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The coupled transport of the charge and orbital angular momentum of electrons is at the heart of orbitronics. Here, we discuss the reciprocal relation between the direct and inverse orbital Hall effects (OHEs) in thin films. We argue that the conventional orbital current is ill-defined as it does not satisfy the reciprocal relation owing to non-conservation of the orbital angular momentum. We resolve the problem by adopting the definition of the so-called \emph{proper} orbital current, which is directly related to orbital accumulation. We prove the reciprocal relation between the \emph{global} response of orbital and charge currents. However, we show that their \emph{local} distributions are generally different, especially due to gigantic contributions at surfaces, which may lead to unintuitive results when charge and orbital currents are locally measured. We demonstrate our predictions by first-principles calculations on W(110) and Pt(111) thin films. In W(110), the direct and inverse OHEs are severely non-reciprocal locally in each layer although the total responses are exactly reciprocal. Interestingly, the SHEs are almost reciprocal locally in each layer. On the other hand, in Pt(111), both OHEs and SHEs are locally non-reciprocal, which we attribute to the pronounced spin-orbit interaction. We propose that the locally distinct responses may be used to distinguish the spin and orbital currents in experiments.

We show that dynamics of the magnetization in ferromagnets can pump the orbital angular momentum, which we denote by orbital pumping. This is the reciprocal phenomenon to the orbital torque that induces magnetization dynamics by the orbital angular momentum in non-equilibrium. The orbital pumping is analogous to the spin pumping established in spintronics but requires the spin-orbit coupling for the orbital angular momentum to interact with the magnetization. We develop a formalism that describes the generation of the orbital angular momentum by magnetization dynamics within the adiabatic perturbation theory. Based on this, we perform first-principles calculation of the orbital pumping in prototypical $3d$ ferromagnets, Fe, Co, and Ni. The results show that the ratio between the orbital pumping and the spin pumping ranges from 5 to 15 percents, being smallest in Fe and largest in Ni. This implies that ferromagnetic Ni is a good candidate for measuring the orbital pumping. Implications of our results on experiments are also discussed.

Harnessing spin and orbital angular momentum is a fundamental concept in condensed matter physics, materials science, and quantum-device applications. In particular, the search for new phenomena that generate a flow of spin angular momentum, a spin current, has led to the development of spintronics, advancing the understanding of angular momentum dynamics at the nanoscale. In contrast to this success, the generation and detection of orbital currents, the orbital counterpart of spin currents, remains a significant challenge. Here, we report the observation of orbital pumping, a phenomenon in which magnetization dynamics pumps an orbital current, a flow of orbital angular momentum. The orbital pumping is the orbital counterpart of the spin pumping, which is one of the most versatile and powerful mechanisms for spin-current generation. We show that the orbital pumping in Ni/Ti bilayers injects an orbital current into the Ti layer, which is detected through the inverse orbital Hall effect. Our findings provide a promising approach for generating orbital currents and pave the way for exploring the physics of orbital transport in solids.

The emerging field of orbitronics exploits the electron orbital momentum $\textit{L}$. Compared to spin-polarized electrons, $\textit{L}$ may allow magnetic-information transfera with significantly higher density over longer distances in more materials. However, direct experimental observation of $\textit{L}$ 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|SiO$_2$ thin-film stacks. The resulting terahertz charge-current bursts exhibit a marked delay and width that grow linearly with W thickness. We consistently ascribe these observations to a ballistic $\textit{L}$ current from Ni through W with giant decay length (~80 nm) and low velocity (~0.1 nm/fs). At the W/SiO$_2$ interface, the $\textit{L}$ 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 $\textit{L}$ transport as possible candidates for future ultrafast devices and an approach to discriminate Hall- and Rashba-Edelstein-like conversion processes.

Modern spintronics relies on the generation of spin currents through spin-orbit coupling. The spin-current generation has been believed to be triggered by current-induced orbital dynamics, which governs the angular momentum transfer from the lattice to the electrons in solids. The fundamental role of the orbital response in the angular momentum dynamics suggests the importance of the orbital counterpart of spin currents: orbital currents. However, evidence for its existence has been elusive. Here, we demonstrate the generation of giant orbital currents and uncover fundamental features of the orbital response. We experimentally and theoretically show that orbital currents propagate over longer distances than spin currents by more than an order of magnitude in a ferromagnet and nonmagnets. Furthermore, we find that the orbital current enables electric manipulation of magnetization with efficiencies significantly higher than the spin counterpart. These findings open the door to orbitronics that exploits orbital transport and spin-orbital coupled dynamics in solid-state devices.

Recent experimental observation of unexpectedly large current-induced spin-orbit torque in surface oxidized Cu on top of a ferromagnet suggested a possible role of the orbital Rashba effect (ORE). With this motivation, we investigate the ORE from first principles by considering an oxygen monolayer on top of a Cu(111) film. We show that surface oxidization of Cu film leads to gigantic enhancement of the ORE for states near the Fermi surface. The resulting chiral orbital texture in the momentum space is exceptionally strong, reaching $\sim 0.5\hbar$ in magnitude. We find that resonant hybridization between O $p$-states and Cu $d$-states is responsible for the emergence of the ORE. We demonstrate that application of an external electric field generates huge orbital Hall current, which is an order of magnitude larger than the spin Hall current found in heavy metals. This implies that "orbital torque" mechanism may be significant in surface oxidized Cu/ferromagnet structures. It also encourages experimental verification of the orbital texture in surface oxidized Cu through optical measurements such as angle-resolved photoemission spectroscopy.

We report the observation of a spin-orbit torque (SOT) originating from the surface Rashba-Edelstein effect. We found that the SOT in a prototypical spin-orbitronic system, a Pt/Co bilayer, can be manipulated by molecular self-assembly on the Pt surface. This evidences that the Rashba spin-orbit coupling at the Pt surface generates a sizable SOT, which has been hidden by the strong bulk and interface spin-orbit coupling. We show that the molecular tuning of the surface Rashba-Edelstein SOT is consistent with density functional theory calculations. These results illustrate the crucial role of the surface spin-orbit coupling in the SOT generation, which alters the landscape of metallic spin-orbitronic devices.

We report that current-induced spin-orbit torques (SOTs) in heavy-metal/ferromagnetic-metal bilayers are strongly altered by the oxidation of the ferromagnetic layer near the interface. We measured damping-like (DL) and field-like (FL) SOTs for Pt/Co and Pt/Ni$_{81}$Fe$_{19}$ (Pt/Py) films using spin-torque ferromagnetic resonance. In the Pt/Co film, we found that the oxidation of the Co layer near the interface enhances both DL and FL SOTs in spite of the insulating nature of the CoO$_x$ layer. The enhancement of the SOTs disappears by inserting a thin Ti layer at the Pt/CoO$_x$ interface, indicating that the dominant source of the SOTs in the Pt/CoO$_x$/Co film is the spin-orbit coupling at the Pt/CoO$_x$ interface. In contrast to the Pt/CoO$_x$/Co film, the SOTs in the Pt/PyO$_x$/Py film are dominated by the bulk spin-orbit coupling. Our result shows that the interfacial oxidation of the Pt/Py film suppresses the DL-SOT and reverses the sign of the FL-SOT. The change of the SOTs can be attributed to the change of the real and imaginary parts of the spin mixing conductance induced by the insertion of the insulating PyO$_x$ layer. These results show that the interfacial oxidation provides an effective way to manipulate the strength and sign of the SOTs.

The electrical manipulation of magnetization by current-induced spin torques has given access to realize a plethora of ultralow power and fast spintronic devices such as non-volatile magnetic memories, spin-torque nano-oscillators, and neuromorphic computing devices. Recent advances have led to the notion that relativistic spin-orbit coupling is an efficient source for current-induced torques, opening the field of spin-orbitronics. Despite the significant progress, however, the fundamental mechanism of magnetization manipulation, the requirement of spin currents in generating current-induced torques, has remained unchanged. Here, we demonstrate the generation of current-induced torques without the use of spin currents. By measuring the current-induced torque for naturally-oxidized-Cu/ferromagnetic-metal bilayers, we observed an exceptionally high effective spin Hall conductivity at low temperatures despite the absence of strong spin-orbit coupling. Furthermore, we found that the direction of the torque depends on the choice of the ferromagnetic layer, which counters the conventional understanding of the current-induced torque. These unconventional features are best interpreted in terms of an orbital counterpart of the spin torque, an orbital torque, which arises from the orbital Rashba effect and orbital current. These findings will shed light on the underlying physics of current-induced magnetization manipulation, potentially altering the landscape of spin-orbitronics.

We investigated spin-orbit torques in prototypical Pt-based spintronic devices. We found that, in Pt/Ni and Pt/Fe bilayers, the damping-like torque efficiency depends on the thickness of the Pt layer. We also found that the damping-like torque efficiency is almost identical in the Pt/Ni and Pt/Fe bilayers despite the stronger spin memory loss at the Pt/Fe interface. These results suggest that although the dominant source of the damping-like torque is the bulk spin Hall effect in the Pt layer, a sizable damping-like torque is generated by the interface in the Pt/Fe bilayer due to the stronger interfacial spin-orbit coupling. In contrast to the damping-like torque, whose magnitude and sign are almost identical in the Pt/Ni and Pt/Fe bilayers, the field-like torque strongly depends on the choice of the ferromagnetic layer. The sign of the field-like torque originating from the bulk spin Hall effect in the Pt layer is opposite between the Pt/Ni and Pt/Fe bilayers, which can be attributed to the opposite sign of the imaginary part of the spin-mixing conductance. These results demonstrate that the spin-orbit torques are quite sensitive to the electronic structure of the FM layer., Comment: The analysis has been revised based on the ST-FMR signals at higher frequencies

Spintronic devices are based on heterojunctions of two materials with different magnetic and electronic properties. Although an energy barrier is naturally formed even at the interface of metallic heterojunctions, its impact on spin transport has been overlooked. Here, using diffusive spin Hall currents, we provide evidence that the inherent energy barrier governs the spin transport even in metallic systems. We find a sizable field-like torque, much larger than the damping-like counterpart, in Ni$_{81}$Fe$_{19}$/Bi$_{0.1}$Sb$_{0.9}$ bilayers. This is a distinct signature of barrier-mediated spin-orbit torques, which is consistent with our theory that predicts a strong modification of the spin mixing conductance induced by the energy barrier. Our results suggest that the spin mixing conductance and the corresponding spin-orbit torques are strongly altered by minimizing the work function difference in the heterostructure. These findings provide a new mechanism to control spin transport and spin torque phenomena by interfacial engineering of metallic heterostructures.

We report intrinsic spin decay length of an antiferromagnetic insulator. We found that at an antiferromagnetic/ferromagnetic interface, a spin current generated by spin pumping is strongly suppressed by two-magnon scattering. By eliminating the two-magnon contribution, we discovered that the characteristic length of spin decay in NiO changes by two-orders of magnitude through the paramagnetic to antiferromagnetic transition. The spin decay length in the antiferromagnetic state is longer than 100 nm, which is an order of magnitude longer than previously believed. These results provide a crucial piece of information for the fundamental understanding of the physics of spin transport.

We investigate the absorption of a spin current at a ferromagnetic-metal/Pt-oxide interface by measuring current-induced ferromagnetic resonance. The spin absorption was characterized by the magnetic damping of the heterostructure. We show that the magnetic damping of a Ni$_{81}$Fe$_{19}$ film is clearly enhanced by attaching Pt-oxide on the Ni$_{81}$Fe$_{19}$ film. The damping enhancement is disappeared by inserting an ultrathin Cu layer between the Ni$_{81}$Fe$_{19}$ and Pt-oxide layers. These results demonstrate an essential role of the direct contact between the Ni$_{81}$Fe$_{19}$ and Pt-oxide to induce sizable interface spin-orbit coupling. Furthermore, the spin-absorption parameter of the Ni$_{81}$Fe$_{19}$/Pt-oxide interface is comparable to that of intensively studied heterostructures with strong spin-orbit coupling, such as an oxide interface, topological insulators, metallic junctions with Rashba spin-orbit coupling. This result illustrates strong spin-orbit coupling at the ferromagnetic-metal/Pt-oxide interface, providing an important piece of information for quantitative understanding the spin absorption and spin-charge conversion at the ferromagnetic-metal/metallic-oxide interface.

We report the observation of the crossover between the extrinsic and intrinsic spin Hall effect induced by alloying. We found that the spin Hall angle, the ratio of the spin Hall conductivity to the electric conductivity, changes drastically by tuning the composition of Au-Cu alloy. The spin Hall angle changes the sign only in a limited range of the Cu concentration due to the extrinsic skew scattering, while the intrinsic contribution becomes dominant with increasing the Cu concentration. This observation provides essential information for fundamental understanding of spin-orbit physics.

We report the observation of the intrinsic damping-like spin-orbit torque (SOT) arising from the Berry curvature in metallic-magnet/CuO$_x$ heterostructures. We show that a robust damping-like SOT, an order of magnitude larger than a field-like SOT, is generated in the heterostructure despite the absence of the bulk spin-orbit effect in the CuO$_x$ layer. Furthermore, by tuning the interface oxidation level, we demonstrate that the field-like SOT changes drastically and even switches its sign, which originates from oxygen modulated spin-dependent disorder. These results provide an important information for fundamental understanding of the physics of the SOTs.

Current-induced magnetization switching through spin-orbit torques (SOTs) is the fundamental building block of spin-orbitronics. The SOTs generally arise from the spin-orbit coupling of heavy metals. However, even in a heterostructure where a metallic magnet is sandwiched by two different insulators, a nonzero current-induced SOT is expected because of the broken inversion symmetry; an electrical insulator can be a spin-torque generator. Here, we demonstrate current-induced magnetization switching using an insulator. We show that oxygen incorporation into the most widely used spintronic material, Pt, turns the heavy metal into an electrically-insulating generator of the SOTs, enabling the electrical switching of perpendicular magnetization in a ferrimagnet sandwiched by electrically-insulating oxides. We further found that the SOTs generated from the Pt oxide can be controlled electrically through voltage-driven oxygen migration. These findings open a route towards energy-efficient, voltage-programmable spin-orbit devices based on solid-state switching of heavy metal oxidation.

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.

We have quantitatively studied the spin-orbit torque purely generated by the spin Hall effect in a wide range of temperatures by intensionally eliminating the Rashba spin-orbit torque using Pt/Co/Pt trilayers with asymmetric thicknesses of the top and bottom Pt layers. The vanishingly small contribution from the Rashba effect has been confirmed through the vector measurements of the current-induced effective fields. In order to precisely determine the value of the spin Hall torque, the complete cancelation of the spin Hall torque has been verified by fabricating symmetric Pt/Co/Pt structure on SiO2 and Gd3Ga5O12 (GGG) substrates. Despite of the complete cance- lation on the GGG substrate, the spin Hall torque cannot be completely canceled out even when the top and bottom Pt layers have same thicknesses on the SiO2 substrate, which suggests that Pt/Co/Pt trilayers on a GGG substrate is a suitable system for precise measurements of the spin Hall torque. The result of the vector measurements on Pt/Co/Pt/GGG from 300 to 10 K shows that the spin Hall torque is almost independent of temperature, which is quantitatively reproduced under the assumption of the temperature-independent spin Hall angle of Pt.

Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators.

We study spin pumping in a $\mathrm{Y_3Fe_5O_{12}(YIG)/Pt/Ni_{81}Fe_{19}(Py)}$ trilayer film by means of the inverse spin Hall effect (ISHE). When the ferromagnets are not excited simultaneously by a microwave, ISHE-induced voltage is of the opposite sign at each ferromagnetic resonance (FMR). The opposite sign is consistent with spin pumping of bilayer films. On the other hand, the voltage is of the same sign at each FMR when both the ferromagnets are excited simultaneously. Futhermore, the voltage greatly increases in magnitude. The observed voltage is unconventional; neither its sign nor magnitude can be expected from spin pumping of bilayer films. Control experiments show that the unconventional voltage is dominantly induced by spin pumping at the Py/Pt interface. Interaction between YIG and Py layers is a possible origin of the unconventional voltage., Comment: 13 pages, 4 figures

Dynamic response of spin accumulation to a time-dependent magnetic field has been investigated in a ferromagnetic/nonmagnetic bilayer under ferromagnetic resonance. In this system, magnetization precession driven by a microwave generates direct-current (dc) and alternate-current (ac) spin accumulation in the nonmagnetic layer by the spin pumping. The ac spin accumulation is coupled with the microwave magnetic field through a dynamical Hanle spin precession, giving rise to rectified spin accumulation comparable with the dc spin accumulation directly generated by the spin pumping., Comment: Accepted for publication in Applied Physics Letters

The spin-orbit interaction in a solid couples the spin of an electron to its momentum. This coupling gives rise to mutual conversion between spin and charge currents: the direct and inverse spin Hall effects. The spin Hall effects have been observed in metals and semiconductors. However, the spin/charge conversion has not been realized in one of the most fundamental semiconductors, silicon, where accessing the spin Hall effects has been believed to be difficult because of its very weak spin-orbit interaction. Here we report observation of the inverse spin Hall effect in silicon at room temperature. The spin/charge current conversion efficiency, the spin Hall angle, is obtained as 0.0001 for a p-type silicon film. In spite of the small spin Hall angle, we found a clear electric voltage due to the inverse spin Hall effect in the p-Si film, demonstrating that silicon can be used as a spin-current detector., Comment: 8 pages, 4 figures, Accepted for publication in Nature Communications

We report the two-dimensional propagation of photoinduced spin wave packets in Bi-doped rare-earth iron garnet. Spin waves were excited nonthermally and impulsively by a circularly polarized light pulse via the inverse Faraday effect. Space- and time resolved spin waves were detected with a magneto-optical pump-probe technique. We investigated propagation in two directions, parallel and perpendicular to the magnetic field. Backward volume magnetostatic waves (BVMSWs) were detected in both directions. The frequency of BVMSWs depends on the propagation direction. The experimental results agreed well with the dispersion relation of BVMSWs., Comment: 4 pages, 5 figures

A spin battery concept is applied for the dynamical generation of pure spin current and spin transport in p-type silicon (p-Si). Ferromagnetic resonance and effective s-d coupling in Ni80Fe20 results in spin accumulation at the Ni80Fe20/p-Si interface, inducing spin injection and the generation of spin current in the p-Si. The pure spin current is converted to a charge current by the inverse spin Hall effect of Pd evaporated onto the p-Si. This approach demonstrates the generation and transport of pure spin current in p-Si at room temperature., Comment: 23pages, 5 figures (To appear in Phys. Rev. Lett.)