Current-induced spin-orbit torques

Theory of spin and orbital Edelstein effects

In systems with broken spatial inversion symmetry, such as surfaces, interfaces, or bulk systems lacking an inversion center, the application of a charge current can generate finite spin and orbital densities associated with a nonequilibrium magnetization, which is known as spin and orbital Edelstein effect (SEE and OEE), respectively. Early reports on this current-induced magnetization focus on two-dimensional Rashba systems, in which an in-plane nonequilibrium spin density is generated perpendicular to the applied charge current. However, until today, a large variety of materials have been theoretically predicted and experimentally demonstrated to exhibit a sizeable Edelstein effect, which comprises contributions from the spin as well as the orbital degrees of freedom, and whose associated magnetization may be out of plane, nonorthogonal, and even parallel to the applied charge current, depending on the system's particular symmetries. In this review, we give an overview on the most commonly used theoretical approaches for the discussion and prediction of the SEE and OEE. Further, we introduce a selection of the most intensely discussed materials exhibiting a finite Edelstein effect, and give a brief summary of common experimental techniques.

Two-dimensional chiral perovskites with large spin Hall angle and collinear spin Hall conductivity

Two-dimensional hybrid organic-inorganic perovskites with chiral spin texture are emergent spin-optoelectronic materials. Despite the wealth of chiro-optical studies on these materials, their charge-to-spin conversion efficiency is unknown. We demonstrate highly efficient electrically driven charge-to-spin conversion in enantiopure chiral perovskites (R/S-MB)2(MA)3Pb4I13 (〈n〉 = 4), where MB is 2-methylbutylamine, MA is methylamine, Pb is lead, and I is iodine. Using scanning photovoltage microscopy, we measured a spin Hall angle θsh of 5% and a spin lifetime of ~75 picoseconds at room temperature in 〈n〉 = 4 chiral perovskites, which is much larger than its racemic counterpart as well as the lower 〈n〉 homologs. In addition to current-induced transverse spin current, the presence of a coexisting out-of-plane spin current confirms that both conventional and collinear spin Hall conductivities exist in these low-dimensional crystals.

Femtosecond Laser-Induced Transient Magnetization Enhancement and Ultrafast Demagnetization Mediated by Domain Wall Origami

Femtosecond laser-induced ultrafast magnetization dynamics are all-optically probed for different remanent magnetic domain states of a [Co/Pt]22 multilayer sample, thus revealing the tunability of the direct transport of spin angular momentum across domain walls. A variety of different magnetic domain configurations (domain wall origami) at remanence achieved by applying different magnetic field histories are investigated by time-resolved magneto-optical Kerr effect magnetometry to probe the ultrafast magnetization dynamics. Depending on the underlying domain landscape, the spin-transport-driven magnetization dynamics show a transition from typical ultrafast demagnetization to being fully dominated by an anomalous transient magnetization enhancement (TME) via a state in which both TME and demagnetization coexist in the system. Thereby, the study reveals an extrinsic channel for the modulation of spin transport, which introduces a route for the development of magnetic spin-texture-driven ultrafast spintronic devices.

Reconfigurable spintronic logic gate utilizing precessional magnetization switching

In traditional von Neumann computing architecture, the efficiency of the system is often hindered by the data transmission bottleneck between the processor and memory. A prevalent approach to mitigate this limitation is the use of non-volatile memory for in-memory computing, with spin-orbit torque (SOT) magnetic random-access memory (MRAM) being a leading area of research. In this study, we numerically demonstrate that a precise combination of damping-like and field-like spin-orbit torques can facilitate precessional magnetization switching. This mechanism enables the binary memristivity of magnetic tunnel junctions (MTJs) through the modulation of the amplitude and width of input current pulses. Building on this foundation, we have developed a scheme for a reconfigurable spintronic logic gate capable of directly implementing Boolean functions such as AND, OR, and XOR. This work is anticipated to leverage the sub-nanosecond dynamics of SOT-MRAM cells, potentially catalyzing further experimental developments in spintronic devices for in-memory computing.

Electrical switching of Ising-superconducting nonreciprocity for quantum neuronal transistor

Nonreciprocal quantum transport effect is mainly governed by the symmetry breaking of the material systems and is gaining extensive attention in condensed matter physics. Realizing electrical switching of the polarity of the nonreciprocal transport without external magnetic field is essential to the development of nonreciprocal quantum devices. However, electrical switching of superconducting nonreciprocity remains yet to be achieved. Here, we report the observation of field-free electrical switching of nonreciprocal Ising superconductivity in Fe3GeTe2/NbSe2 van der Waals (vdW) heterostructure. By taking advantage of this electrically switchable superconducting nonreciprocity, we demonstrate a proof-of-concept nonreciprocal quantum neuronal transistor, which allows for implementing the XOR logic gate and faithfully emulating biological functionality of a cortical neuron in the brain. Our work provides a promising pathway to realize field-free and electrically switchable nonreciprocity of quantum transport and demonstrate its potential in exploring neuromorphic quantum devices with both functionality and performance beyond the traditional devices.

Spin-Orbit Torque in Single-Molecule Junctions from ab Initio

The use of electric fields applied across magnetic heterojunctions that lack spatial inversion symmetry has been previously proposed as a nonmagnetic means of controlling localized magnetic moments through spin-orbit torques (SOT). The implementation of this concept at the single-molecule level has remained a challenge, however. Here, we present first-principles calculations of SOT in a single-molecule junction under bias and beyond linear response. Employing a self-consistency scheme invoking density functional theory and nonequilibrium Green's function theory including spin-orbit interaction, we compute the change of the magnetization with the bias voltage and the associated current-induced SOT. Within the linear regime our quantitative estimates for the SOT in single-molecule junctions yield values similar to those known for magnetic interfaces. Our findings contribute to an improved microscopic understanding of SOT in single molecules.

Ultra-Low Current 10 nm Spin Hall Nano-Oscillators

Nano-constriction based spin Hall nano-oscillators (SHNOs) are at the forefront of spintronics research for emerging technological applications, such as oscillator-based neuromorphic computing and Ising Machines. However, their miniaturization to the sub-50 nm width regime results in poor scaling of the threshold current. Here, it shows that current shunting through the Si substrate is the origin of this problem and studies how different seed layers can mitigate it. It finds that an ultra-thin Al2 O3 seed layer and SiN (200 nm) coated p-Si substrates provide the best improvement, enabling us to scale down the SHNO width to a truly nanoscopic dimension of 10 nm, operating at threshold currents below 30 μ $\umu$ A. In addition, the combination of electrical insulation and high thermal conductivity of the Al2 O3 seed will offer the best conditions for large SHNO arrays, avoiding any significant temperature gradients within the array. The state-of-the-art ultra-low operational current SHNOs hence pave an energy-efficient route to scale oscillator-based computing to large dynamical neural networks of linear chains or 2D arrays.

Phase biasing of a Josephson junction using Rashba-Edelstein effect

A charge-current-induced shift in the spin-locked Fermi surface leads to a non-equilibrium spin density at a Rashba interface, commonly known as the Rashba-Edelstein effect. Since this is an intrinsically interfacial property, direct detection of the spin moment is difficult. Here we demonstrate that a planar Josephson Junction, realized by placing two closely spaced superconducting electrodes over a Rashba interface, allows for a direct detection of the spin moment as an additional phase in the junction. Asymmetric Fraunhofer patterns obtained for Nb-(Pt/Cu)-Nb nano-junctions, due to the locking of Rashba-Edelstein spin moment to the flux quantum in the junction, provide clear signatures of this effect. This simple experiment offers a fresh perspective on direct detection of spin polarization induced by various spin-orbit effects. In addition, this platform also offers a magnetic-field-controlled phase biasing mechanism in conjunction with the Rashba-Edelstein spin-orbit effect for superconducting quantum circuits.

Automated mechanical exfoliation technique: a spin pumping study in YIG/TMD heterostructures

Spintronics devices rely on the generation and manipulation of spin currents. Two-dimensional transition-metal dichalcogenides (TMDs) are among the most promising materials for a spin current generation due to a lack of inversion symmetry at the interface with the magnetic material. Here, we report on the fabrication of Yttrium Iron Garnet(YIG)/TMD heterostructures by means of a crude and fast method. While the magnetic insulator single-crystalline YIG thin films were grown by magnetron sputtering, the TMDs, namely MoS2 and MoSe2, were directly deposited onto YIG films using an automated mechanical abrasion method. Despite the brute force aspect of the method, it produces high-quality interfaces, which are suitable for spintronic device applications. The spin current density and the effective spin mixing conductance were measured by ferromagnetic resonance, whose values found are among the highest reported in the literature. Our method can be scaled to produce ferromagnetic materials/TMD heterostructures on a large scale, further advancing their potential for practical applications.

Local symmetry breaking drives picosecond spin domain formation in polycrystalline halide perovskite films

Photoinduced spin-charge interconversion in semiconductors with spin-orbit coupling could provide a route to optically addressable spintronics without the use of external magnetic fields. However, in structurally disordered polycrystalline semiconductors, which are being widely explored for device applications, the presence and role of spin-associated charge currents remains unclear. Here, using femtosecond circular-polarization-resolved pump-probe microscopy on polycrystalline halide perovskite thin films, we observe the photoinduced ultrafast formation of spin domains on the micrometre scale formed through lateral spin currents. Micrometre-scale variations in the intensity of optical second-harmonic generation and vertical piezoresponse suggest that the spin-domain formation is driven by the presence of strong local inversion symmetry breaking via structural disorder. We propose that this leads to spatially varying Rashba-like spin textures that drive spin-momentum-locked currents, leading to local spin accumulation. Ultrafast spin-domain formation in polycrystalline halide perovskite films provides an optically addressable platform for nanoscale spin-device physics.

Regulating Oxygen Ion Transport at the Nanoscale to Enable Highly Cyclable Magneto-Ionic Control of Magnetism

Magneto-ionics refers to the control of magnetic properties of materials through voltage-driven ion motion. To generate effective electric fields, either solid or liquid electrolytes are utilized, which also serve as ion reservoirs. Thin solid electrolytes have difficulties in (i) withstanding high electric fields without electric pinholes and (ii) maintaining stable ion transport during long-term actuation. In turn, the use of liquid electrolytes can result in poor cyclability, thus limiting their applicability. Here we propose a nanoscale-engineered magneto-ionic architecture (comprising a thin solid electrolyte in contact with a liquid electrolyte) that drastically enhances cyclability while preserving sufficiently high electric fields to trigger ion motion. Specifically, we show that the insertion of a highly nanostructured (amorphous-like) Ta layer (with suitable thickness and electric resistivity) between a magneto-ionic target material (i.e., Co₃O₄) and the liquid electrolyte increases magneto-ionic cyclability from <30 cycles (when no Ta is inserted) to more than 800 cycles. Transmission electron microscopy together with variable energy positron annihilation spectroscopy reveals the crucial role of the generated TaO_x interlayer as a solid electrolyte (i.e., ionic conductor) that improves magneto-ionic endurance by proper tuning of the types of voltage-driven structural defects. The Ta layer is very effective in trapping oxygen and hindering O^2- ions from moving into the liquid electrolyte, thus keeping O^2- motion mainly restricted between Co₃O₄ and Ta when voltage of alternating polarity is applied. We demonstrate that this approach provides a suitable strategy to boost magneto-ionics by combining the benefits of solid and liquid electrolytes in a synergetic manner.

Tunable Valley and Spin Splittings in VSi2N4 Bilayers

The control and manipulation of the valley and spin degrees of freedom have received great interest in fundamental studies and advanced information technologies. Compared with magnetic means, it is highly desirable to realize more energy-efficient electric control of valley and spin. Using the first-principles calculations, we demonstrate tunable valley and spin degeneracy splittings in VSi₂N₄ bilayers, with the aid of the layered structure and associated electric control. Depending on different interlayer magnetic couplings and stacking orders, the VSi₂N₄ bilayers exhibit a variety of combinations of valley and spin degeneracies. Under the action of a vertical electric field, the degeneracy splittings become highly tunable for both the sign and the magnitude. As a result, a series of anomalous Hall currents can be selectively realized with varied indices of valley and spin. These intriguing features offer a practical way for designing energy-efficient devices based on the couplings between multiple electronic degrees of freedom.

Ultrashort spin-orbit torque generated by femtosecond laser pulses

To realize the very objective of spintronics, namely the development of ultra-high frequency and energy-efficient electronic devices, an ultrafast and scalable approach to switch magnetic bits is required. Magnetization switching with spin currents generated by the spin-orbit interaction at ferromagnetic/non-magnetic interfaces is one of such scalable approaches, where the ultimate switching speed is limited by the Larmor precession frequency. Understanding the magnetization precession dynamics induced by spin-orbit torques (SOTs) is therefore of great importance. Here we demonstrate generation of ultrashort SOT pulses that excite Larmor precession at an epitaxial Fe/GaAs interface by converting femtosecond laser pulses into high-amplitude current pulses in an electrically biased p-i-n photodiode. We control the polarity, amplitude, and duration of the current pulses and, most importantly, also their propagation direction with respect to the crystal orientation. The SOT origin of the excited Larmor precession was revealed by a detailed analysis of the precession phase and amplitude at different experimental conditions.

Giant spin-to-charge conversion at an all-epitaxial single-crystal-oxide Rashba interface with a strongly correlated metal interlayer

The two-dimensional electron gas (2DEG) formed at interfaces between SrTiO₃ (STO) and other oxide insulating layers is promising for use in efficient spin-charge conversion due to the large Rashba spin-orbit interaction (RSOI). However, these insulating layers on STO prevent the propagation of a spin current injected from an adjacent ferromagnetic layer. Moreover, the mechanism of the spin-current flow in these insulating layers is still unexplored. Here, using a strongly correlated polar-metal LaTiO_3+δ (LTO) interlayer and the 2DEG formed at the LTO/STO interface in an all-epitaxial heterostructure, we demonstrate giant spin-to-charge current conversion efficiencies, up to ~190 nm, using spin-pumping ferromagnetic-resonance voltage measurements. This value is the highest among those reported for all materials, including spin Hall systems. Our results suggest that the strong on-site Coulomb repulsion in LTO and the giant RSOI of LTO/STO may be the key to efficient spin-charge conversion with suppressed spin-flip scattering. Our findings highlight the hidden inherent possibilities of oxide interfaces for spin-orbitronics applications.

The interface between perovskite-oxide SrTiO₃ and other oxides realizes efficient spin-to-charge current conversion; however, the typically insulating oxides hinder the propagation of spin-currents. Here the authors achieve a record efficiency by replacing an oxide insulator with a strongly-correlated polar metal.

Large Spin-To-Charge Conversion at the Two-Dimensional Interface of Transition-Metal Dichalcogenides and Permalloy

Spin-to-charge conversion is an essential requirement for the implementation of spintronic devices. Recently, monolayers (MLs) of semiconducting transition-metal dichalcogenides (TMDs) have attracted considerable interest for spin-to-charge conversion due to their high spin-orbit coupling and lack of inversion symmetry in their crystal structure. However, reports of direct measurement of spin-to-charge conversion at TMD-based interfaces are very much limited. Here, we report on the room-temperature observation of a large spin-to-charge conversion arising from the interface of Ni₈₀Fe₂₀ (Py) and four distinct large-area (∼5 × 2 mm²) ML TMDs, namely, MoS₂, MoSe₂, WS₂, and WSe₂. We show that both spin mixing conductance and the Rashba efficiency parameter (λ_IREE) scale with the spin-orbit coupling strength of the ML TMD layers. The λ_IREE parameter is found to range between -0.54 and -0.76 nm for the four ML TMDs, demonstrating a large spin-to-charge conversion. Our findings reveal that the TMD/ferromagnet interface can be used for efficient generation and detection of spin current, opening new opportunities for novel spintronic devices.

Magnetoelectric effects in Josephson junctions

The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.

Unconventional Robust Spin-Transfer Torque in Noncollinear Antiferromagnetic Junctions

Ferromagnetic spin valves and tunneling junctions are crucial for spintronics applications and are one of the most fundamental spintronics devices. Motivated by the potential unique advantages of antiferromagnets for spintronics, we theoretically study here junctions built out of noncollinear antiferromagnets. We demonstrate a large and robust magnetoresistance and spin-transfer torque capable of ultrafast switching between parallel and antiparallel states of the junction. In addition, we show that a new type of self-generated torque appears in the noncollinear junctions.

Fabrication of voltage-gated spin Hall nano-oscillators

We demonstrate an optimized fabrication process for electric field (voltage gate) controlled nano-constriction spin Hall nano-oscillators (SHNOs), achieving feature sizes of <30 nm with easy to handle ma-N 2401 e-beam lithography negative tone resist. For the nanoscopic voltage gates, we utilize a two-step tilted ion beam etching approach and through-hole encapsulation using 30 nm HfO_x. The optimized tilted etching process reduces sidewalls by 75% compared to no tilting. Moreover, the HfO_x encapsulation avoids any sidewall shunting and improves gate breakdown. Our experimental results on W/CoFeB/MgO/SiO₂ SHNOs show significant frequency tunability (6 MHz V^-1) even for moderate perpendicular magnetic anisotropy. Circular patterns with diameter of 45 nm are achieved with an aspect ratio better than 0.85 for 80% of the population. The optimized fabrication process allows incorporating a large number of individual gates to interface to SHNO arrays for unconventional computing and densely packed spintronic neural networks.

Novel Spin-Orbit Torque Generation at Room Temperature in an All-Oxide Epitaxial La0.7 Sr0.3 MnO3 /SrIrO3 System

Spin-orbit torques (SOTs) that arise from materials with large spin-orbit coupling offer a new pathway for energy-efficient and fast magnetic information storage. SOTs in conventional heavy metals and topological insulators are explored extensively, while 5d transition metal oxides, which also host ions with strong spin-orbit coupling, are a relatively new territory in the field of spintronics. An all-oxide, SrTiO₃ (STO)//La_0.7 Sr_0.3 MnO₃ (LSMO)/SrIrO₃ (SIO) heterostructure with lattice-matched crystal structure is synthesized, exhibiting an epitaxial and atomically sharp interface between the ferromagnetic LSMO and the high spin-orbit-coupled metal SIO. Spin-torque ferromagnetic resonance (ST-FMR) is used to probe the effective magnetization and the SOT efficiency in LSMO/SIO heterostructures grown on STO substrates. Remarkably, epitaxial LSMO/SIO exhibits a large SOT efficiency, ξ_||  = 1, while retaining a reasonably low shunting factor and increasing the effective magnetization of LSMO by ≈50%. The findings highlight the significance of epitaxy as a powerful tool to achieve a high SOT efficiency, explore the rich physics at the epitaxial interface, and open up a new pathway for designing next-generation energy-efficient spintronic devices.

Prototype Design of a Domain-Wall-Based Magnetic Memory Using a Single Layer La0.67Sr0.33MnO3 Thin Film

Magnetic field-free, nonvolatile magnetic memory with low power consumption is highly desired in information technology. In this work, we report a current-controllable alignment of magnetic domain walls in a single layer La_0.67Sr_0.33MnO₃ thin film with the threshold current density of 2 × 10⁵ A/cm² at room temperature. The vector relationship between current directions and domain-wall orientations indicates the dominant role of spin-orbit torque without an assistance of external magnetic field. Meanwhile, significant planar Hall resistances can be readout in a nonvolatile way before and after the domain-wall reorientation. A domain-wall-based magnetic random-access memory (DW-MRAM) prototype device has been proposed.

Electronic spin separation induced by nuclear motion near conical intersections

Though the concept of Berry force was proposed thirty years ago, little is known about the practical consequences of this force as far as chemical dynamics are concerned. Here, we report that when molecular dynamics pass near a conical intersection, a massive Berry force can appear as a result of even a small amount of spin-orbit coupling (<10⁻³ eV), and this Berry force can in turn dramatically change pathway selection. In particular, for a simple radical reaction with two outgoing reaction channels, an exact quantum scattering solution in two dimensions shows that the presence of a significant Berry force can sometimes lead to spin selectivity as large as 100%. Thus, this article opens the door for organic chemists to start designing spintronic devices that use nuclear motion and conical intersections (combined with standard spin-orbit coupling) in order to achieve spin selection. Vice versa, for physical chemists, this article also emphasizes that future semiclassical simulations of intersystem crossing (which have heretofore ignored Berry force) should be corrected to account for the spin polarization that inevitably arises when dynamics pass near conical intersections.

Spin polarization is at the basis of quantum information and underlies some natural processes, but many aspects still need to be explored. Here, the authors, by quantum mechanical computations, show that even a weak spin-orbit coupling near a conical intersection can induce large spin selection, with consequences for spin manipulation in photochemical or electrochemical reactions.

Helium Ion Microscopy for Reduced Spin Orbit Torque Switching Currents

Spin orbit torque driven switching is a favorable way to manipulate nanoscale magnetic objects for both memory and wireless communication devices. The critical current required to switch from one magnetic state to another depends on the geometry and the intrinsic properties of the materials used, which are difficult to control locally. Here, we demonstrate how focused helium ion beam irradiation can modulate the local magnetic anisotropy of a Co thin film at the microscopic scale. Real-time in situ characterization using the anomalous Hall effect showed up to an order of magnitude reduction of the magnetic anisotropy under irradiation, with multilevel switching demonstrated. The result is that spin-switching current densities, down to 800 kA cm^-2, can be achieved on predetermined areas of the film, without the need for lithography. The ability to vary critical currents spatially has implications not only for storage elements but also neuromorphic and probabilistic computing.

Controlling spin current polarization through non-collinear antiferromagnetism

The interconversion of charge and spin currents via spin-Hall effect is essential for spintronics. Energy-efficient and deterministic switching of magnetization can be achieved when spin polarizations of these spin currents are collinear with the magnetization. However, symmetry conditions generally restrict spin polarizations to be orthogonal to both the charge and spin flows. Spin polarizations can deviate from such direction in nonmagnetic materials only when the crystalline symmetry is reduced. Here, we show control of the spin polarization direction by using a non-collinear antiferromagnet Mn₃GaN, in which the triangular spin structure creates a low magnetic symmetry while maintaining a high crystalline symmetry. We demonstrate that epitaxial Mn₃GaN/permalloy heterostructures can generate unconventional spin-orbit torques at room temperature corresponding to out-of-plane and Dresselhaus-like spin polarizations which are forbidden in any sample with two-fold rotational symmetry. Our results demonstrate an approach based on spin-structure design for controlling spin-orbit torque, enabling high-efficient antiferromagnetic spintronics.

In the typical spin-hall effect, spin-current, charge current, and spin polarisation are all mutually perpendicular, a feature enforced by symmetry. Here, using an anti-ferromagnet with a triangular spin structure, the authors demonstrate a spin-hall effect without a perpendicular spin alignment.

Chemical Reaction Rates for Systems with Spin-Orbit Coupling and an Odd Number of Electrons: Does Berry's Phase Lead to Meaningful Spin-Dependent Nuclear Dynamics for a Two State Crossing?

Within the context of a simple avoided crossing, we investigate the effect of a complex-valued diabatic coupling in determining spin-dependent rate constants and scattering states. We find that, if the molecular geometry is not linear and the Berry force is not zero, one can find significant spin polarization of the products. This study emphasizes that, when analyzing nonadiabatic reactions with spin orbit coupling (and a complex-valued Hamiltonian), one must consider how Berry force affects nuclear motion-at least in the context of gas phase reactions. Work is currently ongoing as far as extrapolating these conclusions to the condensed phase, where interesting spin selection has been observed in recent years.

Out-of-plane carrier spin in transition-metal dichalcogenides under electric current

Absence of spatial inversion symmetry allows a nonequilibrium spin polarization to be induced by electric currents, which, in two-dimensional systems, is conventionally analyzed using the Rashba model, leading to in-plane spin polarization. Given that the material realizations of out-of-plane current-induced spin polarization (CISP) are relatively fewer than that of in-plane CISP, but important for perpendicular-magnetization switching and electronic structure evolution, it is highly desirable to search for new prototypical materials and mechanisms to generate the out-of-plane carrier spin and promote the study of CISP. Here, we propose that an out-of-plane CISP can emerge in ferromagnetic transition-metal dichalcogenide monolayers. Taking monolayer [Formula: see text] and [Formula: see text] as examples, we calculate the out-of-plane CISP based on linear-response theory and first-principles methods. We deduce a general low-energy model for easy-plane ferromagnetic transition-metal dichalcogenide monolayers and find that the out-of-plane CISP is due to an in-plane magnetization together with intrinsic spin-orbit coupling inducing an anisotropic out-of-plane spin splitting in the momentum space. The CISP paves the way for magnetization rotation and electric control of the valley quantum number.

Impact of Spin-Orbit Torque on Spin-Transfer Torque Switching in Magnetic Tunnel Junctions

The paper presents our simulated results showing the substantial improvement of both switching speed and energy consumption in a perpendicular magnetic tunnel junction (p-MTJ), a core unit of Spin-Transfer-Torque Magnetic Random Access Memory (STT-MRAM), by the help of additional Spin-Orbit-Torque (SOT) write pulse current (WPSOT). An STT-SOT hybrid torque module for OOMMF simulation is implemented to investigate the switching behavior of a 20 nm cell in the p-MTJ. We found that the assistance of WPSOT to STT write pulse current (WPSTT) have a huge influence on the switching behavior of the free layer in the p-MTJ. For example, we could dramatically reduce the switching time (tSW) by 80% and thereby reduce the write energy over 70% as compared to those in the absence of the WPSOT. Even a very tiny amplitude of WPSOT (JSOT of the order of 102 A/m2) substantially assists to reduce the critical current density for switching of the free layer and thereby decreases the energy consumption as well. It is worth to be pointed out that the energy can be saved further by tuning the WPSOT parameters, i.e., amplitude and duration along at the threshold WPSTT. Our findings show that the proposed STT-SOT hybrid switching scheme has a great impact on the MRAM technology seeking the high speed and low energy consumption.

Edelstein and inverse Edelstein effects caused by the pristine surface states of topological insulators

The Edelstein effect caused by the pristine surface states of three-dimensional topological insulators is investigated by means of a semiclassical approach. The combined effect of random impurity scattering and the spin-momentum locking of the gapless Dirac cone yields a current-induced surface spin accumulation that depends on the surface cleanliness, but is independent from chemical potential and temperature. Through combing the semiclassical approach with the Bloch equation, the inverse Edelstein effect that converts the spin pumping spin current into a charge current is well explained, and the conversion efficiency [Formula: see text] is revealed to be independent from the disorder. Consistency of these results with various experiments is elaborated in detail.

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.

Resistive State of Superconductor-Ferromagnet-Superconductor Josephson Junctions in the Presence of Moving Domain Walls

We describe resistive states of the system combining two types of orderings-a superconducting and a ferromagnetic one. It is shown that in the presence of magnetization dynamics such systems become inherently dissipative and in principle cannot sustain any amount of the superconducting current because of the voltage generated by the magnetization dynamics. We calculate generic current-voltage characteristics of a superconductor-ferromagnet-superconductor Josephson junction with an unpinned domain wall and find the low-current resistance associated with the domain wall motion. We suggest the finite slope of Shapiro steps as the characteristic feature of the regime with domain wall oscillations driven by the ac external current flowing through the junction.

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.

Reconfigurable nanoscale spin-wave directional coupler using spin-orbit torque

We present a reconfigurable nanoscale spin-wave directional coupler based on spin-orbit torque (SOT). By micromagnetic simulations, it is demonstrated that the functionality and operating frequency of proposed device can be dynamically switched by inverting the whole or part of the relative magnetic configuration of the dipolar-coupled waveguides using SOT. Utilizing the effect of sudden change in coupling length, the functionality of power divider can be realized. The proposed reconfigurable spin-wave directional coupler opens a way for two-dimensional planar magnonic integrated circuits.

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.

Dynamic Imaging of the Delay- and Tilt-Free Motion of Néel Domain Walls in Perpendicularly Magnetized Superlattices

We report on the time-resolved investigation of current- and field-induced domain wall motion in the flow regime in perpendicularly magnetized microwires exhibiting antisymmetric exchange interaction by means of scanning transmission X-ray microscopy with a 200 ps time step. The sub-ns time step of the dynamical images allowed us to observe the absence of incubation times for the motion of the domain wall within an uncertainty of 200 ps, together with indications for a negligible inertia of the domain wall. Furthermore, we observed that, for short current and magnetic field pulses, the magnetic domain walls do not exhibit a tilting during their motion, providing a mechanism for the fast, tilt-free, current-induced motion of magnetic domain walls.

All-optical generation and ultrafast tuning of non-linear spin Hall current

Spin Hall effect, one of the cornerstones in spintronics refers to the emergence of an imbalance in the spin density transverse to a charge flow in a sample under voltage bias. This study points to a novel way for an ultrafast generation and tuning of a unidirectional nonlinear spin Hall current by means of subpicosecond laser pulses of optical vortices. When interacting with matter, the optical orbital angular momentum (OAM) carried by the vortex and quantified by its topological charge is transferred to the charge carriers. The residual spin-orbital coupling in the sample together with confinement effects allow exploiting the absorbed optical OAM for spatio-temporally controlling the spin channels. Both the non-linear spin Hall current and the dynamical spin Hall angle increase for a higher optical topological charge. The reason is the transfer of a higher amount of OAM and the enhancement of the effective spin-orbit interaction strength. No bias voltage is needed. We demonstrate that the spin Hall current can be all-optically generated in an open circuit geometry for ring-structured samples. These results follow from a full-fledged propagation of the spin-dependent quantum dynamics on a time-space grid coupled to the phononic environment. The findings point to a versatile and controllable tool for the ultrafast generation of spin accumulations with a variety of applications such as a source for ultrafast spin transfer torque and charge and spin current pulse emitter.

Development of a scanning electron microscopy with polarization analysis system for magnetic imaging with ns time resolution and phase-sensitive detection

Scanning electron microscopy with polarization analysis is a powerful lab-based magnetic imaging technique offering simultaneous imaging of multiple magnetization components and a very high spatial resolution. However, one drawback of the technique is the long required acquisition time resulting from the low inherent efficiency of spin detection, which has limited the applicability of the technique to certain quasi-static measurement schemes and materials with high magnetic contrast. Here we demonstrate the ability to improve the signal-to-noise ratio for particular classes of measurements involving periodic excitation of the magnetic structure via the implementation of a digital phase-sensitive detection scheme facilitated by the integration of a time-to-digital converter to the system. The modified setup provides dynamic imaging capabilities using selected time windows and finally full time-resolved imaging with a demonstrated time resolution of better than 2 ns.

Persistent spin texture enforced by symmetry

Persistent spin texture (PST) is the property of some materials to maintain a uniform spin configuration in the momentum space. This property has been predicted to support an extraordinarily long spin lifetime of carriers promising for spintronics applications. Here, we predict that there exists a class of noncentrosymmetric bulk materials, where the PST is enforced by the nonsymmorphic space group symmetry of the crystal. Around certain high symmetry points in the Brillouin zone, the sublattice degrees of freedom impose a constraint on the effective spin-orbit field, which orientation remains independent of the momentum and thus maintains the PST. We illustrate this behavior using density-functional theory calculations for a handful of promising candidates accessible experimentally. Among them is the ferroelectric oxide BiInO3-a wide band gap semiconductor which sustains a PST around the conduction band minimum. Our results broaden the range of materials that can be employed in spintronics.

Theory of in-plane current induced spin torque in metal/ferromagnet bilayers

Using a semiclassical approach that simultaneously incorporates the spin Hall effect (SHE), spin diffusion, quantum well states, and interface spin-orbit coupling (SOC), we address the interplay of these mechanisms as the origin of the spin-orbit torque (SOT) induced by in-plane currents, as observed in the normal metal/ferromagnetic metal bilayer thin films. Focusing on the bilayers with a ferromagnet much thinner than its spin diffusion length, such as Pt/Co with  ∼10 nm thickness, our approach addresses simultaneously the two contributions to the SOT, namely the spin-transfer torque (SHE-STT) due to SHE-induced spin injection, and the inverse spin Galvanic effect spin-orbit torque (ISGE-SOT) due to SOC-induced spin accumulation. The SOC produces an effective magnetic field at the interface, hence it modifies the angular momentum conservation expected for the SHE-STT. The SHE-induced spin voltage and the interface spin current are mutually dependent and, hence, are solved in a self-consistent manner. The result suggests that the SHE-STT and ISGE-SOT are of the same order of magnitude, and the spin transport mediated by the quantum well states may be an important mechanism for the experimentally observed rapid variation of the SOT with respect to the thickness of the ferromagnet.

Ferromagnetic domain walls as spin wave filters and the interplay between domain walls and spin waves

Spin waves (SW) are low energy excitations of magnetization in magnetic materials. In the promising field of magnonics, fundamental SW modes, magnons, are accessible in magnetic nanostructure waveguides and carry information. The SW propagates in both metals and insulators via magnetization dynamics. Energy dissipation through damping can be low compared to the Joule heating in conventional circuits. We performed simulations in a quasi-one-dimensional ferromagnetic strip and found that the transmission of the propagating SW across the domain wall (DW) depends strongly on the tilt angle of the magnetization at low frequencies. When the SW amplitude is large, the magnetization tilt angle inside the DW changes due to the effective fields. The SW transmission, the DW motion, and the magnetization tilt angle couple to each other, which results in complex DW motion and SW transmission. Both SW filtering and DW motions are key ingredients in magnonics.

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system

We present a novel class of nonlinear dynamical systems-a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

Writing and reading antiferromagnetic Mn2Au by Néel spin-orbit torques and large anisotropic magnetoresistance

Using antiferromagnets as active elements in spintronics requires the ability to manipulate and read-out the Néel vector orientation. Here we demonstrate for Mn₂Au, a good conductor with a high ordering temperature suitable for applications, reproducible switching using current pulse generated bulk spin-orbit torques and read-out by magnetoresistance measurements. Reversible and consistent changes of the longitudinal resistance and planar Hall voltage of star-patterned epitaxial Mn₂Au(001) thin films were generated by pulse current densities of ≃10⁷ A/cm². The symmetry of the torques agrees with theoretical predictions and a large read-out magnetoresistance effect of more than ≃6% is reproduced by ab initio transport calculations.

The zero net moment of antiferromagnets makes them insensitive to magnetic fields and enables ultrafast dynamics promising for novel spintronics. Here the authors achieved pulse current induced Néel vector switching in Mn₂Au(001) epitaxial thin films, which is associated with a large magnetoresistive effect allowing simple read-out.

Spin transport in graphene/transition metal dichalcogenide heterostructures

This review summarizes the theoretical and experimental studies of spin transport in graphene interfaced with transition metal dichalcogenides, and assesses its potential for future spintronic applications.

New Boundary-Driven Twist States in Systems with Broken Spatial Inversion Symmetry

A full description of a magnetic sample includes a correct treatment of the boundary conditions (BCs). This is in particular important in thin film systems, where even bulk properties might be modified by the properties of the boundary of the sample. We study generic ferromagnets with broken spatial inversion symmetry and derive the general micromagnetic BCs of a system with Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that the BCs require the full tensorial structure of the third-rank DMI tensor and not just the antisymmetric part, which is usually taken into account. Specifically, we study systems with C_{∞v} symmetry and explore the consequences of the DMI. Interestingly, we find that the DMI already in the simplest case of a ferromagnetic thin film leads to a purely boundary-driven magnetic twist state at the edges of the sample. The twist state represents a new type of DMI-induced spin structure, which is completely independent of the internal DMI field. We estimate the size of the texture-induced magnetoresistance effect being in the range of that of domain walls.

Deterministic Spin-Orbit Torque Induced Magnetization Reversal In Pt/[Co/Ni] n /Co/Ta Multilayer Hall Bars

Spin-orbit torque (SOT) induced by electric current has attracted extensive attention as an efficient method of controlling the magnetization in nanomagnetic structures. SOT-induced magnetization reversal is usually achieved with the aid of an in-plane bias magnetic field. In this paper, we show that by selecting a film stack with weak out-of-plane magnetic anisotropy, field-free SOT-induced switching can be achieved in micron sized multilayers. Using direct current, deterministic bipolar magnetization reversal is obtained in Pt/[Co/Ni]₂/Co/Ta structures. Kerr imaging reveals that the SOT-induced magnetization switching process is completed via the nucleation of reverse domain and propagation of domain wall in the system.

Effect of quantum tunneling on spin Hall magnetoresistance

We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on the spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/Y₃Fe₅O₁₂) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.

Films based on group IV–V–VI elements for the design of a large-gap quantum spin Hall insulator with tunable Rashba splitting

Rashba spin–orbit coupling (SOC) in topological insulators (TIs) has recently attracted significant interest due to its potential applications in spintronics.

Evidence for spin-to-charge conversion by Rashba coupling in metallic states at the Fe/Ge(111) interface

The spin-orbit coupling relating the electron spin and momentum allows for spin generation, detection and manipulation. It thus fulfils the three basic functions of the spin field-effect transistor. However, the spin Hall effect in bulk germanium is too weak to produce spin currents, whereas large Rashba effect at Ge(111) surfaces covered with heavy metals could generate spin-polarized currents. The Rashba spin splitting can actually be as large as hundreds of meV. Here we show a giant spin-to-charge conversion in metallic states at the Fe/Ge(111) interface due to the Rashba coupling. We generate very large charge currents by direct spin pumping into the interface states from 20 K to room temperature. The presence of these metallic states at the Fe/Ge(111) interface is demonstrated by first-principles electronic structure calculations. By this, we demonstrate how to take advantage of the spin-orbit coupling for the development of the spin field-effect transistor.

Spin-torque generator engineered by natural oxidation of Cu

The spin Hall effect is a spin–orbit coupling phenomenon, which enables electric generation and detection of spin currents. This relativistic effect provides a way for realizing efficient spintronic devices based on electric manipulation of magnetization through spin torque. However, it has been believed that heavy metals are indispensable for the spin–torque generation. Here we show that the spin Hall effect in Cu, a light metal with weak spin–orbit coupling, is significantly enhanced through natural oxidation. We demonstrate that the spin–torque generation efficiency of a Cu/Ni₈₁Fe₁₉ bilayer is enhanced by over two orders of magnitude by tuning the surface oxidation, reaching the efficiency of Pt/ferromagnetic metal bilayers. This finding illustrates a crucial role of oxidation in the spin Hall effect, opening a route for engineering the spin–torque generator by oxygen control and manipulating magnetization without using heavy metals.

In thin film spintronic devices, heavy metals with strong spin-orbit coupling are required to achieve a sizeable spin Hall effect. Here, the authors demonstrate an enhancement of the spin Hall effect in Cu, a material with weak spin-orbit coupling, via natural oxidation.

Rashba-Edelstein Magnetoresistance in Metallic Heterostructures

We report the observation of magnetoresistance originating from Rashba spin-orbit coupling (SOC) in a metallic heterostructure: the Rashba-Edelstein (RE) magnetoresistance. We show that the simultaneous action of the direct and inverse RE effects in a Bi/Ag/CoFeB trilayer couples current-induced spin accumulation to the electric resistance. The electric resistance changes with the magnetic-field angle, reminiscent of the spin Hall magnetoresistance, despite the fact that bulk SOC is not responsible for the magnetoresistance. We further found that, even when the magnetization is saturated, the resistance increases with increasing the magnetic-field strength, which is attributed to the Hanle magnetoresistance in this system.