings shed light on the origin of enhancement and are promising in shaping future utilization of mechanical strain for energy-efficient devices.

Spin-Flip Diffusion Length in 5d Transition Metal Elements: A First-Principles Benchmark

Little is known about the spin-flip diffusion length l_{sf}, one of the most important material parameters in the field of spintronics. We use a density-functional-theory based scattering approach to determine values of l_{sf} that result from electron-phonon scattering as a function of temperature for all 5d transition metal elements. l_{sf} does not decrease monotonically with the atomic number Z but is found to be inversely proportional to the density of states at the Fermi level. By using the same local current methodology to calculate the spin Hall angle Θ_{sH} that characterizes the efficiency of the spin Hall effect, we show that the products ρ(T)l_{sf}(T) and Θ_{sH}(T)l_{sf}(T) are constant.

Acoustic spin Hall effect in strong spin-orbit metals

We report on the observation of the acoustic spin Hall effect that facilitates lattice motion-induced spin current via spin-orbit interaction (SOI). Under excitation of surface acoustic wave (SAW), we find that a spin current flows orthogonal to the SAW propagation in nonmagnetic metals (NMs). The acoustic spin Hall effect manifests itself in a field-dependent acoustic voltage in NM/ferromagnetic metal bilayers. The acoustic voltage takes a maximum when the NM layer thickness is close to its spin diffusion length, vanishes for NM layers with weak SOI, and increases linearly with the SAW frequency. To account for these results, we find that the spin current must scale with the SOI and the time derivative of the lattice displacement. These results, which imply the strong coupling of electron spins with rotating lattices via the SOI, show the potential of lattice dynamics to supply spin current in strong spin-orbit metals.

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.

Detection of ferromagnetic resonance from 1 nm-thick Co

To explore the further possibilities of nanometer-thick ferromagnetic films (ultrathin ferromagnetic films), we investigated the ferromagnetic resonance (FMR) of 1 nm-thick Co film. Whilst an FMR signal was not observed for the Co film grown on a SiO₂ substrate, the insertion of a 3 nm-thick amorphous Ta buffer layer beneath the Co enabled the detection of a salient FMR signal, which was attributed to the smooth surface of the amorphous Ta. This result implies the excitation of FMR in an ultrathin ferromagnetic film, which can pave the way to controlling magnons in ultrathin ferromagnetic films.

Topological flat bands in frustrated kagome lattice CoSn

Electronic flat bands in momentum space, arising from strong localization of electrons in real space, are an ideal stage to realize strongly-correlated phenomena. Theoretically, the flat bands can naturally arise in certain geometrically frustrated lattices, often with nontrivial topology if combined with spin-orbit coupling. Here, we report the observation of topological flat bands in frustrated kagome metal CoSn, using angle-resolved photoemission spectroscopy and band structure calculations. Throughout the entire Brillouin zone, the bandwidth of the flat band is suppressed by an order of magnitude compared to the Dirac bands originating from the same orbitals. The frustration-driven nature of the flat band is directly confirmed by the chiral d-orbital texture of the corresponding real-space Wannier functions. Spin-orbit coupling opens a large gap of 80 meV at the quadratic touching point between the Dirac and flat bands, endowing a nonzero Z2 invariant to the flat band. These findings demonstrate that kagome-derived flat bands are a promising platform for novel emergent phases of matter at the confluence of strong correlation and topology.

The spin Hall effect of Bi-Sb alloys driven by thermally excited Dirac-like electrons

We have studied the charge to spin conversion in Bi_1-x Sb _x /CoFeB heterostructures. The spin Hall conductivity (SHC) of the sputter-deposited heterostructures exhibits a high plateau at Bi-rich compositions, corresponding to the topological insulator phase, followed by a decrease of SHC for Sb-richer alloys, in agreement with the calculated intrinsic spin Hall effect of Bi_1-x Sb _x . The SHC increases with increasing Bi_1-x Sb _x thickness before it saturates, indicating that it is the bulk of the alloy that predominantly contributes to the generation of spin current; the topological surface states, if present, play little role. Unexpectedly, the SHC is found to increase with increasing temperature, following the trend of carrier density. These results suggest that the large SHC at room temperature, with a spin Hall efficiency exceeding 1 and an extremely large spin current mobility, is due to increased number of thermally excited Dirac-like electrons in the L valley of the narrow gap Bi_1-x Sb _x alloy.

Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems

Motivated by the importance of understanding various competing mechanisms to the current-induced spin-orbit torque on magnetization in complex magnets, we develop a theory of current-induced spin-orbital coupled dynamics in magnetic heterostructures. The theory describes angular momentum transfer between different degrees of freedom in solids, e.g., the electron orbital and spin, the crystal lattice, and the magnetic order parameter. Based on the continuity equations for the spin and orbital angular momenta, we derive equations of motion that relate spin and orbital current fluxes and torques describing the transfer of angular momentum between different degrees of freedom, achieved in a steady state under an applied external electric field. We then propose a classification scheme for the mechanisms of the current-induced torque in magnetic bilayers. We evaluate the sources of torque using density functional theory, effectively capturing the impact of the electronic structure on these quantities. We apply our formalism to two different magnetic bilayers, Fe/W(110) and Ni/W(110), which are chosen such that the orbital and spin Hall effects in W have opposite sign and the resulting spin- and orbital-mediated torques can compete with each other. We find that while the spin torque arising from the spin Hall effect of W is the dominant mechanism of the current-induced torque in Fe/W(110), the dominant mechanism in Ni/W(110) is the orbital torque originating in the orbital Hall effect of the non-magnetic substrate. Thus the effective spin Hall angles for the total torque are negative and positive in the two systems. Our prediction can be experimentally identified in moderately clean samples, where intrinsic contributions dominate. This clearly demonstrates that our formalism is ideal for studying the angular momentum transfer dynamics in spin-orbit coupled systems as it goes beyond the "spin current picture" by naturally incorporating the spin and orbital degrees of freedom on an equal footing. Our calculations reveal that, in addition to the spin and orbital torque, other contributions such as the interfacial torque and self-induced anomalous torque within the ferromagnet are not negligible in both material systems.

Current-induced magnetization switching in all-oxide heterostructures

The electrical switching of magnetization through spin-orbit torque (SOT)¹ holds promise for application in information technologies, such as low-power, non-volatile magnetic memory. Materials with strong spin-orbit coupling, such as heavy metals^2-4 and topological insulators^5,6, can convert a charge current into a spin current. The spin current can then execute a transfer torque on the magnetization of a neighbouring magnetic layer, usually a ferromagnetic metal like CoFeB, and reverse its magnetization. Here, we combine a ferromagnetic transition metal oxide⁷ with an oxide with strong spin-orbit coupling⁸ to demonstrate all-oxide SOT devices. We show current-induced magnetization switching in SrIrO₃/SrRuO₃ bilayer structures. By controlling the magnetocrystalline anisotropy of SrRuO₃ on (001)- and (110)-oriented SrTiO₃ (STO) substrates, we designed two types of SOT switching schemes. For the bilayer on the STO(001) substrate, a magnetic-field-free switching was achieved, which remained undisturbed even when the external magnetic field reached 100 mT. The charge-to-spin conversion efficiency for the bilayer on the STO(110) substrate ranged from 0.58 to 0.86, depending on the directionality of the current flow with respect to the crystalline symmetry. All-oxide SOT structures may help to realize field-free switching through a magnetocrystalline anisotropy design.

Anisotropic spin-orbit torque generation in epitaxial SrIrO3 by symmetry design

Spin-orbit coupling (SOC), the interaction between the electron spin and the orbital angular momentum, can unlock rich phenomena at interfaces, in particular interconverting spin and charge currents. Conventional heavy metals have been extensively explored due to their strong SOC of conduction electrons. However, spin-orbit effects in classes of materials such as epitaxial 5d-electron transition-metal complex oxides, which also host strong SOC, remain largely unreported. In addition to strong SOC, these complex oxides can also provide the additional tuning knob of epitaxy to control the electronic structure and the engineering of spin-to-charge conversion by crystalline symmetry. Here, we demonstrate room-temperature generation of spin-orbit torque on a ferromagnet with extremely high efficiency via the spin-Hall effect in epitaxial metastable perovskite SrIrO₃ We first predict a large intrinsic spin-Hall conductivity in orthorhombic bulk SrIrO₃ arising from the Berry curvature in the electronic band structure. By manipulating the intricate interplay between SOC and crystalline symmetry, we control the spin-Hall torque ratio by engineering the tilt of the corner-sharing oxygen octahedra in perovskite SrIrO₃ through epitaxial strain. This allows the presence of an anisotropic spin-Hall effect due to a characteristic structural anisotropy in SrIrO₃ with orthorhombic symmetry. Our experimental findings demonstrate the heteroepitaxial symmetry design approach to engineer spin-orbit effects. We therefore anticipate that these epitaxial 5d transition-metal oxide thin films can be an ideal building block for low-power spintronics.

Variation of the giant intrinsic spin Hall conductivity of Pt with carrier lifetime

More than a decade after the first theoretical and experimental studies of the spin Hall conductivity (SHC) of Pt, both its dominant origin and amplitude remain in dispute. We report the experimental determination of the rapid variation of the intrinsic SHC of Pt with the carrier lifetime (τ) in the dirty-metal regime by incorporating finely dispersed MgO intersite impurities into the Pt, while maintaining its essential band structure. This conclusively validates the theoretical prediction that the SHC in Pt in the dirty-metal regime should be dominated by the intrinsic contribution, and should decrease rapidly with shortening τ. When interfacial spin backflow is taken into account, the intrinsic SHC of Pt in the clean limit is at least 1.6 × 10⁶ (ℏ/2e) ohm^-1 m^-1, more than 3.5 times greater than the available theoretical predictions. Our work also establishes a compelling spin Hall metal Pt_0.6(MgO)_0.4 with an internal giant spin Hall ratio of 0.73.

Exceptionally High, Strongly Temperature Dependent, Spin Hall Conductivity of SrRuO3

Spin-orbit torques (SOT) in thin film heterostructures originate from strong spin-orbit interactions (SOI) that, in the bulk, generate a spin current due either to extrinsic spin-dependent, skew, or/and side-jump scattering or to intrinsic Berry curvature in the conduction bands. While most SOT studies have focused on materials with heavy metal components, the oxide perovskite SrRuO₃ has been predicted to have a pronounced Berry curvature. Through quantification of its spin current by the SOT exerted on an adjacent Co ferromagnetic layer, we determine that SrRuO₃ has a strongly temperature ( T)-dependent spin Hall conductivity σ _SH, increasing with the electrical conductivity, consistent with expected behavior of the intrinsic effect in the "dirty metal" regime. σ _SH is very high at low T, e.g., σ _SH > (ℏ/2 e)3 × 10⁵ Ω^-1 m^-1 at 60 K, and is largely unaffected by the SrRuO₃ ferromagnetic transition at T _c ≈ 150 K, which agrees with a recent theoretical determination that the intrinsic spin Hall effect is magnetization independent. Below T _c smaller nonstandard SOT components also develop associated with the magnetism of the oxide. Our results are consistent with the degree of RuO₆ octahedral tilt being correlated with the strength of the SOI in this complex oxide, as predicted by recent theoretical work on strontium iridate. These results establish SrRuO₃ as a very promising candidate material for implementing strong spintronics functionalities in oxide electronics.

Giant intrinsic spin Hall effect in W3Ta and other A15 superconductors

The spin Hall effect (SHE) is the conversion of charge current to spin current, and nonmagnetic metals with large SHEs are extremely sought after for spintronic applications, but their rarity has stifled widespread use. Here, we predict and explain the large intrinsic SHE in β-W and the A15 family of superconductors: W3Ta, Ta3Sb, and Cr3Ir having spin Hall conductivities (SHCs) of -2250, -1400, and 1210ℏ e ( S / cm ) , respectively. Combining concepts from topological physics with the dependence of the SHE on the spin Berry curvature (SBC) of the electronic bands, we propose a simple strategy to rapidly search for materials with large intrinsic SHEs based on the following ideas: High symmetry combined with heavy atoms gives rise to multiple Dirac-like crossings in the electronic structure; without sufficient symmetry protection, these crossings gap due to spin-orbit coupling; and gapped crossings create large SBC.

Absence of strong skew scattering in crystals with multi-sheeted Fermi surfaces

We consider an extrinsic contribution to the anomalous and spin Hall effect in dilute alloys based on Fe, Co, Ni, and Pt hosts with different substitutional impurities. It is shown that a strong skew-scattering mechanism is absent in such crystals with multi-sheeted Fermi surfaces. Based on this finding, we conclude on the mutual exclusion of strong intrinsic and skew-scattering contributions to the considered transport phenomena. It also allows us to draw general conclusions in which materials with a giant anomalous Hall effect caused by the skew scattering can be achieved.

Dirac Nodal Line Metal for Topological Antiferromagnetic Spintronics

Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which exploits the Néel vector to control the topological electronic states and the associated spin-dependent transport properties. A recently discovered Néel spin-orbit torque has been proposed to electrically manipulate Dirac band crossings in antiferromagnets; however, a reliable AFM material to realize these properties in practice is missing. In this Letter, we predict that room-temperature AFM metal MnPd_{2} allows the electrical control of the Dirac nodal line by the Néel spin-orbit torque. Based on first-principles density functional theory calculations, we show that reorientation of the Néel vector leads to switching between the symmetry-protected degenerate state and the gapped state associated with the dispersive Dirac nodal line at the Fermi energy. The calculated spin Hall conductivity strongly depends on the Néel vector orientation and can be used to experimentally detect the predicted effect using a proposed spin-orbit torque device. Our results indicate that AFM Dirac nodal line metal MnPd_{2} represents a promising material for topological AFM spintronics.

Near-unity spin Hall ratio in Ni x Cu1-x alloys

We report a large spin Hall effect in the 3d transition metal alloy Ni _x Cu_1-x for x ∈ {0.3, 0.75}, detected via the ferromagnetic resonance of a permalloy (Py = Ni₈₀Fe₂₀) film deposited in a bilayer with the alloy. A thickness series at x = 0.6, for which the alloy is paramagnetic at room temperature, allows us to determine the spin Hall ratio θ _SH ≈ 1, spin diffusion length λ_s, spin mixing conductance G _⇅, and damping due to spin memory loss α_SML. We compare our results with similar experiments on Py/Pt bilayers measured using the same method. Ab initio band structure calculations with disorder and spin-orbit coupling suggest an intrinsic spin Hall effect in Ni _x Cu_1-x alloys, although the experiments here cannot distinguish between extrinsic and intrinsic mechanisms.

Magnetic Moments and Electron Transport through Chromium-Based Antiferromagnetic Nanojunctions

We report the electronic, magnetic and transport properties of a prototypical antiferromagnetic (AFM) spintronic device. We chose Cr as the active layer because it is the only room-temperature AFM elemental metal. We sandwiched Cr between two non-magnetic metals (Pt or Au) with large spin-orbit coupling. We also inserted a buffer layer of insulating MgO to mimic the structure and finite resistivity of a real device. We found that, while spin-orbit has a negligible effect on the current flowing through the device, the MgO layer plays a crucial role. Its effect is to decouple the Cr magnetic moment from Pt (or Au) and to develop an overall spin magnetization. We have also calculated the spin-polarized ballistic conductance of the device within the Büttiker⁻Landauer framework, and we have found that for small applied bias our Pt/Cr/MgO/Pt device presents a spin polarization of the current amounting to ≃25%.

Broadband Terahertz Generation via the Interface Inverse Rashba-Edelstein Effect

Novel mechanisms for electromagnetic wave emission in the terahertz frequency regime emerging at the nanometer scale have recently attracted intense attention for the purpose of searching next-generation broadband THz emitters. Here, we report broadband THz emission, utilizing the interface inverse Rashba-Edelstein effect. By engineering the symmetry of the Ag/Bi Rashba interface, we demonstrate a controllable THz radiation (∼0.1-5  THz) waveform emitted from metallic Fe/Ag/Bi heterostructures following photoexcitation. We further reveal that this type of THz radiation can be selectively superimposed on the emission discovered recently due to the inverse spin Hall effect, yielding a unique film thickness dependent emission pattern. Our results thus offer new opportunities for versatile broadband THz radiation using the interface quantum effects.

Intrinsic Spin and Orbital Hall Effects from Orbital Texture

We show theoretically that both the intrinsic spin Hall effect (SHE) and orbital Hall effect (OHE) can arise in centrosymmetric systems through momentum-space orbital texture, which is ubiquitous even in centrosymmetric systems unlike spin texture. The OHE occurs even without spin-orbit coupling (SOC) and is converted into the SHE through SOC. The resulting spin Hall conductivity is large (comparable to that of Pt) but depends on the SOC strength in a nonmonotonic way. This mechanism is stable against orbital quenching. This work suggests a path for an ongoing search for materials with stronger SHE. It also calls for experimental efforts to probe orbital degrees of freedom in the OHE and SHE. Possible ways for experimental detection are briefly discussed.

Tunable inverse spin Hall effect in nanometer-thick platinum films by ionic gating

Electric gating can strongly modulate a wide variety of physical properties in semiconductors and insulators, such as significant changes of conductivity in silicon, appearance of superconductivity in SrTiO₃, the paramagnet–ferromagnet transition in (In,Mn)As, and so on. The key to such modulation is charge accumulation in solids. Thus, it has been believed that such modulation is out of reach for conventional metals where the number of carriers is too large. However, success in tuning the Curie temperature of ultrathin cobalt gave hope of finally achieving such a degree of control even in metallic materials. Here, we show reversible modulation of up to two orders of magnitude of the inverse spin Hall effect—a phenomenon that governs interconversion between spin and charge currents—in ultrathin platinum. Spin-to-charge conversion enables the generation and use of electric and spin currents in the same device, which is crucial for the future of spintronics and electronics.

The ability to electrically control spintronic materials significantly widens their potential for integration into devices, but it is difficult to achieve in metals with high carrier densities. Here the authors demonstrate ionic liquid gated control of the inverse spin Hall effect in platinum.

Theory of Large Intrinsic Spin Hall Effect in Iridate Semimetals

We theoretically investigate the mechanism to generate large intrinsic spin Hall effect in iridates or more broadly in 5d transition metal oxides with strong spin-orbit coupling. We demonstrate such a possibility by taking the example of orthorhombic perovskite iridate with nonsymmorphic lattice symmetry, SrIrO₃, which is a three-dimensional semimetal with nodal line spectrum. It is shown that large intrinsic spin Hall effect arises in this system via the spin-Berry curvature originating from the nearly degenerate electronic spectra surrounding the nodal line. This effect exists even when the nodal line is gently gapped out, due to the persistent nearly degenerate electronic structure. The magnitude of the spin Hall conductivity is shown to be comparable to the best known example such as doped topological insulators and the biggest in any transition metal oxides. To gain further insight, we compute the intrinsic spin Hall conductivity in both bulk and thin film systems. We find that the geometric confinement in thin films leads to significant modifications of the electronic states, leading to even bigger spin Hall conductivity in certain cases. We compare our findings with the recent experimental report on the discovery of large spin Hall effect in SrIrO₃ thin films.

Complex Terahertz and Direct Current Inverse Spin Hall Effect in YIG/Cu1-xIrx Bilayers Across a Wide Concentration Range

We measure the inverse spin Hall effect of Cu_1-xIr_x thin films on yttrium iron garnet over a wide range of Ir concentrations (0.05 ⩽ x ⩽ 0.7). Spin currents are triggered through the spin Seebeck effect, either by a continuous (dc) temperature gradient or by ultrafast optical heating of the metal layer. The spin Hall current is detected by electrical contacts or measurement of the emitted terahertz radiation. With both approaches, we reveal the same Ir concentration dependence that follows a novel complex, nonmonotonous behavior as compared to previous studies. For small Ir concentrations a signal minimum is observed, whereas a pronounced maximum appears near the equiatomic composition. We identify this behavior as originating from the interplay of different spin Hall mechanisms as well as a concentration-dependent variation of the integrated spin current density in Cu_1-xIr_x. The coinciding results obtained for dc and ultrafast stimuli provide further support that the spin Seebeck effect extends to terahertz frequencies, thus enabling a transfer of established spintronic measurement schemes into the terahertz regime. Our findings also show that the studied material allows for efficient spin-to-charge conversion even on ultrafast time scales.

Evidence for Dyakonov-Perel-like Spin Relaxation in Pt

We utilize nanoscale spin valves with Pt spacer layers to characterize spin relaxation in Pt. Analysis of the spin lifetime indicates that Elliott-Yafet spin scattering is dominant at room temperature, but an unexpected intrinsic Dyakonov-Perel-like spin relaxation becomes dominant at cryogenic temperatures. We also observe suppression of spin relaxation in a Pt layer interfaced with a ferromagnet, likely caused by the competition between the effective exchange and spin-orbit fields.

Thermally driven anomalous Hall effect transitions in FeRh

Materials exhibiting controllable magnetic phase transitions are currently in demand for many spintronics applications. Here we investigate from first principles the electronic structure and intrinsic anomalous Hall, spin Hall and anomalous Nernst response properties of the FeRh metallic alloy which undergoes a thermally driven antiferromagnetic-to-ferromagnetic phase transition. We show that the energy band structures and underlying Berry curvatures have important signatures in the various Hall effects. Specifically, the suppression of the anomalous Hall and Nernst effects in the AFM state and a sign change in the spin Hall conductivity across the transition are found. It is suggested that the FeRh can be used a spin current detector capable of differentiating the spin Hall effect from other anomalous transverse effects. The implications of this material and its thermally driven phases as a spin current detection scheme are also discussed.

The spin Nernst effect in tungsten

The spin Hall effect allows the generation of spin current when charge current is passed along materials with large spin-orbit coupling. It has been recently predicted that heat current in a nonmagnetic metal can be converted into spin current via a process referred to as the spin Nernst effect. We report the observation of the spin Nernst effect in W. In W/CoFeB/MgO heterostructures, we find changes in the longitudinal and transverse voltages with magnetic field when temperature gradient is applied across the film. The field dependence of the voltage resembles that of the spin Hall magnetoresistance. A comparison of the temperature gradient-induced voltage and the spin Hall magnetoresistance allows direct estimation of the spin Nernst angle. We find the spin Nernst angle of W to be similar in magnitude but opposite in sign to its spin Hall angle. Under an open-circuit condition, this sign difference results in the spin current generation larger than otherwise. These results highlight the distinct characteristics of the spin Nernst and spin Hall effects, providing pathways to explore materials with unique band structures that may generate large spin current with high efficiency.

Magneto-Optical Detection of the Spin Hall Effect in Pt and W Thin Films

The conversion of charge currents into spin currents in nonmagnetic conductors is a hallmark manifestation of spin-orbit coupling that has important implications for spintronic devices. Here we report the measurement of the interfacial spin accumulation induced by the spin Hall effect in Pt and W thin films using magneto-optical Kerr microscopy. We show that the Kerr rotation has opposite sign in Pt and W and scales linearly with current density. By comparing the experimental results with ab initio calculations of the spin Hall and magneto-optical Kerr effects, we quantitatively determine the current-induced spin accumulation at the Pt interface as 5×10^{-12}  μ_{B} A^{-1} cm^{2} per atom. From thickness-dependent measurements, we determine the spin diffusion length in a single Pt film to be 11±3  nm, which is significantly larger compared to that of Pt adjacent to a magnetic layer.

Interface-Induced Phenomena in Magnetism

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Tuning Spin Hall Angles by Alloying

Within a combined experimental and theoretical study it is shown that the spin Hall angle of a substitutional alloy system can be continuously varied via its composition. For the alloy system Au_{x}Pt_{1-x} a substantial increase of the maximum spin Hall angle compared to the pure alloy partners could be achieved this way. The experimental findings for the longitudinal charge conductivity σ, the transverse spin Hall conductivity σ_{SH}, and the spin Hall angle α_{SH} could be confirmed by calculations based on Kubo's linear response formalism. Calculations of these response quantities for different temperatures show that the divergent behavior of σ and σ_{SH} is rapidly suppressed with increasing temperature. As a consequence, σ_{SH} is dominated at higher temperatures by its intrinsic contribution that has only a rather weak temperature dependence.

Strong Intrinsic Spin Hall Effect in the TaAs Family of Weyl Semimetals

Since their discovery, topological insulators are expected to be ideal spintronic materials owing to the spin currents carried by surface states with spin-momentum locking. However, the bulk doping problem remains an obstacle that hinders such an application. In this work, we predict that a newly discovered family of topological materials, the Weyl semimetals, exhibits a large intrinsic spin Hall effect that can be utilized to generate and detect spin currents. Our ab initio calculations reveal a large spin Hall conductivity in the TaAs family of Weyl materials. Considering the low charge conductivity of semimetals, Weyl semimetals are believed to present a larger spin Hall angle (the ratio of the spin Hall conductivity over the charge conductivity) than that of conventional spin Hall systems such as the 4d and 5d transition metals. The spin Hall effect originates intrinsically from the bulk band structure of Weyl semimetals, which exhibit a large Berry curvature and spin-orbit coupling, so the bulk carrier problem in the topological insulators is naturally avoided. Our work not only paves the way for employing Weyl semimetals in spintronics, but also proposes a new guideline for searching for the spin Hall effect in various topological materials.