Spin-orbit Correlations Research Articles

Chiral-even twist-3 GPDs for the proton in a spectator diquark model

We investigate the chiral-even twist-3 generalized parton distributions (GPDs) of valence quarks in the proton at nonzero skewness ξ, using a spectator model with scalar and axial-vector diquarks. We consider the exponential form factor for the nucleon-quark-diquark vertex and the axial-vector diquark with light-cone transverse polarization. We analyze the dependence of GPDs on the longitudinal momentum fraction x at different ξ, and on the square of the transverse momentum transfer ΔT2 at different x. Our numerical results reveal distinct discontinuities in all twist-3 GPDs except G1 and G˜1. By taking the forward limit, we obtain the twist-3 parton distribution function gT, which encodes the transverse spin distribution of quarks. We also compare the kinetic orbital angular momentum and the spin-orbit correlations of quarks defined by the twist-2 and twist-3 GPDs, respectively. Published by the American Physical Society 2024

Orbital torque switching in perpendicularly magnetized materials

The orbital Hall effect in light materials has attracted considerable attention for developing orbitronic devices. Here we investigate the orbital torque efficiency and demonstrate the switching of the perpendicularly magnetized materials through the orbital Hall material, i.e., Zr. The orbital torque efficiency of approximately 0.78 is achieved in the Zr orbital Hall material with the perpendicularly magnetized [Co/Pt]3 sample, which significantly surpasses that of the perpendicularly magnetized CoFeB/Gd/CoFeB sample (approximately 0.04). Such a notable difference is attributed to the different spin-orbit correlation strength between the [Co/Pt]3 sample and the CoFeB/Gd/CoFeB sample, confirmed through theoretical calculations. Furthermore, the full magnetization switching of the [Co/Pt]3 samples with a switching current density of approximately 2.6×106 A/cm2 has been realized through Zr, which even outperforms that of the W spin Hall material. Our finding provides a guideline to understand orbital torque efficiency and paves the way for developing energy-efficient orbitronic devices.

Twist analysis of the spin-orbit correlation in QCD

We present a QCD analysis of the twist-three parton distribution functions associated with the spin-orbit correlation of quarks and gluons in spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} and spin-0 hadrons. We derive exact non-perturbative identities decomposing the spin-orbit correlations into the Wandzura-Wilczek part and the genuine twist-three part. In the spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} case, the result is partially related to the kinematical twist-three part of the gT (x) distribution familiar in the context of transverse spin physics. We use these identities to obtain a novel longitudinal momentum sum rule which may be regarded as the momentum version of the Jaffe-Manohar spin sum rule. We explore the physical interpretation of the sum rule and make a connection to the color Lorentz forces and their associated potential energies.

Quark spin-orbit correlations in spin-0 and spin-1 mesons using the light-front quark model

We investigate the spin-orbital angular momentum correlations for the active quark inside the light and heavy mesons for both the spin-0 and spin-1 cases. These correlations can be derived from the generalized transverse-momentum-dependent distributions as well as the generalized parton distributions. We employ the overlap representation of light-front wave functions in the light-front quark model to calculate our analytical results. The dependence of spin-orbit correlations (SOCs) on the longitudinal momentum fraction x as well as the transverse-momentum-dependence k⊥ is graphically presented. Even though the SOCs have already been studied for the spin-0 pions and kaons in other approaches, no calculations for the other light and heavy spin-0 mesons have been reported in the literature. Further, the correlations for any of the light and heavy spin-1 mesons are studied for the first time in the present work. Published by the American Physical Society 2024

Chiral-odd generalized parton distributions of sea quarks at ξ=0 in the light-cone quark model

We study the chiral-odd generalized parton distributions (GPDs) of the u¯ and d¯ quarks inside the proton at zero skewness using the overlap representation within the light-cone formalism. Utilizing the light-cone wave functions of the proton obtained from the baryon-meson fluctuation model in terms of the |qq¯B⟩ Fock states, we provide expressions for the GPDs H˜Tq¯/P(x,0,t), HTq¯/P(x,0,t), and ETq¯/P(x,0,t) where q¯=u¯ and d¯. Numerical results for these GPDs in momentum space as well as in impact parameter space are presented. Additionally, we investigate specific combinations of the chiral-odd GPDs in impact parameter space, focusing on the spin-orbit correlation effect of the sea quarks. Published by the American Physical Society 2024

Composition dependence of the orbital torque in [formula omitted] and [formula omitted] alloys: Spin-orbit correlation analysis

The spin-orbit correlation in ferromagnet (FM) is an important factor that affects the orbital torque efficiency in the FM. We investigate the spin-orbit correlation in FM alloys, CoxFe1−x and NixFe1−x, with varying their composition. We find spots where the spin-orbit correlation is significantly strong near the Fermi surface in Co0.125Fe0.875, Co0.25Fe0.75, Co0.875Fe0.125, and Ni0.5Fe0.5, while no such spot appears in Co0.5Fe0.5, and Ni0.75Fe0.25. These results imply that in the former structures, the orbital polarized current injected into these spots can provide a strong torque to the magnetization of the FM through the orbital torque mechanism. These results also show that even in the same alloy system, the difference in alloy composition can lead to different orbital torque efficiency.

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Wigner distributions of sea quarks in the light-cone quark model

We investigate the Wigner distributions of u¯ and d¯ quarks in a proton using the overlap representation within the light cone formalism. Using the light-cone wave functions which are obtained from the baryon-meson fluctuation model in terms of the |qq¯B⟩ Fock states, we calculate the Wigner distributions for the unpolarized/longitudinally polarized sea quarks in an unpolarized/longitudinally polarized proton. The Wigner distributions can be obtained through a Fourier transform on the generalized transverse-momentum dependent parton distributions (GTMDs). We also calculate the GTMDs of u¯ and d¯ quarks in the intermediate step. Numerical results for the Wigner distributions of u¯ and d¯ quarks in transverse momentum space, impact parameter space and the mixed plane are presented. We also study the orbital angular momentum and the spin-orbit correlations of the sea quarks. Published by the American Physical Society 2024

Study of electronic structure and optical transition properties of low-lying excited states of AuB molecules based on configuration interaction method

High-level configuration interaction method including the spin-orbit coupling is used to investigate the low-lying excited electronic states of AuB that is not reported experimentally. The electronic structure in our work is preformed through the three steps stated below. First of all, Hartree-Fock method is performed to compute the singlet-configuration wavefunction as the initial guess. Next, we generate a multi-reference wavefunction by using the state-averaged complete active space self-consistent field (SACASSCF). Finally, the wavefunctions from CASSCF are utilized as reference, the exact energy point values are calculated by the explicitly correlated dynamic multi-reference configuration interaction method (MRCI). The Davidson correction (+Q) is put forward to solve the size-consistence problem caused by the MRCI method. To ensure the accuracy, the spin-orbit effect and correlation for inner shell electrons and valence shell electrons are considered in our calculation. The potential energy curves of 12 Λ-S electronic states are obtained. According to the explicit potential energy curves, we calculate the spectroscopic constants through solving radial Schrödinger equation numerically. We analyze the influence of electronic state configuration on the dipole moment by using the variation of dipole moment with nuclear distance. The spin-orbit matrix elements for parts of low-lying exciting states are computed, and the relation between spin-orbit coupling and predissociation is discussed. The predissociation is analyzed by using the obtained spin-orbit matrix elements of the 4 Λ-S states which spilt into 12 Ω states. It indicates that due to the absence of the intersections between the curves of spin-orbit matrix elements related with the 4 low-lying Λ-S states, the predissociation for these low-lying exciting states will not occur. Finally, the properties of optical transition between the ground Ω state <inline-formula><tex-math id="M3">\begin{document}$ {\rm A}^{1}{{{\Pi}}}_{1} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M3.png"/></alternatives></inline-formula> and first excited Ω state <inline-formula><tex-math id="M4">\begin{document}$ {{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M4.png"/></alternatives></inline-formula> are discussed in laser-cooling filed by analyzing the Franck-Condon factors and radiative lifetime. And the transition dipole moment is also calculated. But our results reveal that the AuB is not an ideal candidate for laser-cooling. In conclusion, this work is helpful in deepening the understanding of AuB, especially the structures of electronic states, interaction between excited states, and optical transition properties. All the data presented in this paper are openly available at <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://www.doi.org/10.57760/sciencedb.j00213.00009">https://www.doi.org/10.57760/sciencedb.j00213.00009</ext-link>.

Instanton effects in twist-3 generalized parton distributions

The instanton vacuum picture is used to study hadronic matrix elements of the twist-3 (dimension-4, spin-1) QCD operators measuring the quark spin density and spin-orbit correlations. The QCD operators are converted to effective operators in the low-energy effective theory emerging after chiral symmetry breaking, in a systematic approach based on the diluteness of the instanton medium and the 1/Nc expansion. The instanton fields induce spin-flavor-dependent “potential” terms in the effective operators, complementing the “kinetic” terms from the quark field momenta. As a result, the effective operators obey the same equation-of-motion relations as the original QCD operators. The spin-orbit correlations are qualitatively different from naive quark model expectations.

Anomalous enhancement of spin-orbital correlation effects induced by Mg doping in spinel MnV2O4

The magnetization and magnetostriction properties of Mn1−xMgxV2O4 (x = 0.00, 0.10, 0.15, 0.20) single crystals have been investigated under both static and pulsed magnetic fields, in which the magnetization and magnetostriction behaviors exhibit field-sweep-rate dependence, which are related to the spin-orbital-lattice coupling in these systems. Especially, anomalous enhancement of spin-orbital correlation was observed for x = 0.15. We attribute this enhancement to the tuning on the canting angle of V3+ ions by Mg2+-ions substitution. Furthermore, while the inter-vanadium distance RV-V is important to determine the evolution of the properties in the doped cases proposed by many studies, our result suggests that RV-V is not always dominant, the spin-orbital correlation effect can survive from the disordering induced by the variation of RV-V and even be enhanced at proper doping level.

Spin–orbit coupling and magnetism in

With one electron in the degenerate orbital sector, the compound exhibits active orbital degree of freedom, resulting in strongly enhanced orbital and spin-orbital correlations due to Coulomb interaction induced renormalization of the otherwise weak bare spin–orbit coupling (SOC) in this 3d transition metal compound. Finite temperature orbital fluctuations strongly reduce spin-orbital correlations, effective SOC strength, and magnon excitation energy. Orbital and magnetic transition temperatures estimated from the calculated orbiton and (renormalized) magnon energies are in good agreement with the experimental values obtained from susceptibility and resistivity anomalies in recent high-pressure studies.

Spin-orbital correlations in the two-orbital Hubbard model

We use exact diagonalization results to investigate how the ground state of a two-site, two-orbital Hubbard model evolves in terms of the crystal field energy and a magnetic spin symmetry breaking field. We show that, based on the behavior of a properly defined composite spin-orbital correlation function, the different regions of the related phase diagrams can be classified according to the extent to which spin and orbital degrees of freedom turn out to be correlated.

Spin-orbital mechanisms for negative thermal expansion in Ca2RuO4

The phenomenon of negative thermal expansion (NTE) deals with the increase of the lattice parameters and the volume of the unit cell when the material is thermally cooled. The NTE is typically associated with thermal phonons and anomalous spin-lattice coupling at low temperatures. However, the underlying mechanisms in the presence of strong electron correlations in multiorbital systems are not yet fully established. Here, we investigate the role of Coulomb interaction in the presence of lattice distortions in setting out the NTE effect, by focusing on the physical case of layered ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$ with the ${d}^{4}$ configuration at each Ru ion site. We employ the Slater-Koster parametrization to describe the electron-lattice coupling through the dependence of the d-p hybridization on the Ru-O-Ru bond angle. The evaluation of the minimum of the free energy at finite temperature by fully solving the multiorbital many-body problem on a finite-size cluster allows us to identify the regime for which the system is prone to exhibit NTE effects. The analysis shows that the nature of the spin-orbital correlations is relevant to drive the reduction of the bond angle by cooling, and in turn the tendency toward a NTE. This is confirmed by the fact that a changeover of the electronic and orbital configuration from ${d}^{4}$ to ${d}^{3}$ by transition metal substitution is shown to favor the occurrence of a NTE in ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$. This finding is in agreement with the experimental observations of a NTE effect which is significantly dependent on the transition metal substitution in the ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$ compound.

Giant efficiency of long-range orbital torque in Co/Nb bilayers

We report unambiguously experimental evidence of a strong orbital current in Nb films with weak spin-orbit coupling via the spin-torque ferromagnetic resonance (ST-FMR) spectrum for Fe/Nb and Co/Nb bilayers. The sign change of the damping-like torque in Co/Nb demonstrates a large spin-orbit correlation and thus great efficiency of orbital torque in Co/Nb. By studying the efficiency as a function of the thickness of Nb sublayer, we reveal a long orbital diffusion length (~3.1 nm) of Nb. Further planar Hall resistance (PHE) measurements at positive and negative applying current confirm the nonlocal orbital transport in ferromagnetic-metal/Nb heterostructures.

The asymmetric nuclear matter correlated states in the LOCV framework

The nucleon-nucleon correlations of asymmetric nuclear matter (ASM) in the 3S1-3D1 and the 3P2-3F2 states with the AV18 and the AV’6 potentials are studied in the lowest order constrained variational (LOCV) method. In these computations, the tensor (or the spin-orbit) correlations are considered in the 3S1-3D1 (3P2-3F2) state. The energy, as well as the healing distance of the ASM in the mentioned states, are reported. It is demonstrated that by decreasing the proton to neutron ratio, the non-central correlations (healing distances) of the coupled states grow. It is shown that the ASM non-central correlations and energies in the 3P2-3F2 state are more sensitive to the interaction than those of 3S1-3D1 state.

In situ controllable magnetic phases in doped twisted bilayer transition metal dichalcogenides

We study the electronic structure of hole-doped transition metal dichalcogenides for small twist-angels, where the onsite repulsion is extremely strong. Using unbiased diagrammatic Monte Carlo simulations, we find evidence for magnetic correlations which are driven by delocalization and can be controlled in situ via the dielectric environment. For weak spin-orbit coupling, we find that the moderately doped system becomes anti-ferromagnetic, whilst the regime of strong spin-orbit coupling features ferromagnetic correlations. We show that this behavior is accurately predicted by an analytical theory based on moment expansion of the Hamiltonian, and analysis of corresponding particle trajectories.

Experimental realization of neutron helical waves.

Methods of preparation and analysis of structured waves of light, electrons, and atoms have been advancing rapidly. Despite the proven power of neutrons for material characterization and studies of fundamental physics, neutron science has not been able to fully integrate these techniques because of small transverse coherence lengths, the relatively poor resolution of spatial detectors, and low fluence rates. Here, we demonstrate methods that are practical with the existing technologies and show the experimental achievement of neutron helical wavefronts that carry well-defined orbital angular momentum values. We discuss possible applications and extensions to spin-orbit correlations and material characterization techniques.

Recent Highlights from Spin-Physics Experiments

A snapshot of the current experimental status of spin-dependent nucleon structure prior to the arrival of the Electron Ion Collider will be attempted. Highlights of recent results from fixed-target experiments at JLab, Fermilab, CERN and DESY and collider experiments from RHIC are presented. Many of the recent results address the topics of transverse proton or parton spin and transverse parton momenta (TMDs), and their their (spin-orbit) correlations. Results on generalized parton distributions (GPDs), which provide an alternative pathway to mapping nucleon structure, are also discussed.

Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory.

As the relativistic corrections become stronger for late-row elements, the fully perturbative treatment of spin-orbit coupling and dynamic correlation may become inadequate for accurate descriptions of chemical properties. In this work, we introduce a determinant-based Kramers-unrestricted exact-two-component multireference second-order perturbation (X2C-MRPT2) method which variationally includes relativistic corrections with a perturbative dynamic correlation. The restricted active space partitioning scheme is employed to provide an adjustable correlation space for the second-order perturbation treatment. The multistate perturbation theory is also developed to improve the descriptions of ground and excited states. Benchmark studies of atomic fine-structure splittings and spectroscopic constants of molecular monohydrides using X2C-MRPT2 are compared to the other perturbative and variational approaches. The results suggest that X2C-MRPT2 is a highly accurate alternative to the fully variational multireference configuration interaction method at only a small fraction of the computational cost.