Orbital Hall Research Articles

Intrinsic orbital and spin Hall effect in bismuth semimetal

We investigate the intrinsic orbital Hall conductivity (OHC) and spin Hall conductivity (SHC) in a bismuth semimetal, by employing an $sp$-orbital tight-binding model. We report a notable difference between the anisotropy of OHC and SHC whose orbital and spin polarizations lie within the basal plane. We do not observe a substantial correlation between the orbital and spin Berry curvatures with spin-orbit coupling (SOC) at the Fermi energy, disproving the correlation between OHC and SHC in a strong SOC regime. We argue the huge SHC in a Bi semimetal is attributed to its gigantic SOC which strongly affects the hybridization of the $p$ orbitals, despite its relatively small magnitude of OHC. We hope the distinct anisotropy of OHC and SHC provides a feasible means to differentiate between the two effects in experiments.

The Ferris ferromagnetic resonance technique: Principles and applications

Measurements of ferromagnetic resonance (FMR) are pivotal to modern magnetism and spintronics. Recently, we reported on the Ferris FMR technique, which relies on large-amplitude modulation of the externally applied magnetic field. It was shown to benefit from high sensitivity while being broadband. The Ferris FMR also expanded the resonance linewidth such that the sensitivity to spin currents was enhanced as well. Eventually, the spin Hall angle (θSH) was measurable even in wafer-level measurements that require low current densities to reduce the Joule heating. Despite the various advantages, analysis of the Ferris FMR response is limited to numerical modeling, where the linewidth depends on multiple factors such as the field modulation profile and the magnetization saturation. Here, we describe, in detail, the basic principles of operation of the Ferris FMR and discuss its applicability and engineering considerations. We demonstrated these principles in a measurement of the orbital Hall effect taking place in Cu using an Au layer as the orbital-to-spin current converter. This illustrates the potential of the Ferris FMR for the future development of spintronics technology.

Inverse orbital Hall effect and orbitronic terahertz emission observed in the materials with weak spin-orbit coupling

The Orbital Hall effect, which originates from materials with weak spin-orbit coupling, has attracted considerable interest for spin-orbitronic applications. Here, we demonstrate the inverse effect of the orbital Hall effect and observe orbitronic terahertz emission in the Ti and Mn materials. Through spin-orbit transition in the ferromagnetic layer, the generated orbital current can be converted to charge current in the Ti and Mn layers via the inverse orbital Hall effect. Furthermore, the inserted W layer provides an additional conversion of the orbital-charge current in the Ti and Mn layers, significantly enhancing the orbitronic terahertz emission. Moreover, the orbitronic terahertz emission can be manipulated by cooperating with the inverse orbital Hall effect and the inverse spin Hall effect in the different sample configurations. Our results not only discover the physical mechanism of condensed matter physics but also pave the way for designing promising spin-orbitronic devices and terahertz emitters.

Electrical Manipulation of Orbital Current Via Oxygen Migration in Ni81 fe19 /Cuox /Tan Heterostructure.

The orbital Hall effect and the interfacial Rashba effect provide new approaches to generate orbital current and spin-orbit torque (SOT) efficiently without the use of heavy metals. However, achieving efficient dynamic control of orbital current and SOT in light metal oxides has proven challenging. In this study, we demonstrate that a sizable magnetoresistance effect related to orbital current and SOT can be observed in Ni81 Fe19 /CuOx /TaN heterostructures with various CuOx oxidisation concentrations. The ionic liquid gating induces migration of oxygen ions, which modulates the oxygen concentration at the Ni81 Fe19 /CuOx interface, leading to reversible manipulation of the magnetoresistance effect and SOT. The existence of a thick TaN capping layer allows for sophisticated internal oxygen ion reconstruction in the CuOx layer, rather than conventional external ion exchange. These results provide a method for the reversible and dynamic manipulation of the orbital current and SOT generation efficiency, thereby advancing the development of spin-orbitronics devices through ionic engineering. This article is protected by copyright. All rights reserved.

Orbital torque originating from orbital Hall effect in Zr

We investigate current-induced torques generated by Zr. We show that the generation efficiency of the current-induced torque increases with increasing the thickness of the Zr layer in ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}/\mathrm{Zr}$ and Ni/Zr bilayers, which indicates that the observed current-induced torque originates from the bulk of the Zr layer. We find that the sign of the current-induced torques is opposite to that expected from the spin Hall effect but is consistent with that expected from the orbital Hall effect in the Zr layer. Furthermore, we find that the torque efficiency increases with increasing the thickness of the ferromagnetic layer, which is consistent with the prediction of long-range orbital transport in ferromagnets. These observations demonstrate that the orbital Hall effect in the Zr layer is the main source of the current-induced torque. This finding highlights the important role of orbital transport in generating current-induced torques, advancing the understanding of angular momentum dynamics in solid-state devices with $4d$ transition metals.

Detection of long-range orbital-Hall torques

We report and quantify a large orbital-Hall torque generated by Nb and Ru, which we identify from a strong dependence of torques on the ferromagnets. This is manifested as a sign reversal and strong enhancement in the damping-like torques measured in Nb (or Ru)/Ni bilayers as compared to Nb (or Ru)/FeCoB bilayers. The long-range nature of orbital transport in the ferromagnet is revealed by the thickness dependences of Ni in Nb (or Ru)/Ni bilayers which are markedly different from the regular spin absorption in the ferromagnet that takes place within a few angstroms and thus it uniquely distinguishes the orbital Hall torque from the spin Hall torque.

Nonlocal orbital torques in magnetic multilayers

We investigate current-induced torques in Ni/Ti/Fe/Ti multilayers. In the multilayers, we find that the damping-like torque acting on the Ni magnetization increases with the thickness of the bottom Ti layer, despite the negligible spin Hall conductivity of Ti and the presence of the Fe interlayer that effectively absorbs the transverse spins. The nonlocal nature of the observed torque is consistent with the orbital torque arising from the orbital Hall effect in the Ti layer and orbital transport through the Fe layer. This observation highlights the unique features of the orbital currents, offering enhanced flexibility in the design of spintronic devices.

Hall Effect at the Focus of an Optical Vortex with Linear Polarization.

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively.

Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides.

Monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase have been recently classified as higher-order topological insulators (HOTIs), protected by C_{3} rotation symmetry. In addition, theoretical calculations show an orbital Hall plateau in the insulating gap of TMDs, characterized by an orbital Chern number. We explore the correlation between these two phenomena in TMD monolayers in two structural phases: the noncentrosymmetric 2H and the centrosymmetric 1T. Using density functional theory, we confirm the characteristics of 2H TMDs and reveal that 1T TMDs are identified by a Z_{4} topological invariant. As a result, when cut along appropriate directions, they host conducting edge states, which cross their bulk energy-band gaps and can transport orbital angular momentum. Our linear response calculations thus indicate that the HOTI phase is accompanied by an orbital Hall effect. Using general symmetry arguments, we establish a connection between the two phenomena with potential implications for orbitronics and spin orbitronics.

Spintronic Heterostructures for Artificial Intelligence: A Materials Perspective

With the advent of the Big Data era, neuromorphic computing (NC) (also known as brain‐inspired computing) has gained a lot of research interest. Spintronic devices are the emerging candidates for implementing the NC due to their intrinsic nonvolatility, extremely high endurance, low‐power consumption, and complementary metal‐oxide compatibility. Many research groups have proposed various NC architectures based on spintronic devices. Herein, a collective survey of different spintronic‐based approaches is given for NC. The reviewed approaches include the progress of stochastic magnetic tunnel junction (MTJ) devices, spin‐torque nano‐oscillator, spin‐Hall nano‐oscillator, domain walls, and skyrmion devices. In all of these approaches, spin–orbit torque (SOT)‐based magnetization control, which is achieved via spintronics heterostructures, plays a significant role. Various heterostructures of heavy metal and ferromagnetic layers that have been proposed are reviewed for generating SOT. In addition, the phenomena and materials involved in the generation of orbital torque are summarized due to the orbital Hall effect (OHE), which has recently gained researchers’ attention. Finally, an outlook on the opportunities and challenges for spintronic‐based NC hardware is provided, shedding light on its great potential for artificial intelligence (AI) applications.

Orbital magnetoelectric effect in nanoribbons of transition metal dichalcogenides

The orbital magnetoelectric effect (OME) generically refers to the appearance of an orbital magnetization induced by an applied electric field. Here, we show that nanoribbons of transition metal dichalcogenides (TMDs) with zigzag (ZZ) edges may exhibit a sizeable OME activated by an electric field applied along the ribbons' axis. We examine nanoribbons extracted from a monolayer (1L) and a bilayer (2L) of MoS$_2$ in the trigonal (H) structural phase. Transverse profiles of the induced orbital angular momentum accumulations are calculated to first order in the longitudinally applied electric field. Our results show that close to the nanoribbon's edge-state crossings energy, the orbital angular momentum accumulations take place mainly around the ribbons' edges. They have two contributions: one arising from the orbital Hall effect (OHE) and the other consists in the OME. The former is transversely anti-symmetric with respect to the principal axis of the nanoribbon, whereas the latter is symmetric, and hence responsible for the resultant orbital magnetization induced in the system. We found that the orbital accumulation originating from the OHE for the 1L-nanoribbon is approximately half that of a 2L-nanoribbon. Furthermore, while the OME can reach fairly high values in 1L-TMD nanoribbons, it vanishes in the 2L ones that preserve spatial inversion symmetry.The microscopic features that justify our findings are also discussed.

Generalized Poincaré Beams in Tight Focus

We study the tight focus of generalized (hybrid) Poincaré beams. A conventional Poincaré beam is a coaxial superposition of two optical vortices, one with left circular polarization and a topological charge (TC) of m, while the other has a right circular polarization and a TC of −m. The generalized Poincaré beams are also composed of two optical vortices, but their TCs are different, for instance, p and q. Here, we theoretically investigate the generalized Poincaré beams with the TCs p = m + 1 and q = −m in tight focus. In this case, both transverse components of the strength vector of the initial electric field have a topological charge of 1/2, and the beam itself is a cylindrical vector beam of fractional order m + 1/2. Analytical expressions are derived for the components of the strength vectors of the electric and magnetic field at the focus as well as for the intensity distribution, the longitudinal component of the spin angular momentum (SAM), and for the components of the Poynting vector (energy flow density). We show that the intensity at the focus has 2m − 1 local maxima residing evenly in a certain circle radius with the center on the optical axis. We also demonstrate that the radial spin and orbital Hall effects occur at the focus, i.e., the longitudinal SAM component has different signs in the circles of different radii, and the azimuthal component of the transverse Poynting vector also has different signs.

High-Order Orbital and Spin Hall Effects at the Tight Focus of Laser Beams

In this paper, using a Richards–Wolf method, which describes the behavior of electromagnetic waves at the sharp focus, we show that high-order spin and orbital Hall effects take place at the focal plane of tightly focused laser beams. We reveal that four local subwavelength regions are formed at the focus of a linearly polarized optical vortex with unit topological charge, where the spin angular momentum behaves in a special way. Longitudinal projections of the spin angular momentum are oppositely directed in the adjacent regions. We conclude that this is because photons falling into the neighboring regions at the focus have the opposite spin. This newly observed phenomenon may be called a spin Hall effect of the 4-th order. We also show that tightly focusing the superposition of cylindrical vector beams of the m-th and zero-order produces 2m subwavelength regions in the focal plane, such that longitudinal projections of the orbital angular momentum are oppositely directed in the neighboring regions. This occurs because photons falling into the neighboring regions at the focus have the opposite signs of the on-axis projections of the orbital angular momentum. This phenomenon may be termed an orbital Hall effect of the 2m-th order.

Orbital torque of Cr-induced magnetization switching in perpendicularly magnetized Pt/Co/Pt/Cr heterostructures

The spin–orbit torque via the spin Hall effect of heavy metals has shown promising prospect in driving the magnetization switching in spintronic devices due to the generated spin current from heavy metals. Recently, the 3d-light metals have been predicted the ability to generate orbital current and the associated orbital torques from the orbital Hall effect. However, few experiments have been carried out since it is quite hard to directly detect the orbital current-generated orbital torque. Here, we report an effective method to demonstrate the strong orbital torques in light metal Cr through a conversion process from orbital current to spin current by introducing the Pt interfacial layer in perpendicularly magnetized symmetric Pt/Co/Pt structures. A quite large and monotonically growth of orbital torque efficiency in Pt/Co/Pt/Cr with the increase of the thickness of Cr layer is obtained with the largest effective orbital torque efficiency around 2.6 Oe/(MA⋅cm−2) (1 Oe = 79.5775 A⋅m−1). The ability of orbital torque to drive the magnetization switching is also reported with the critical switching current density down to the order of 106 A⋅cm−2. Our findings prove the efficiency for switching the magnetization from light metal Cr layers through the orbital Hall effect.

Revisiting the photonic orbital Hall effect with the vortex mode decomposition

The photonic orbital Hall effect (POHE) refers to the vortex-dependent beam shifts, which is generally believed to result from the conversion of intrinsic orbital angular momentum (IOAM) to extrinsic orbital angular momentum (EOAM). However, the physical mechanism of the POHE, such as how the IOAM is converted to the EOAM, remains further elucidation. In this paper, we re-examine the POHE of a vortex beam with additional IOAM illuminating at an optically thin slab by means of vortex mode decomposition. By considering the competition and coupling between the radial and azimuthal vortex harmonics of the abnormal mode in the transmitted beam, it is found that the underlying mechanism of the POHE is in fact a spin-to-orbital angular momentum (OAM) conversion process. And the IOAM carried by the incident beam is directly superimposed on the OAM obtained during the conversion. Our findings not only offer an alternative perspective for understanding the POHE, but also exhibit application potential in orbit–orbit and spin–orbit optical components.

The giant orbital Hall effect in Cr/Au/Co/Ti multilayers

The spin–orbit torques originating from the spin Hall effect of heavy metals are of vital importance for applications in spintronics due to its low consumption of energy. Theoretical calculations have predicted that 3d and 4d light metals can produce a similar amount of torques to heavy metals via the strong orbital Hall effect (OHE). However, few experiments have been conducted since it is technically challenging to directly detect the orbital current from the OHE. Here, we report an effective approach to demonstrate the strong orbital torques in the light metal Cr with the aid of a conversion process from the orbital current to the spin current by introducing an Au interfacial layer in the Cr/ferromagnet structures. A rather large orbital torque efficiency and an increase with the increasing thickness of the Cr-layer are attained in the perpendicularly magnetized Cr/Au/Co/Ti multilayers. Moreover, an energy efficient magnetization switching and the domain wall motion in Cr/Au/Co/Ti multilayers induced by the OHE have also been observed. Our findings confirm the existence of the orbital Hall torques in Cr and provide an effective way to investigate the OHE.

Generation of spin currents by the orbital Hall effect in Cu and Al and their measurement by a Ferris-wheel ferromagnetic resonance technique at the wafer level

We present a new ferromagnetic resonance (FMR) method that we term the Ferris FMR. It is wideband, has significantly higher sensitivity as compared to conventional FMR systems, and measures the absorption line rather than its derivative. It is based on large-amplitude modulation of the externally applied magnetic field that effectively magnifies signatures of the spin-transfer torque making its measurement possible even at the wafer-level. Using the Ferris FMR, we report on the generation of spin currents from the orbital Hall effect taking place in pure Cu and Al. To this end, we use the spin-orbit coupling of a thin Pt layer introduced at the interface that converts the orbital current to a measurable spin current. While Cu reveals a large effective spin Hall angle exceeding that of Pt, Al possesses an orbital Hall effect of opposite polarity in agreement with the theoretical predictions. Our results demonstrate additional spin- and orbit- functionality for two important metals in the semiconductor industry beyond their primary use as interconnects with all the advantages in power, scaling, and cost.

Orbital Hall effect in crystals: Interatomic versus intra-atomic contributions

The orbital Hall effect (OHE) designates the generation of a charge-neutral flow of orbital angular momentum transverse to an initial charge current. Recent theoretical investigations suggest that transition metals display sizable OHE, encouraging experimental search along this direction. Nonetheless, most of these theories assume that the orbital moment originates from the region immediately surrounding the atom core, adopting the so-called {\it atomic center approximation}. In periodic crystals though, the contribution of the interstitial regions is crucial and can lead to a severe misestimation of the OHE. By applying the "modern theory" of orbital magnetization to the OHE, we assess the relative importance of intra-atomic and inter-atomic contributions in selected materials from first principles. We find that whereas the OHE is mostly of intra-atomic origin for wide band-gap semiconductors (e.g., MoS$_2$), the inter-atomic contribution becomes crucial in narrow band-gap semiconductors (SnTe, PbTe) and transition metals (Pt, V etc.). These predictions invalidate the atomic center approximation adopted in some of the previous works and open perspectives for the realization of efficient sources of orbital currents.

First-principles theory of intrinsic spin and orbital Hall and Nernst effects in metallic monoatomic crystals

The generation of spin and orbital currents is of crucial importance in the field of spin-orbitronics. In this work, using relativistic density functional theory and the Kubo linear-response formalism, we systematically investigate the spin Hall and orbital Hall effects for 40 monoatomic metals. The spin Hall conductivity and orbital Hall conductivity (OHC) are computed as a function of the electrochemical potential and the influence of the spin-orbit interaction strength is also investigated. Our calculations predict a rather small OHC in $sp$ metals, but a much larger OHC in $d$-band metals, with maximum values $[\ensuremath{\sim}8000(\ensuremath{\hbar}/e)\phantom{\rule{0.28em}{0ex}}{(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}]$ near the middle of the $d$ series. Using the Mott formula, we evaluate the thermal counterparts of the spin and orbital Hall effects, the spin Nernst effect (SNE), and the orbital Nernst effect (ONE). We find that the as-yet unobserved ONE is significantly larger $(\ensuremath{\sim}10\ifmmode\times\else\texttimes\fi{})$ than the SNE and has maximum values for group 10 elements (Ni, Pd, and Pt). Our work provides a broad overview of electrically and thermally induced spin and orbital transport in monoatomic metals.

Theory of magnetic spin and orbital Hall and Nernst effects in bulk ferromagnets

The magnetic spin Hall effect (MSHE) is an anomalous charge-to-spin conversion phenomenon which occurs in ferromagnetic materials. In contrast to the conventional spin Hall effect (SHE), being a time-reversal even effect, the magnetic counterpart is time-reversal odd. In this work, we use ab initio calculations to investigate the MSHE for the bulk ferromagnets Fe, Co, and Ni. The magnitudes of the MSHE of Fe and Co are comparable to those of the SHE, but the MSHE is strongly dependent on the electron lifetime and the MSHE and SHE can moreover have opposite signs. For Ni the MSHE is smaller than the SHE, but in general, the MSHE cannot be ignored for spin-orbit torques. Considering a charge current we analyze how both the MSHE and SHE contribute to a total Hall angle. We extend our analysis of the MSHE to its orbital counterpart, that is, the magnetic orbital Hall effect (MOHE), for which we show that the MOHE is in general smaller than the orbital Hall effect (OHE). We compute furthermore the thermal analogs, i.e., the spin and orbital Nernst effects, and their magnetic counterparts. Here our calculations show that the magnetic spin and orbital Nernst effects of Ni are substantially larger than those of Fe and Co.