Orbital Effects Research Articles

Relativistic versus Jahn-Teller effects in tantalum and tungsten clusters

We juxtapose the interplay of relativistic and Jahn-Teller effects in small tantalum and tungsten clusters. We employ relativistic techniques to study the low-lying electronic states of Tan for 2 ≤ n ≤ 6. We have used the complete active space MCSCF (CASSCF) techniques for the low-lying electronic states of Ta2 together with DFT techniques including spin–orbit corrections for large clusters that employed relativistic effective core potentials. The results thus obtained were compared with CASSCF/MRCI computations together with the inclusion of spin–orbit coupling for the tungsten trimer. Our computations reveal that unlike clusters containing lighter atoms, the spin–orbit effects overcome Jahn-Teller stabilization effects resulting in more symmetrical structures for tantalum and tungsten clusters. We have also computed the 3D-potential energy surfaces of different interesting regions of the Mexican hat surfaces. Whereas for the trimer and tetramer spin–orbit stabilization seems to overtake Jahn-Teller stabilization, thus resulting in the stabilization of symmetric structures, the Jahn-Teller stabilizations are larger than spin–orbit effects for larger clusters, thus resulting in distorted structures for larger clusters. We have provided a double group and graph-theoretical analysis of the electronic states of tantalum clusters to gain insights into the effect of spin–orbit coupling and pseudorotation on the electronic states of these clusters. The absorption spectra for these clusters are computed using time dependent density functional theory (TDDFT).

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.

Spin relaxation in copper channels with submicron cross sections

We review our recent experimental studies of the spin relaxation processes in the submicron copper channels of nonlocal spin valves (NLSV). Long spin relaxation lengths up to 3.0 μm at low temperatures are demonstrated in highly conductive copper channels with residual resistivity ratios up to 6. An unexpected anisotropy of spin relaxation is observed and can be attributed to the surface spin–orbit effects. An unusual scaling of the Kondo spin relaxation is established experimentally and can be explained by overlapping Kondo screening clouds. Our results demonstrate the technological potential of copper as a spin transport channel in spintronics and highlights unanswered fundamental questions related to the spin relaxation processes.

Spin-orbit transitions in the N+(PJA3)+H2→ NH+(X2Π,4Σ-) + H(2S) reaction, using adiabatic and mixed quantum-adiabatic statistical approaches.

The cross section and rate constants for the title reaction are calculated for all the spin-orbit states of N+(PJA3) using two statistical approaches, one purely adiabatic and the other one mixing quantum capture for the entrance channel and adiabatic treatment for the products channel. This is made by using a symmetry adapted basis set combining electronic (spin and orbital) and nuclear angular momenta in the reactants channel. To this aim, accurate ab initio calculations are performed separately for reactants and products. In the reactants channel, the three lowest electronic states (without spin-orbit couplings) have been diabatized, and the spin-orbit couplings have been introduced through a model localizing the spin-orbit interactions in the N+ atom, which yields accurate results as compared to ab initio calculations, including spin-orbit couplings. For the products, 11 purely adiabatic spin-orbit states have been determined with ab initio calculations. The reactive rate constants thus obtained are in very good agreement with the available experimental data for several ortho-H2 fractions, assuming a thermal initial distribution of spin-orbit states. The rate constants for selected spin-orbit JA states are obtained, to provide a proper validation of the spin-orbit effects to obtain the experimental rate constants.

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits.

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

Boundary effects on orbital magnetization for a bilayer system with different Chern numbers

The real space formalism of orbital magnetization (OM) is an average of the local OM over some appropriate region of the system. Previous studies prefer a bulk average (i.e., without including boundaries). Based on a bilayer model with an adjustable Chern number at half filling, we numerically investigate the effects of boundaries on the real space expressions of OM. The size convergence processes of its three constituent terms ${M}_{\mathrm{LC}}$, ${M}_{\mathrm{IC}}$, and ${M}_{\mathrm{BC}}$ are analyzed. The topological term ${M}_{\mathrm{BC}}$ makes a nonnegligible contribution from boundaries as a manifestation of edge states, especially in the case of nonzero Chern numbers. However, we show that the influence of the boundary on ${M}_{\mathrm{LC}}$ and ${M}_{\mathrm{IC}}$ exactly compensates that on ${M}_{\mathrm{BC}}$. This compensation effect leads to the conclusion that the whole sample average is also a correct algorithm in the thermodynamic limit, which gives the same value as those from the bulk average and the $k$-space formula. This clarification will be beneficial to further studies on orbitronics, as well as the orbital magnetoelectric effects in higher dimensions.

Competition between orbital effects, Pauli limiting, and Fulde–Ferrell–Larkin–Ovchinnikov states in 2D transition metal dichalcogenide superconductors

We compare the upper critical field of bulk single-crystalline samples of the two intrinsic transition metal dichalcogenide superconductors, 2H-NbSe2 and 2H-NbS2, in high magnetic fields where their layer structure is aligned strictly parallel and perpendicular to the field, using magnetic torque experiments and a high-precision piezo-rotary positioner. While both superconductors show that orbital effects still have a significant impact when the layer structure is aligned parallel to the field, the upper critical field of NbS2 rises above the Pauli limiting field and forms a Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state, while orbital effects suppress superconductivity in NbSe2 just below the Pauli limit, which excludes the formation of the FFLO state. From the out-of-plane anisotropies, the coherence length perpendicular to the layers of 31 Å in NbSe2 is much larger than the interlayer distance, leading to a significant orbital effect suppressing superconductivity before the Pauli limit is reached, in contrast to the more 2D NbS2.

Local angular momentum induced dual orbital effect

Spin angular momentum (SAM) and orbital angular momentum (OAM) are two important fundamental degrees of freedom of light and play crucial roles in various light–matter interactions. SAM usually makes the microparticle rotate around its axis, while OAM causes orbital motion of the microparticles around the beam axis. For an optical field with only SAM, the spin-to-orbit conversion may occur under the tightly focused condition, leading to the orbital motion of probing particles. However, it is invalid for weakly focused conditions. Here, we generated an annular optical field without intrinsic OAM by weakly focusing (i.e., negligible spin-to-orbit conversion) a circularly polarized light with a linearly varying radial phase and then observed a kind of dual orbital motion of asymmetric probing particles (Janus particles) in the focal plane. The two orbital motions have opposite directions on both sides across the strongest ring of the annular optical field. In addition to the SAM, the local angular momentum (AM) density also depends on the radial intensity gradient. The radial intensity gradient has the opposite signs on both sides across the strongest ring of the annular optical field, which results in the opposite orbital motions of trapped particles. The manipulation of the local AM density and the resulting novel dual orbital effect in the absence of intrinsic OAM provide a new scene to understand the physics underlying the light–matter interaction, paving the way to some new applications involving the sorting and delivery of microparticles.

Effect of the nickel molar content on the preparation and properties of spinel-type black ceramic pigment by microwave processing from stainless steelmaking dust

The transformation of stainless steel dust(SSD) rich in transition metal elements into Fe-Cr-Ni series spinel-type black ceramic pigment can solve a number of problems associated with traditional high-temperature SSD treatment while also maximizing resource efficiency and harmlessness utilization. Microwave heating and calcination at 900 °C using SSD, Cr2O3, and NiO as the main raw materials, altering the molar ratio of Fe and Cr in the raw materials to 1, and gradually adding NiO, were used to make black spinel ceramic pigments in this study. The solid solution phase is gradually replaced by the spinel phase as the amount of NiO added increases, and the primary phases are Ni(FeCr)O4 and NiCr2O4. The generated pigment phases are completely transformed to spinel when the Fe/Cr/Ni molar ratio is altered to 1:1:0.5. Because NiO can react with spinel in SSD, increasing the NiO content of the raw material will increase the intensity of the spinel phase diffraction peak. According to morphological examination, the prepared spinel pigments have a characteristic polyhedral shape. Furthermore, as the amount of NiO increases, so does the average grain size of the spinel phase, the orbital hybridization effect, the degree of atomic inversion in tetrahedra and octahedra, and oxygen vacancies and deficiencies, resulting in an increase in visible light absorbance and a decrease in band gap width. The prepared spinel pigments are fired in ceramics and exhibit good color rendering and adaptation properties.

Tunable Spin and Orbital Edelstein Effect at (111) LaAlO3/SrTiO3 Interface.

Converting charge current into spin current is one of the main mechanisms exploited in spintronics. One prominent example is the Edelstein effect, namely, the generation of a magnetization in response to an external electric field, which can be realized in systems with lack of inversion symmetry. If a system has electrons with an orbital angular momentum character, an orbital magnetization can be generated by the applied electric field, giving rise to the so-called orbital Edelstein effect. Oxide heterostructures are the ideal platform for these effects due to the strong spin–orbit coupling and the lack of inversion symmetries. Beyond a gate-tunable spin Edelstein effect, we predict an orbital Edelstein effect an order of magnitude larger then the spin one at the (111) LaAlO/SrTiO interface for very low and high fillings. We model the material as a bilayer of orbitals using a tight-binding approach, whereas transport properties are obtained in the Boltzmann approach. We give an effective model at low filling, which explains the non-trivial behaviour of the Edelstein response, showing that the hybridization between the electronic bands crucially impacts the Edelstein susceptibility.

DFT study of common anions adsorption at graphene surface due to anion-π interaction

Using density functional theory (DFT) calculations, we researched the different anions adsorption on the graphene and found that anions can be stably adsorbed on the graphene surface due to the anion-π interaction. The adsorption energy decreased as the order of HPO42- > SO42- > F- > CH3COO- > ClO3- > NO3- > ClO4- > SCN- > Cl- > Br-. The adsorption energy markedly increased as the valence of anion increased from negative monovalence (< -20kcal/mol) to negative bivalence (> -40kcal/mol). The energy decomposition analysis (EDA) showed that anion-π interaction is mainly induced by orbital effect. This work provides new insights for understanding Hofmeister effect at graphene interface from the molecular level and indicates that the anion-π interaction cannot be ignored at the interface, especially for the substrate with π-electron-rich carbon-based nanomaterials.

Analysis of a deep learning-based method for generation of SPECT projections based on a large Monte Carlo simulated dataset

BackgroundIn recent years, a lot of effort has been put in the enhancement of medical imaging using artificial intelligence. However, limited patient data in combination with the unavailability of a ground truth often pose a challenge to a systematic validation of such methodologies. The goal of this work was to investigate a recently proposed method for an artificial intelligence-based generation of synthetic SPECT projections, for acceleration of the image acquisition process based on a large dataset of realistic SPECT simulations.MethodsA database of 10,000 SPECT projection datasets of heterogeneous activity distributions of randomly placed random shapes was simulated for a clinical SPECT/CT system using the SIMIND Monte Carlo program. Synthetic projections at fixed angular increments from a set of input projections at evenly distributed angles were generated by different u-shaped convolutional neural networks (u-nets). These u-nets differed in noise realization used for the training data, number of input projections, projection angle increment, and number of training/validation datasets. Synthetic projections were generated for 500 test projection datasets for each u-net, and a quantitative analysis was performed using statistical hypothesis tests based on structural similarity index measure and normalized root-mean-squared error. Additional simulations with varying detector orbits were performed on a subset of the dataset to study the effect of the detector orbit on the performance of the methodology. For verification of the results, the u-nets were applied to Jaszczak and NEMA physical phantom data obtained on a clinical SPECT/CT system.ResultsNo statistically significant differences were observed between u-nets trained with different noise realizations. In contrast, a statistically significant deterioration was found for training with a small subset (400 datasets) of the 10,000 simulated projection datasets in comparison with using a large subset (9500 datasets) for training. A good agreement between synthetic (i.e., u-net generated) and simulated projections before adding noise demonstrates a denoising effect. Finally, the physical phantom measurements show that our findings also apply for projections measured on a clinical SPECT/CT system.ConclusionOur study shows the large potential of u-nets for accelerating SPECT/CT imaging. In addition, our analysis numerically reveals a denoising effect when generating synthetic projections with a u-net. Clinically interesting, the methodology has proven robust against camera orbit deviations in a clinically realistic range. Lastly, we found that a small number of training samples (e.g., ~ 400 datasets) may not be sufficient for reliable generalization of the u-net.

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.

Epitaxial NiCo2O4 film as an emergent spintronic material: Magnetism and transport properties

The ferrimagnetic inverse spinel NiCo2O4 has attracted extensive research interest for its versatile electrochemical properties, robust magnetic order, high conductivity, and fast spin dynamics, as well as its highly tunable nature due to the closely coupled charge, spin, orbital, lattice, and defect effects. Single-crystalline epitaxial thin films of NiCo2O4 present a model system for elucidating the intrinsic physical properties and strong tunability, which are not viable in bulk single crystals. In this Perspective, we discuss the recent advances in epitaxial NiCo2O4 thin films, focusing on understanding its unusual magnetic and transport properties in light of crystal structure and electronic structure. The perpendicular magnetic anisotropy in compressively strained NiCo2O4 films is explained by considering the strong spin–lattice coupling, particularly on Co ions. The prominent effect of growth conditions reveals the complex interplay between the crystal structure, cation stoichiometry, valence state, and site occupancy. NiCo2O4 thin films also exhibit various magnetotransport anomalies, including linear magnetoresistance and sign change in anomalous Hall effect, which illustrate the competing effects of band-intrinsic Berry phase and impurity scattering. The fundamental understanding of these phenomena will facilitate the functional design of NiCo2O4 thin films for nanoscale spintronic applications.

Spectral and timing analysis of BeXRB eRASSU J050810.4–660653 recently discovered in the Large Magellanic Cloud (LMC)

ABSTRACT We have studied the Be/X-ray binary (BeXRB) pulsar eRASSU J050810.4–660653 recently discovered in the Large Magellanic Cloud (LMC). Timing and spectral features of the source have been discussed in detail using NuSTAR and XMM–Newton observations. Coherent pulsation of the source was detected at ∼40.578 ± 0.001 s using NuSTAR observation. We analysed pulse profiles of the source in different energy bands using NuSTAR and XMM–Newton data. The pulse-profile evolved with time but was generally suggestive of a pencil-beam dominated pattern, which combined with the measured luminosity, indicates that the source may be accreting in the sub-critical regime. The pulse fraction follows a linearly increasing trend with photon energy and is anticorrelated with luminosity. In the 1-yr interval between the XMM and NuSTAR observations, the pulse period shortened by 0.021 s which could be consistent with spin-up or orbital Doppler effect. The average flux of the source in (3–50) keV energy range is found to be $\sim 5.56 \times 10^{-11}\, {\rm erg}\, {\rm cm}^{-2}\, \mathrm{s}^{-1}$ and the corresponding luminosity is $\sim 1.66 \times 10^{37}\, {\rm erg}\, \mathrm{s}^{-1}$. The variation of spectral parameters with pulse phase is studied using phase resolved spectroscopy which reveals that the observed photon index becomes harder with increasing flux.

Relative habitability of exoplanet systems with two giant planets

ABSTRACT The architecture of a planetary system can influence the habitability of a planet via orbital effects, particularly in the areas of stability and eccentricity. Some of these effects are readily apparent, particularly when they occur on short time-scales that are easily numerically calculable. However, the appearance and evolution of life can take place on gigayear time-scales, long enough that secular effects become important. These effects are difficult to investigate, as a direct integration requires significant computational time. In this paper, we apply a semi-analytic framework in conjunction with N-body integrations and predictive techniques to determine the relative habitability for an Earth-like planet in a system with two giant companions over a multidimensional parameter space. Relative habitability quantifies the integrated habitability probability compared to a system containing only a single Earth-like planet. We find trends with mass, eccentricity, location, spacing, inclination, and alignment of the giant planets, including configurations where the system is more habitable due to the giant planets. As long as the system remains stable, a moderate eccentricity excitation of the terrestrial planet can be beneficial by increasing the outer boundary of the habitable zone through higher mean irradiance. In our simulations, the median (±1σ) habitable planet has an eccentricity of $0.11^{+0.16}_{-0.08}$, though it started circular. Low-mass, widely separated, and moderately eccentric perturbing giants can accomplish this, an ‘ultra-habitable’ configuration of companions.

Direct Light Orbital Angular Momentum Detection in Mid-Infrared Based on the Type-II Weyl Semimetal TaIrTe4.

The direct photocurrent detection capability of light orbital angular momentum (OAM) has recently been realized with topological Weyl semimetals, but it is limited to the near-infrared wavelength range. The extension of the direct OAM detection capability to the mid-infrared band, which is a wave band that plays an important role in a vast range of applications, has not yet been realized. This is because the photocurrent responses of most photodetectors are neither sensitive to the phase information nor efficient in the mid-infrared region. In this study, a photodetector based on the type-II Weyl semimetal tantalum iridium telluride (TaIrTe4 ) is designed with peculiar electrode geometries to directly detect the topological charge of the OAM using the orbital photogalvanic effect (OPGE). The results indicate that the helical phase gradient of light can be distinguished by a current winding around the optical beam axis, with a magnitude proportional to its quantized OAM mode number. The topologically enhanced responses in the mid-infrared region of TaIrTe4 further help overcome the low responsivity issues and finally render direct OAM detection capability. This study enables on-chip-integrated OAM detection, and thus OAM-sensitive focal plane arrays in the mid-infrared region.

Tailoring Neuromorphic Switching by CuNx -Mediated Orbital Currents

Current-induced spin-orbit torque (SOT) is regarded as a promising mechanism for driving neuromorphic behavior in spin-orbitronic devices. In principle, the strong SOT in a heavy-metal-based magnetic heterostructure is attributed to the spin-orbit coupling (SOC)-induced spin Hall effect and/or the spin Rashba-Edelstein effect. Recently, SOC-free mechanisms such as the orbital-angular-momentum-induced orbital Hall effect and/or the orbital Rashba-Edelstein effect have been proposed to generate sizable torques comparable to those from the conventional spin Hall mechanism. In this work, we show that the orbital current can be effectively generated by the nitrided light metal $\mathrm{Cu}$. The overall dampinglike SOT efficiency, which consists of both the spin and the orbital current contributions, can be tailored from ${\ensuremath{\xi}}_{\mathrm{DL}}\ensuremath{\approx}0.06\text{ to }0.4$ in a $\mathrm{Pt}/\mathrm{Co}/{\mathrm{Cu}\mathrm{N}}_{x}$ magnetic heterostructure by tuning the nitrogen doping concentration. Current-induced magnetization switching further verifies the efficacy of such orbital current with a critical switching current density as low as ${J}_{c}$ \ensuremath{\sim} 5 \ifmmode\times\else\texttimes\fi{} ${10}^{10}\phantom{\rule{0.25em}{0ex}}{\mathrm{A}/\mathrm{m}}^{2}$. Most importantly, orbital-current-mediated memristive switching behavior can be observed in such heterostructures, which reveals that gigantic SOT and efficient magnetization switching are the trade-offs for the applicable window of memristive switching. Our work provides insights into the role that orbital current might play in SOT neuromorphic devices for making energy-efficient spin-orbitronic devices.

Electronic densities and valence bond wave functions.

Valence bond (VB) wave functions are studied from the density point of view. The density is plotted as a difference with the quasi-state built on the same orbitals. The densities of the components of the VB wave function are also shown. The breathing orbital effect leads to small modifications of the density. It is shown that while the densities of ionic and covalent components are the same, their coupling ends-up in modifications of the electronic density.

Intrinsic Vortex–Antivortex Interaction of Light

AbstractThe spin–orbit interaction and the extrinsic orbit–orbit interaction of light have been thoroughly studied, which have led to important phenomena including the spin Hall effect, orbital Hall effect, and spin–orbit Hall effect of light. Nevertheless, the concept of optical intrinsic orbit–orbit interaction, which is named as vortex–antivortex interaction, is scarcely known to the authors knowledge. Here, such a novel interaction process is theoretically and experimentally demonstrated, which emerges due to mutual interplays among reciprocal helicities of singular cores in a freely propagating light field. A general model describing the process is presented, which includes a linearly independent term and a nonlinearly coupling term. It is revealed that the strong coupling leads to intuitive mutual attraction between two reciprocal vortices, while the weak coupling, in contrast, results in a counterintuitive repulsive phenomenon. The vortex–antivortex interaction enables the predictions and observations of the orbital angular momentum Hall effect, as well as the stable propagation of an appropriately structured vortex arrays without nonlinear light–matter interactions. The results expand the scope of interaction processes among different forms of optical angular momenta, and open opportunities for studies of new effects using the presented coupling mechanism.