Orbitally dominated Rashba-Edelstein effect in noncentrosymmetric antiferromagnets

Nonlinear Optics-Driven Spin Reorientation in Ferromagnetic Materials

Based on nonlinear optics, we propose that light irradiation could induce a nonequilibrium steady state magnetization variation. We formulize a band theory to elucidate its general microscopic mechanisms, which are rooted by the quantum geometric structure and topological nature of electronic Bloch wave functions. The existence is determined by the light polarization and specific material symmetry, based on the magnetic group theory. In general, for a magnetic system, both circularly and linearly polarized light could exert an effective magnetic field and a magnetic "velocity" (magnetization variation rate over time, serving as an effective torque) to reorient the magnetization direction. They are contributed by spin and orbital angular momenta simultaneously. Aided by group theory and first-principles calculations, we illustrate this theory using a showcase example of monolayer NiCl2, showing that light irradiation effectively generates an out-of-plane effective magnetic torque, which lifts its in-plane easy magnetization. According to magnetic dynamic simulations, under light with a modest intensity, this switching could occur on the order of 0.1-1 ns time scale, demonstrating its ultrafast nature that is desirable for quantum manipulation.

Signatures of magnetism control by flow of angular momentum

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

Terahertz oscillation driven by optical spin-orbit torque

Antiferromagnets are promising for nano-scale oscillator in a wide frequency range from gigahertz up to terahertz. Experimentally realizing antiferromagnetic moment oscillation via spin-orbit torque, however, remains elusive. Here, we demonstrate that the optical spin-orbit torque induced by circularly polarized laser can be used to drive free decaying oscillations with a frequency of 2 THz in metallic antiferromagnetic Mn2Au thin films. Due to the local inversion symmetry breaking of Mn2Au, ultrafast a.c. current is generated via spin-to-charge conversion, which can be detected through free-space terahertz emission. Both antiferromagnetic moments switching experiments and dynamics analyses unravel the antiferromagnetic moments, driven by optical spin-orbit torque, deviate from its equilibrium position, and oscillate back in 5 ps once optical spin-orbit torque is removed. Besides the fundamental significance, our finding opens a new route towards low-dissipation and controllable antiferromagnet-based spin-torque oscillators.

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.

Colossal Orbital Current Induced by Gradient Oxidation for High-Efficiency Magnetization Switching

Orbital angular momentum flow can be used to develop a low-dissipation electronic information device by manipulating the orbital current. However, efficiently generating and fully harnessing orbital currents is a formidable challenge. In this study, an approach is presented that induces a colossal orbital current by gradient oxidation in Pt/Ta to enhance spin-orbit torque (SOT) and achieve high-efficiency magnetization switching. The maximum efficiency of the SOT before and after the gradient oxidation of Ta is improved relative to that of Pt by ≈600 and 1200%, respectively. The large SOT originates from the colossal orbital current because of the orbital Rashba-Edelstein effect induced by the gradient oxidation of Ta. In addition, a large spin-to-charge conversion efficiency is observed in yttrium iron garnet/Pt/TaOx because of the inverse orbital Rashba-Edelstein effect. Harnessing the orbital current can help effectively minimize the critical current density of the current-induced magnetization switching to 2.26-1.08 × 106 A cm-2, marking a 12-fold reduction compared to that using Pt. This findings provide a new path for research on low-dissipation spin-orbit devices and improve the tunability of orbital current generation.

Orbital Torque in Rare-Earth Transition-Metal Ferrimagnets

Orbital currents have recently emerged as a promising tool to achieve electrical control of the magnetization in thin-film ferromagnets. Efficient orbital-to-spin conversion is required in order to torque the magnetization. Here, we show that the injection of an orbital current in a ferrimagnetic Gd_{y}Co_{100-y} alloy generates strong orbital torques whose sign and magnitude can be tuned by changing the Gd content and temperature. The effective spin-orbital Hall angle reaches up to -0.25 in a Gd_{y}Co_{100-y}/CuO_{x} bilayer compared to +0.03 in Co/CuO_{x} and +0.13 in Gd_{y}Co_{100-y}/Pt. This behavior is attributed to the local orbital-to-spin conversion taking place at the Gd sites, which is about 5 times stronger and of the opposite sign relative to Co. Furthermore, we observe a manyfold increase in the net orbital torque at low temperature, which we attribute to the improved conversion efficiency following the magnetic ordering of the Gd and Co sublattices.

Dominance of Extrinsic Scattering Mechanisms in the Orbital Hall Effect: Graphene, Transition Metal Dichalcogenides, and Topological Antiferromagnets

The theory of the orbital Hall effect (OHE), a transverse flow of orbital angular momentum (OAM) in response to an electric field, has concentrated on intrinsic mechanisms. Here, using a quantum kinetic formulation, we determine the full OHE in the presence of short-range disorder using 2D massive Dirac fermions as a prototype. We find that, in doped systems, extrinsic effects associated with the Fermi surface (skew scattering and side jump) provide ≈95% of the OHE. This suggests that, at experimentally relevant transport densities, the OHE is primarily extrinsic.

Monopole-like orbital-momentum locking and the induced orbital transport in topological chiral semimetals

The interplay between chirality and topology nurtures many exotic electronic properties. For instance, topological chiral semimetals display multifold chiral fermions that manifest nontrivial topological charge and spin texture. They are an ideal playground for exploring chirality-driven exotic physical phenomena. In this work, we reveal a monopole-like orbital-momentum locking texture on the three-dimensional Fermi surfaces of topological chiral semimetals with B20 structures (e.g., RhSi and PdGa). This orbital texture enables a large orbital Hall effect (OHE) and a giant orbital magnetoelectric (OME) effect in the presence of current flow. Different enantiomers exhibit the same OHE which can be converted to the spin Hall effect by spin-orbit coupling in materials. In contrast, the OME effect is chirality-dependent and much larger than its spin counterpart. Our work reveals the crucial role of orbital texture for understanding OHE and OME effects in topological chiral semimetals and paves the path for applications in orbitronics, spintronics, and enantiomer recognition.

Orbital Hanle Magnetoresistance in a 3d Transition Metal

The Hanle magnetoresistance is a telltale signature of spin precession in nonmagnetic conductors, in which strong spin-orbit coupling generates edge spin accumulation via the spin Hall effect. Here, we report the existence of a large Hanle magnetoresistance in single layers of Mn with weak spin-orbit coupling, which we attribute to the orbital Hall effect. The simultaneous observation of a sizable Hanle magnetoresistance and vanishing small spin Hall magnetoresistance in BiYIG/Mn bilayers corroborates the orbital origin of both effects. We estimate an orbital Hall angle of 0.016, an orbital relaxation time of 2 ps and diffusion length of the order of 2 nm in disordered Mn. Our findings indicate that current-induced orbital moments are responsible for magnetoresistance effects comparable to or even larger than those determined by spin moments, and provide a tool to investigate nonequilibrium orbital transport phenomena.

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

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

Simulations of magnetization reversal in FM/AFM bilayers with THz frequency pulses

It is widely known that antiferromagnets (AFMs) display a high frequency response in the terahertz (THz) range, which opens up the possibility for ultrafast control of their magnetization for next generation data storage and processing applications. However, because the magnetization of the different sublattices cancel, their state is notoriously difficult to read. One way to overcome this is to couple AFMs to ferromagnets-whose state is trivially read via magneto-resistance sensors. Here we present conditions, using theoretical modelling, that it is possible to switch the magnetization of an AFM/FM bilayer using THz frequency pulses with moderate field amplitude and short durations, achievable in experiments. Consistent switching is observed in the phase diagrams for an order of magnitude increase in the interface coupling and a tripling in the thickness of the FM layer. We demonstrate a range of reversal paths that arise due to the combination of precession in the materials and the THz-induced fields. Our analysis demonstrates that the AFM drives the switching and results in a much higher frequency dynamics in the FM due to the exchange coupling at the interface. The switching is shown to be robust over a broad range of temperatures relevant for device applications.

Observation of the orbital Hall effect in a light metal Ti

The orbital Hall effect¹ refers to the generation of electron orbital angular momentum flow transverse to an external electric field. Contrary to the common belief that the orbital angular momentum is quenched in solids, theoretical studies^2,3 predict that the orbital Hall effect can be strong and is a fundamental origin of the spin Hall effect^4-7 in many transition metals. Despite the growing circumstantial evidence^8-11, its direct detection remains elusive. Here we report the magneto-optical observation of the orbital Hall effect in the light metal titanium (Ti). The Kerr rotation by the orbital magnetic moment accumulated at Ti surfaces owing to the orbital Hall current is measured, and the result agrees with theoretical calculations semi-quantitatively and is supported by the orbital torque¹² measurement in Ti-based magnetic heterostructures. This result confirms the orbital Hall effect and indicates that the orbital angular momentum is an important dynamic degree of freedom in solids. Moreover, this calls for renewed studies of the orbital effect on other degrees of freedom such as spin^2,3,13,14, valley^15,16, phonon^17-19 and magnon^20,21 dynamics.

Current-driven writing process in antiferromagnetic Mn2Au for memory applications

Current pulse driven Néel vector rotation in metallic antiferromagnets is one of the most promising concepts in antiferromagnetic spintronics. We show microscopically that the Néel vector of epitaxial thin films of the prototypical compound Mn₂Au can be reoriented reversibly in the complete area of cross shaped device structures using single current pulses. The resulting domain pattern with aligned staggered magnetization is long term stable enabling memory applications. We achieve this switching with low heating of ≈20 K, which is promising regarding fast and efficient devices without the need for thermal activation. Current polarity dependent reversible domain wall motion demonstrates a Néel spin-orbit torque acting on the domain walls.

Direct visualization of Rashba-split bands and spin/orbital-charge interconversion at KTaO3 interfaces

Rashba interfaces have emerged as promising platforms for spin-charge interconversion through the direct and inverse Edelstein effects. Notably, oxide-based two-dimensional electron gases display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide two-dimensional electron gases is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO₃ two-dimensional electron gases and evidence their Rashba-split bands using angle resolved photoemission spectroscopy. Fitting the bands with a tight-binding Hamiltonian, we extract the effective Rashba coefficient and bring insight into the complex multiorbital nature of the band structure. Our calculations reveal unconventional spin and orbital textures, showing compensation effects from quasi-degenerate band pairs which strongly depend on in-plane anisotropy. We compute the band-resolved spin and orbital Edelstein effects, and predict interconversion efficiencies exceeding those of other oxide two-dimensional electron gases. Finally, we suggest design rules for Rashba systems to optimize spin-charge interconversion performance.

Visualization of the Rashbasplit bands in oxide two-dimensional electron gases is lacking, which hampers understanding of their rich spin-orbit physics. Here, the authors investigate KTaO₃ two dimensional electron gases and their Rashba-split bands.

Colossal Orbital Edelstein Effect in Noncentrosymmetric Superconductors

In superconductors that lack inversion symmetry, the flow of supercurrent can induce a nonvanishing magnetization, a phenomenon which is at the heart of nondissipative magnetoelectric effects, also known as Edelstein effects. For electrons carrying spin and orbital moments, a question of fundamental relevance deals with the orbital nature of magnetoelectric effects in conventional spin-singlet superconductors with Rashba coupling. Remarkably, we find that the supercurrent-induced orbital magnetization is more than 1 order of magnitude greater than that due to the spin, giving rise to a colossal magnetoelectric effect. The induced orbital magnetization is shown to be sign tunable, with the sign change occurring for the Fermi level lying in proximity of avoiding crossing points in the Brillouin zone. In the presence of superconducting phase inhomogeneities, a modulation of the Edelstein signal on the scale of the superconducting coherence length appears, leading to domains with opposite orbital moment orientations. These hallmarks are robust to real-space self-consistent treatment of the superconducting order parameter. The orbital-dominated magnetoelectric phenomena, hence, have clear-cut marks for detection both in the bulk and at the edge of the system and are expected to be a general feature of multiorbital superconductors with inversion symmetry breaking.

Orbital Dynamics in Centrosymmetric Systems

Orbital dynamics in time-reversal-symmetric centrosymmetric systems is examined theoretically. Contrary to common belief, we demonstrate that many aspects of orbital dynamics are qualitatively different from spin dynamics because the algebraic properties of the orbital and spin angular momentum operators are different. This difference generates interesting orbital responses, which do not have spin counterparts. For instance, the orbital angular momentum expectation values may oscillate even without breaking neither the time-reversal nor the inversion symmetry. Our quantum Boltzmann approach reproduces the previous result on the orbital Hall effect and reveals additional orbital dynamics phenomena, whose detection schemes are discussed briefly. Our work will be useful for the experimental differentiation of the orbital dynamics from the spin dynamics.

Observation of the Orbital Rashba-Edelstein Magnetoresistance

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

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

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

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.