Orbital Edelstein Effect as a Condensed-Matter Analog of Solenoids

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.

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.

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.

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.

Magnetochiral tunneling in paramagnetic Co1/3NbS2

Electric currents have the intriguing ability to induce magnetization in nonmagnetic crystals with sufficiently low crystallographic symmetry. Some associated phenomena include the non-linear anomalous Hall effect in polar crystals and the nonreciprocal directional dichroism in chiral crystals when magnetic fields are applied. In this work, we demonstrate that the same underlying physics is also manifested in the electronic tunneling process between the surface of a nonmagnetic chiral material and a magnetized scanning probe. In the paramagnetic but chiral metallic compound Co1/3NbS2, the magnetization induced by the tunneling current is shown to become detectable by its coupling to the magnetization of the tip itself. This results in a contrast across different chiral domains, achieving atomic-scale spatial resolution of structural chirality. To support the proposed mechanism, we used first-principles theory to compute the chirality-dependent current-induced magnetization and Berry curvature in the bulk of the material. Our demonstration of this magnetochiral tunneling effect opens up an avenue for investigating atomic-scale variations in the local crystallographic symmetry and electronic structure across the structural domain boundaries of low-symmetry nonmagnetic crystals.

Optoelectronic Manifestation of Orbital Angular Momentum Driven by Chiral Hopping in Helical Se Chains

Chiral materials have garnered significant attention in the field of condensed matter physics. Nevertheless, the magnetic moment induced by the chiral spatial motion of electrons in helical materials, such as elemental Te and Se, remains inadequately understood. In this work, we investigate the development of quantum angular momentum enforced by chirality by using static and time-dependent density functional theory calculations for an elemental Se chain. Our findings reveal the emergence of an unconventional orbital texture driven by the chiral geometry, giving rise to a nonvanishing current-induced orbital moment. By incorporating spin-orbit coupling, we demonstrate that current-induced spin accumulation arises in the chiral chain, which fundamentally differs from the conventional Edelstein effect. Furthermore, we demonstrate optoelectronic detection of the orbital angular momentum in the chiral Se chain, providing an alternative to the interband Berry curvature, which is ill-defined in low dimensions.

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.

Recent advances in 2D TMD circular photo-galvanic effects

Two-dimensional (2D) layered semiconductors are appealing materials for high-specific-power photovoltaic systems due to their unique optoelectronic properties. The 2D materials can be naturally thin, and their properties can be altered in a variety of ways. Therefore, these materials may be used to develop high-performance opto-spintronic and photovoltaic devices. The most recent and promising strategies were used to induce circular photo-galvanic effects (CPGEs) in 2D TMD materials with broken inversion symmetry. The majority of quantum devices were manufactured by mechanical exfoliation to investigate the electrical behavior of ultrathin 2D materials. The investigation of CPGEs in 2D materials could enable the exploration of spin-polarized optoelectronics to produce more energy-efficient computing systems. The current research on nanomaterial-based materials paves the way for developing materials to store, manipulate, and transmit information with better performance. Finally, this study concludes by summarizing the current challenges and prospects.

Generalization of microscopic multipoles and cross-correlated phenomena by their orderings

The generalization of the atomic-scale multipoles is discussed. By introducing the augmented multipoles defined in the hybrid orbitals or in the site/bond-cluster, any of electronic degrees of freedom can be expressed in accordance with the crystallographic point group. These multipoles are useful to describe the cross-correlated phenomena, band-structure deformation, and generation of effective spin-orbit coupling due to antiferromagnetic ordering in a systematic and comprehensive manner. Such a symmetry-adapted multipole basis set could be a promising descriptor for materials design and informatics.

Rotation, Electric-Field Responses, and Absolute Enantioselection in Chiral Crystals

The microscopic origin of chirality, possible electric-field induced static rotational lattice deformation, and rotation-field induced electric polarization are investigated. By building up a realistic tight-binding model for the elemental Te crystal in terms of a symmetry-adapted basis, we identify the microscopic origin of the chirality and essential couplings among polar and axial vectors with the same time-reversal properties. Based on this microscopic model, we elucidate quantitatively that an interband process, driven by nearest-neighbor spin-dependent imaginary hopping, is the key factor in the electric-field induced rotation and its inverse response. From the symmetry point of view, these couplings and responses are characteristic and common to any chiral material, leading to a possible experimental approach to achieve absolute enantioselection by simultaneously applied electric and rotation fields, or a magnetic field and electric current, and so on, as a conjugate field of the chirality.

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.

Magneto-chiral anisotropy: From fundamentals to perspectives

The interplay between chirality and magnetic fields gives rise to a cross effect referred to as magneto-chiral anisotropy (MChA), which can manifest itself in different physical properties of chiral magnetized materials. The first experimental demonstration of MChA was by optical means with visible light. Further optical manifestations of MChA have been evidenced across most of the electromagnetic spectrum, from terahertz to X-rays. Moreover, exploiting the versatility of molecular chemistry toward chiral magnetic systems, many efforts have been made to identify the microscopic origins of optical MChA, necessary to advance the effect toward technological applications. In parallel, the replacement of light by electric current has allowed the observation of nonreciprocal electrical charge transport in both molecular and inorganic conductors as a result of electrical MChA (eMChA). MChA in other domains such as sound propagation, photochemistry, and electrochemistry are still in their infancy, with only a few experimental demonstrations, and offer wide perspectives for further studies with potentially large impact, like the understanding of the homochirality of life. After a general introduction to MChA, we give a complete review of all these phenomena, particularly during the last decade.

Spinterface Origin for the Chirality-Induced Spin-Selectivity Effect

When electrons are injected through a chiral molecule, the resulting current may become spin polarized. This effect, known as the chirality-induced spin-selectivity (CISS) effect, has been suggested to emerge due to the interplay between spin-orbit interactions and the chirality within the molecule. However, such explanations require unrealistically large values for the molecular spin-orbit interaction. Here, we present a theory for the CISS effect based on the interplay between spin-orbit interactions in the electrode, the chirality of the molecule (which induces a solenoid field), and spin-transfer torque at the molecule-electrode interface. Using a mean-field calculation with simple models for the molecular junction, we show that our phenomenological theory can qualitatively account for all key experimental observations, most importantly the magnitude of the CISS with realistic parameters. We also provide a set of predictions which can be readily tested experimentally.

Disentangling Orbital and Valley Hall Effects in Bilayers of Transition Metal Dichalcogenides

It has been recently shown that monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase exhibit relatively large orbital Hall conductivity plateaus within their energy band gaps, where their spin Hall conductivities vanish [Canonico et al., Phys. Rev. B 101, 161409 (2020)PRBMDO2469-995010.1103/PhysRevB.101.161409; Bhowal and Satpathy, Phys. Rev. B 102, 035409 (2020)PRBMDO2469-995010.1103/PhysRevB.102.035409]. However, since the valley Hall effect (VHE) in these systems also generates a transverse flow of orbital angular momentum, it becomes experimentally challenging to distinguish between the two effects in these materials. The VHE requires inversion symmetry breaking to occur, which takes place in the TMD monolayers but not in the bilayers. We show that a bilayer of 2H-MoS_{2} is an orbital Hall insulator that exhibits a sizeable orbital Hall effect in the absence of both spin and valley Hall effects. This phase can be characterized by an orbital Chern number that assumes the value C_{L}=2 for the 2H-MoS_{2} bilayer and C_{L}=1 for the monolayer, confirming the topological nature of these orbital-Hall insulator systems. Our results are based on density functional theory and low-energy effective model calculations and strongly suggest that bilayers of TMDs are highly suitable platforms for direct observation of the orbital Hall insulating phase in two-dimensional materials. Implications of our findings for attempts to observe the VHE in TMD bilayers are also discussed.

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.

Orbitally dominated Rashba-Edelstein effect in noncentrosymmetric antiferromagnets

Efficient manipulation of magnetic order with electric current pulses is desirable for achieving fast spintronic devices. The Rashba-Edelstein effect, wherein spin polarization is electrically induced in noncentrosymmetric systems, provides a mean to achieve staggered spin-orbit torques. Initially predicted for spin, its orbital counterpart has been disregarded up to now. Here we report a generalized Rashba-Edelstein effect, which generates not only spin polarization but also orbital polarization, which we find to be far from being negligible. We show that the orbital Rashba-Edelstein effect does not require spin-orbit coupling to exist. We present first-principles calculations of the frequency-dependent spin and orbital Rashba-Edelstein tensors for the noncentrosymmetric antiferromagnets CuMnAs and Mn[Formula: see text]Au. We show that the electrically induced local magnetization can exhibit Rashba-like or Dresselhaus-like symmetries, depending on the magnetic configuration. We compute sizable induced magnetizations at optical frequencies, which suggest that electric-field driven switching could be achieved at much higher frequencies.

Mixed topological semimetals driven by orbital complexity in two-dimensional ferromagnets

The concepts of Weyl fermions and topological semimetals emerging in three-dimensional momentum space are extensively explored owing to the vast variety of exotic properties that they give rise to. On the other hand, very little is known about semimetallic states emerging in two-dimensional magnetic materials, which present the foundation for both present and future information technology. Here, we demonstrate that including the magnetization direction into the topological analysis allows for a natural classification of topological semimetallic states that manifest in two-dimensional ferromagnets as a result of the interplay between spin-orbit and exchange interactions. We explore the emergence and stability of such mixed topological semimetals in realistic materials, and point out the perspectives of mixed topological states for current-induced orbital magnetism and current-induced domain wall motion. Our findings pave the way to understanding, engineering and utilizing topological semimetallic states in two-dimensional spin-orbit ferromagnets.