Spin-orbit Coupling Contributions Research Articles

Tight-binding model of Pt-based jacutingaites as combination of the honeycomb and kagome lattices

We introduce a refined tight-binding (TB) model for Pt-based jacutingaite materialsPt2NX3, (N= Zn, Cd, Hg; X = S, Se, Te), offering a detailed representation of the low-energy physics of its monolayers. This model incorporates all elements with significant spin-orbit coupling contributions, which are essential for understanding the topological energy gaps in these materials. Through comparison with first-principles calculations, we meticulously fitted the TB parameters, ensuring an accurate depiction of the energy bands near the Fermi level. Our model reveals the intricate interplay between the Pt 3eandNmetal orbitals, forming distinct kagome and honeycomb lattice structures. Applying this model, we explore the edge states of Pt-based jacutingaite monolayer nanoribbons, highlighting the sensitivity of the topological edge states dispersion bands to the nanostructures geometric configurations. These insights not only deepen our understanding of jacutingaite materials but also assist in tailoring their electronic properties for future applications.

Controllable magnetic anisotropy in two-dimensional 1T-CrTe2 with electrides sublayer

Exploring the controlled magnetic anisotropy energy (MAE) in two-dimensional (2D) ferromagnets is an essential step towards the emergent magnetic tunnel junctions (MTJs) with robust storage stability and low-power consumption. In addition to the transitional charge doping method, we propose that stacking 2D ferromagnet 1T-CrTe2 with electrides substrate can achieve not only the high interfacial charge transfer up to 5.24×1014 cm−2 and but also efficient modification of magnetic behaviors via interfacial engineering. Employing first-principles calculations, we show that the 1T-CrTe2/Ca2N(Y2C) heterostructures exhibit a significant reduction in MAE with a spin reorientation. Notably, the synergistic effect of internal charge transfer, external strain and charge doping shows a significant influence on the magnetic behaviors of the bilayer structures, enabling an efficient modulating of their MAE with distinct dependences. We elucidate that the underlying mechanism is the synergistic effect induced alteration of the spin-polarized px and py states on the Te atom located at the interfaces, which in turn changes the competitive spin-orbit coupling (SOC) contributions to the MAE. These findings provide a practical path toward the controllable MAE in 2D ferromagnets, and make the proposed heterostructures promising candidates for emergent spintronic devices.

Spin-Orbit Coupling of Color Centers for Quantum Applications

Color centers in 4H-SiC and diamond are candidates for single photon sources and qubits for the implementation of quantum applications. The CI-cRPA method is able to correctly reproduce the structure of the underlying highly correlated wave functions for low and high spin multiplets. Aiming for a more complete understanding of spin-orbit mediated intersystem crossing between such states, we have extended CI-cRPA by a first order treatment of the spin-orbit interactions. We present preliminary results for intercrossing matrix elements and contributions of spin-orbit coupling to the zero field splitting of the silicon vacancy and di-vacancy in 4H-SiC, as well as the NV center in diamond using this approach.

Iodine Clusters in the Atmosphere I: Computational Benchmark and Dimer Formation of Oxyacids and Oxides.

The contribution of iodine-containing compounds to atmospheric new particle formation is still not fully understood, but iodic acid and iodous acid are thought to be significant contributors. While several quantum chemical studies have been carried out on clusters containing iodine, there is no comprehensive benchmark study quantifying the accuracy of the applied methods. Here, we present the first study in a series that investigate the role of iodine species in atmospheric cluster formation. In this work, we have studied the iodic acid, iodous acid, iodine tetroxide, and iodine pentoxide monomers and their dimers formed with common atmospheric precursors. We have tested the accuracy of commonly applied methods for calculating the geometry of the monomers, thermal corrections of monomers and dimers, the contribution of spin-orbit coupling to monomers and dimers, and finally, the accuracy of the electronic energy correction calculated at different levels of theory. We find that optimizing the structures either at the ωB97X-D3BJ/aug-cc-pVTZ-PP or the M06-2X/aug-cc-pVTZ-PP level achieves the best thermal contribution to the binding free energy. The electronic energy correction can then be calculated at the ZORA-DLPNO-CCSD(T0) level with the SARC-ZORA-TZVPP basis for iodine and ma-ZORA-def2-TZVPP for non-iodine atoms. We applied this methodology to calculate the binding free energies of iodine-containing dimer clusters, where we confirm the qualitative trends observed in previous studies. However, we identify that previous studies overestimate the stability of the clusters by several kcal/mol due to the neglect of relativistic effects. This means that their contributions to the currently studied nucleation pathways of new particle formation are likely overestimated.

Quantum chemical calculations of electron affinities of alkaline earth metal atoms (Ca, Sr, Ba, and Ra)

We performed high-level ab initio quantum chemical calculations, incorporating higher-order excitations, spin–orbit coupling (SOC), and the Gaunt interaction, to calculate the electron affinities (EAs) of alkaline earth (AE) metal atoms (Ca, Sr, Ba, and Ra), which are notably small. The coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method is insufficient to accurately calculate the EAs of AE metal atoms. Higher-order excitations proved crucial, with the coupled-cluster singles, doubles, and triples with perturbative quadruples [CCSDT(2)Q] method effectively capturing dynamic electron correlation effects. The contributions of SOC (ΔESOs) to the EAs calculated using the multireference configuration interaction method with the Davidson correction, including SOC, positively enhance the EAs; however, these contributions are overestimated. The Dirac–Hartree–Fock (DHF)-CCSD(T) method addresses this overestimation and provides reasonable values for ΔESO (ΔESO−D). Employing additional sets of diffuse and core–valence correlation basis sets is critical for accurately calculating the EAs of AE metal atoms. The contributions of the Gaunt interaction (ΔEGaunt) to the EAs of AE metal atoms are negligible. Notably, the CCSDT(2)Q with the complete basis set limit + ΔESO−D + ΔEGaunt produced EA values for Ca, Sr, and Ba that closely aligned with experimental data and achieved accuracy exceeding the chemical accuracy. Based on our findings, the accurately proposed EA for Ra is 9.88 kJ/mol.

MRCI Study of the Electronic Structure and Transition Properties of a Tin Dimer.

The ground and excited states of Sn2 are calculated using the multireference configuration interaction method combined with Davidson correction (MRCI+Q). The influence of the spin-orbit coupling (SOC) effect on the electronic structure is also considered by the state interaction method of Breit-Pauli Hamiltonian. In the calculations, the potential energy curves and spectroscopic constants of 23 Λ-S states and 31 Ω states of Sn2 are obtained. The prominent spectral features in the visible region, new constants, and potential energy curves are discussed. The intensity of weak magnetic and quadrupole transitions in the near IR spectra is also calculated. From a computational point of view, we predict that the weak v'(0-2)-v″(0-5) bands of the magnetic b1Σg,0++-X3Σg,1(Ms=±1)- transition may be detected experimentally; the sub-bands (0, 0), (1, 0), and (2, 0) of the a1Δg,2-X3Σg,1(Ms=±1)- transition also may be observed in experiments since they are not overlapped by the strong electric dipole transition in the same IR region. According to the SOC matrix elements and contributions of the 15Πu0+, 15Πu1 (|Σ| = 0), and 15Πu1 (|Σ| = 2) states to the predissociation line width of the 13Σu- -X3Σg1- transition, the broading and other predissociation features of the 13Σu- state are analyzed. From our calculations, it follows that the strong coupling between the bound 13Σu- state and the repulsive 15Πu state causes the predissociation of the 13Σu- state at the vibrational levels v' ≥ 8. In addition, our results suggest that the previously observed bands of Sn2 in the visible range of 19000-20000 cm-1 should be reassigned into the mixing transitions among the X3Σg,1--23Σu,0-+ and X3Σg,0+--23Σu,1+ manifold. The results are expected to provide new comprehensive information for better understanding the spectra and dynamics of the electronic excited states of the Sn2 molecule.

A Comprehensive Study of Electronic, Optical, and Thermoelectric Characteristics of Cs2PbI2Br2 Inorganic Layered Ruddlesden-Popper Mixed Halide Perovskite through Systematic First-Principles Analysis.

In this research, we present a comprehensive study on the influence of layer-dependent structural, electronic, and optical properties in the two-dimensional (2D) Ruddlesden-Popper (RP) perovskite Cs2PbI2Br2. Employing first-principles computations within the density functional theory method, including spin orbit coupling contribution, we examine the impact of various factors on the material. Our results demonstrate that the predicted 2D-layered RP perovskite Cs2PbI2Br2 structures exhibit remarkable stability both structurally and energetically, making them promising candidates for experimental realization. Furthermore, we observe that the electronic band gap and optical absorption coefficients of Cs2PbI2Br2 strongly depend on the thickness variation of the layers. Interestingly, Cs2PbI2Br2 exhibits a notable absorption coefficient in the visible region. Using a combination of density functional theory and Boltzmann transport theory, the thermoelectric properties were forecasted. The calculation involved determining the Seebeck coefficient (S) and other associated thermoelectric characteristics, such as electronic and thermal conductivities, as they vary with the chemical potential at room temperature. These findings open up exciting opportunities for the application of this 2D RP perovskite in solar cells and thermoelectric devices, owing to its unique properties.

Systematic first-principles investigation of electronic, optical and thermoelectric properties of all-inorganic layered ruddlesden-popper mixed halide perovskite Cs2SnI2Br2

Report on systematic study of the impact of layer dependent structural properties, electronic structures and optical characteristics on the two-dimensional (2D) Ruddlesden–Popper (RP) perovskite Cs2SnI2Br2 using first principles computation within the density functional theory method including a spin orbit coupling contribution. Our results reveal that the predicted 2D-layered RP perovskite Cs2SnI2Br2 are structurally and energetically stable which can be realized in experiments. It is also shown that the band gap and optical absorption characteristics of the 2D-layered RP perovskite Cs2SnI2Br2 are dependent on thickness variation. Interestingly, Cs2SnI2Br2 exhibited an interesting absorption coefficient in the visible region. The transport equations were solved in order to evaluate the effect of the Sn based 2D-layered RP perovskite on thermoelectric performance. It is found that Cs2SnI2Br2 has lower thermal conductivity and higher electrical conductivity for T = 300 K. In addition, Cs2SnI2Br2 is expected to get the highest figure of merit. This result provides an outstanding opportunity for this 2D RP perovskite with potential applications in solar cells and thermoelectric applications.

First-principles study of the spin-orbit coupling contribution to anisotropic magnetic interactions

First-principles study of the spin-orbit coupling contribution to anisotropic magnetic interactions

Spin Currents Induced in Open-Shell Molecules by Static and Uniform Magnetic and Electric Fields in the Presence of a Spin-Orbit Coupling Interaction and Conservation Law.

The derivation of the total induced current density vector field, in the presence of static and uniform magnetic and electric fields, is illustrated in a more clear and formally correct language together with a discussion on the charge-current conservation law not presented before for the spin-orbit coupling contribution. The theory here exposed turns out to be in fully agreement with the theory of Special Relativity and it is applicable to open-shell molecules in the presence of a nonvanishing spin orbit coupling. The discussion here exposed turns out to be accurately valid for a strictly central field due to the chosen approximation of the spin-orbit coupling Hamiltonian, but it is appropriate to deal correctly with molecular systems. The ab initio calculation of spin current densities has been implemented at both unrestricted Hartree-Fock and unrestricted DFT levels of theory. Some maps of spin currents on molecules of interest, i.e., the CH3 radical and the superoctazethrene molecule are also illustrated.

Compacton existence and spin-orbit density dependence in Bose-Einstein condensates.

We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intraspecies Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intraspecies scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components. This gives rise to density dependent SOC parameters that strongly influence the existence and the stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for the metastable case). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intraspecies interactions is also suggested.

Studies on the EPR parameters and local angular distortion for the tetragonal Cu2+ center in CaWO4 crystal.

The electron paramagnetic resonance (EPR) parameters-g factors gi (i = || and ⊥) and hyperfine structure constants Ai (M) and Ai (N), with M and N belonging to isotopes 63 Cu2+ and 65 Cu2+ -and local structure of Cu2+ ion occupying W6+ site in CaWO4 crystal are theoretically studied based on the perturbation formulas of these parameters for a 3d9 ion under tetragonally elongated tetrahedra. In these formulas, the ligand orbital (LO) and spin-orbit coupling (SOC) contributions are included due to the shorter impurity-ligand distance R (≈1.83 Å) and hence the strong covalency of the studied [CuO4 ]6- cluster, and the related molecular orbital coefficients are quantitatively determined from the cluster approach in a uniform way; meanwhile, the required crystal field (CF) parameters for the tetragonally distorted tetrahedron (TDT) are estimated from the superposition model and the local structure of the impurity Cu2+ center. According to the calculation, the bond angle θ between the four equivalent Cu2+ -O2- bonds and the C4 axis in the CaWO4 :Cu2+ is found to be about 2.1° smaller than that (θ0 ≈ 54.74°) for an ideal tetrahedron due to the Jahn-Teller (JT) effect and the size mismatch. The fitted results agree well with the observed values, and the validity of the present assignment for the local structure of the Cu2+ center is also discussed.

Charge densities of transition-metal compounds

Irreducible tensor operators formulism has been employed to derive basis set charge densities from the expressions of t 2 g and e g eigenstates. The resulting basis set has been utilized to generate and visualized charge densities of pure and hybrid charge densities of single d electron and many-electron systems of transition-metal compounds. The role-plays by spin–orbit coupling contribution in mixing the densities have been demonstrated. The ground states of pentagonal bipyramidal, square planar, and trigonal bipyramidal complexes are due to spin–orbit coupling. The resulting charge densities are in full agreement with previous works in the literature.

Behavior of local quantum Fisher information and local quantum uncertainty in dipolar spin system with DM and KSEA interactions

In this paper, a two-spin-1/2 particle coupled via dipolar interaction with the interplay of antisymmetric Dzyaloshinskii–Moriya and symmetric Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions is considered at thermal equilibrium. The local quantum uncertainty and local quantum Fisher information are investigated as the pairwise nonclassical correlations quantifiers. The effects of the different system parameters on the quantified quantum correlation are analyzed in detail. Our results showed that the two studied thermal quantum correlation measures have similar qualitative behavior as well as quantitative sometimes. Also, it is shown that the quantumness of correlations is lost as the temperature rises sufficiently. Nevertheless, the antisymmetric and symmetric contributions of spin-orbit coupling considerably improve the amount of quantum correlations. Our analysis emphasized also that the local quantum uncertainty is bounded by local quantum Fisher information.

Stibnite at modified Becke-Johnson exchange potential

The demand for cheaper, nontoxic and earth-abundant materials as absorbing layer for solar cell is immensely needed to replace scarce, toxic and expensive one. In this regard, chalcogenide materials have considerably attracted the attention of a lot of researchers because of showing a great potential for different applications. Stibnite (Sb2S3), a chalcogenide binary material is intensively investigated for exploiting its potential for different energy technologies being a less toxic, abundantly available, stable and efficient one, which are the fundamentals for sustainability as well as to realize the dream of green energy. In this study, a computational study of the structural, electronic and optical properties of the stibnite (Sb2S3) crystal structure is presented using the full potential (FP) linearized augmented plane wave (LAPW) method framed within the density functional theory (DFT). For the estimation of the exchange-correlation potential part, besides the local density approximation (LDA), Wu-Cohen parameterized generalized gradient approximation (WC-GGA) Perdew-Burke-Ernzerhof parameterized generalized gradient approximation (PBE-GGA), and Perdew-Burke-Ernzerhof generalized gradient approximation for solids and surfaces (PBEsol-GGA), the Trans-Blaha approach of the modified Becke-Johnson (TB-mBJ) potential is used to improve the fundamental band gap value. Moreover, these calculations are performed by involving spin-orbit coupling (SOC) contribution as well. Additionally, optical properties, such as imaginary and real parts of the dielectric function, optical conductivity absorption coefficient, refractive index, reflectivity, and electron energy loss function were investigated as well. The obtained results of the band gap energy and optical properties with TB-mBJ potential were found closer to the experimental data and endorse its potentiality for the photovoltaics applications.

Magneto-optic effects of monolayer transition metal dichalcogenides induced by ferrimagnetic proximity effect

Monolayer transition metal dichalcogenides upon the application of proximity exchange interactions have recently attracted great attention due to their abilities of producing the anomalous Hall effect and tunable spin polarized edge currents. However, the magnetic distribution of the magnetic exchange field mainly focuses on the ferromagnetic order. Here, we argue that the nonzero magneto-optical responses can be excited in monolayer transition metal dichalcogenides subject to magnetic exchange field with ferrimagnetic order, which are the hallmarks of magneto-optical materials. This unusual effect comes from the joint contribution of spin orbit coupling and the ferrimagnetic order of magnetic exchange field, whose broken time reversal symmetry is confirmed by the topology of energy spectra. Our results suggest an alternative pathway to control the magnetooptical effects of monolayer transition metal dichalcogenides, which might stimulate further theoretical and experimental interest.

Structure, optical and magnetic properties of the pyridinium cobaltate (C6H9N2)2[CoCl4

The reaction of 2-amino-4-methylpyridine (L) with CoCl2·6H2O in hydrochloric acid gave the chlorocobaltate (HL)2[CoCl4] in 82% yield. X-ray diffraction of the blue crystalline material showed isolated [CoCl4]2– tetrahedra in the structure, connected to the aromatic 2-amino-4-methyl pyridinium cations through H bonding while the cations show π-stacking. FT-IR spectroscopy in conjunction with Hirshfeld surface analysis confirmed the importance of the 2-amino function in the cations for the hydrogen bonding. The material is thermally stable up to 270 °C. Intense UV–vis absorptions in the range 200–400 nm were assigned to π–π* transitions in the pyridinium cation, weaker features in the range 600–750 nm were due to ligand-field transitions in the d7 high-spin system [CoCl4]2–. Excitation at 370 nm led to an intense blue-green emission at λem = 473 nm attributable to excited π–π* states. The molar susceptibility measured over a range of 5–300 K reveals paramagnetic behavior at high temperature range with an effective magnetic moment of µeff = 4.74 µB indicating a significant spin–orbit coupling contribution adding to the spin-only value of 3.87 µB expected for Co(II) with 3d7 high spin configuration.

Many Body Current Density from Foldy–Wouthuysen Transformation of the Dirac–Coulomb Hamiltonian

This paper analyzes how special relativity changes the equation for the many-body-induced current density starting from the Foldy–Wouthuysen diagonalization of the Dirac–Coulomb Hamiltonian. This current density differs from that obtained with the Gordon decomposition due to the presence of a spin-orbit coupling contribution not considered before for many-body molecular systems. This contribution diverges on atomic nuclei due to the nature of the point charges considered in the nonrelativistic approach, demonstrating that conventionally used nonrelativistic methods are not suitable for dealing with spin effects such as spin-orbit coupling or effects smaller than α2, with α the fine structure constant, and that a fully relativistic approach with a finite charge should be used. Despite the singularity, the spin-orbit coupling current becomes an important contribution to the total current in open-shell systems with high-spin multiplicity and a high atomic number in the nuclear proximity. On long ranges, this contribution is overcome by the Coulomb potential and the derived electric field which decays very quickly for small distances from nuclear charges. An evaluation of this spin-orbit current has been performed in the linear response approach at the HF/DFT level of theory.

Theoretical studies on the EPR parameters and local structure of Cu2+ center in [Co(nicotinamide)2(H2O)4](saccharinate)2 crystal

Local structure and electron paramagnetic resonance (EPR) parameters for Cu2+ center in [Co(nicotinamide)2(H2O)4](saccharinate)2 (CoNAS) crystal are theoretically investigated using high-order perturbation formulas for 3d9 ions in rhombically elongated octahedra. In the calculated formulas, the related molecular orbital coefficients are acquired from the superposition model which enables to correlate the crystal field parameters and hence the EPR parameters with the studied Cu2+ center, the admixtures of d-orbitals in the ground state wave function as well as the ligand orbital and spin–orbit coupling contributions are taken into account. Based on the studies, the [CuO4N2]12− cluster of the studied Cu2+ center are found to suffer the axial and perpendicular bond length variations Δz (≈ 0.0612 Å) along z-axis and δr (≈ 0.0360 Å) along x- and y-axes, respectively, due to the Jahn–Teller effect.

Local electronic structure of rutile RuO2

Recently, rutile ${\mathrm{RuO}}_{2}$ has raised interest for its itinerant antiferromagnetism, crystal Hall effect, and strain-induced superconductivity. Understanding and manipulating these properties demands resolving the electronic structure and the relative roles of the rutile crystal field and $4d$ spin-orbit coupling (SOC). Here, we use O-K and Ru ${M}_{3}$ x-ray absorption and Ru ${M}_{3}$ resonant inelastic x-ray scattering to disentangle the contributions of crystal field, SOC, and electronic correlations in ${\mathrm{RuO}}_{2}$. The locally orthorhombic site symmetry of the Ru ions introduces significant crystal field contributions beyond the approximate octahedral coordination yielding a crystal field energy scale of $\mathrm{\ensuremath{\Delta}}({t}_{2g})\ensuremath{\approx}1\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ breaking the degeneracy of the ${t}_{2g}$ orbitals. This splitting exceeds the Ru SOC ($\ensuremath{\approx}160$ meV) suggesting a more subtle role of SOC, primarily through the modification of itinerant (rather than local) $4d$ electronic states, ultimately highlighting the importance of the local symmetry in ${\mathrm{RuO}}_{2}$. Remarkably, our analysis can be extended to other members of the rutile family, thus advancing the comprehension of the interplay among crystal field symmetry, electron correlations, and SOC in transition metal compounds with the rutile structure.