Spin-orbit 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 materials Pt2NX3, (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 Pt3eandNmetal 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.

Spin waves and orbital contribution to ferromagnetism in a topological metal

Honeycomb and kagome lattices can host propagating excitations with non-trivial topology as defined by their evolution along closed paths in momentum space. Excitations on such lattices can also be momentum-independent, and the associated flat bands are of interest due to strong interactions between heavy quasiparticles. Here, we report the discovery — using circularly polarized X-rays for the unambiguous isolation of magnetic signals — of a nearly flat spin-wave band and large (compared to elemental iron) orbital moment in the metallic ferromagnet Fe3Sn2 with compact AB-stacked kagome bilayers. As a function of out-of-plane momentum, the nearly flat optical mode and the global rotation symmetry-restoring acoustic mode are out of phase, consistent with a bilayer exchange coupling that is larger than the already large in-plane couplings. The defining units of this topological metal are therefore triangular lattices of octahedral iron clusters rather than weakly coupled kagome planes. The spin waves are strongly damped when compared to elemental iron, opening the topic of topological boson–fermion interactions for deeper exploration within this material platform.

DAPD Set of Pd-Containing Diatomic Molecules: Accurate Molecular Properties and the Great Lengths to Obtain Them.

In the present study, we obtained reliable bond energy, bond length, and zero-point vibrational frequency for a set of diatomic Pd species (the DAPD set). It includes PdH, Pd2, and PdX (X = B, C, N, O, F, Al, Si, P, S, and Cl). Our highest-level protocol (W4X-L) represents scalar and spin-orbit relativistic, valence- and inner-valence correlated, extrapolated CCSDTQ(5) energy. The DAPD set of molecules is challenging for computational chemistry methods in different manners; for Pd2, the spin-orbit contribution to the bond energy is fairly large, whereas for PdC and PdSi, the post-CCSD(T) correlation components are considerable. The diverse range of requirements represents a significant challenge for lower-level methods. While density functional theory (DFT) methods generally yield good agreements for bond lengths and vibrational frequencies, large deviations are found for bond energies. In general, hybrid DFT methods are more accurate than nonhybrid functionals, but the agreement in individual cases varies. This illustrates the critical role that new high-quality reference data would play in the continual development of lower-cost methods.

Topological phase transition in the antiferromagnetic topological insulator MnBi_2Te_4 from the point of view of axion-like state realization

This work aims to study the conditions of topological phase transition (TPT) between the topological and trivial states in the antiferromagnetic topological insulator (AFM TI) MnBi_2Te_4 and propose some theory about the relationship of this TPT with the possibility of axion-like state realization in this material. Using the density functional approach we have analyzed the changes in the electronic and spin structure of topological surface states (TSSs) and the nearest conduction and valence bands (CB and VB) including the changes in the bulk band gap as well as the Dirac point (DP) gap in TSSs under variation of the spin-orbit coupling strength in the region of the TPT for infinite crystal and slab with a surface both. We have shown that in both cases the TPT occurs with inversion of the contributions of the Bi-p_z and Te-p_z states of different parity at the gap edges related to change in the gap sign. In the case of surface calculations, the Bi-p_z and Te-p_z states at the edges of the bulk band gap and their inversion at the TPT point are transformed into the TSSs with an energy gap at the DP. In this case the TPT takes place without closing the band gap, i.e. with a “jump” through zero and the formation of the nonzero gap during such a transition. Our calculations show that the TPT point is also characterized by an inversion of the out-of-plane spin polarization s_z at the Gamma point for lower and upper parts of the Dirac cone and a significant spatial redistribution of the TSSs between the surface and the bulk. We suppose that the nonzero Dirac gap can have some relationship with the formation of the axion-like state, which presumably couples nonmagnetic spin-orbit and magnetic contributions at the boundary between the topological and trivial phases for a system with parameters close to the TPT conditions. A practically realized system is proposed - the AFM TI with a stoichiometry close to that of MnBi_2Te_2Se_2 with partial (about 50%) substitution of Te atoms for Se atoms in MnBi_2Te_4 which can be an experimental platform for the implementation and experimental analysis of the TPT and the corresponding possibility of the axion-like state realization in Condensed Matter. Besides, such system could serve as a good platform for studying the dynamic axion effect, where the axion field fluctuations are maximised when a small external field is applied to the system which state is close to the TPT.

Spin-orbit contribution to radiative losses for spinning binaries with aligned spins

Spin-orbit contribution to radiative losses for spinning binaries with aligned spins

Revision and Analysis of the Formation Constants of Rare Earth Diketonates.

Over the course of the past several decades, spectroscopic surveys have unveiled the intricate nature of the aqueous chelation of Rare Earth Metals. Herein, we have collected a large data set about the interaction between 16 metal ions (Sc3+, Y3+, La3+, Ce3+, Pr3+, Nd3+, Sm3+, Eu3+, Gd3+, Tb3+, Dy3+, Ho3+, Er3+, Tm3+, Yb3+, and Lu3+) and perfluorinated nonsymmetric β-diketones, which contain chalcogen-bearing heterocyclic rings or aromatic moiety. The role and influence of the side ions on the chelation processes have been re-estimated to obtain revised stability constants. After analysis of more than 150 revised formation constants, a better periodic correlation has been shown. Scrutinizing the effects of the substituted group has revealed an "anti-Coulomb" behavior within the chalcogen group of diketones and a strictly electrostatic trend within the Rare Earth Metals series. Within the first-order approximation, the spin-orbit contribution to the Gibbs free energy of chelation has been estimated.

Comparison of state-interaction and spinor-representation calculations of spin-orbit coupling within exact two-component coupled-cluster theories

A benchmark study of state-interaction and spinor-representation calculations of spin-orbit coupling using the exact two-component Hamiltonians with atomic mean-field integrals (the X2CAMF schemes) at the equation-of-motion coupled-cluster singles and doubles level is reported. We adopt a version of the X2CAMF scheme with spin-orbit integrals correct to first order for the state-interaction calculations and a version correct to infinite order for the spinor-representation calculations. The differences between the state-interaction calculations with minimum active spaces to account for (quasi-)degeneracy and the spinor-representation calculations thus correspond to higher-order spin-orbit contributions. This state-interaction approach with scalar-relativistic effects accurately included in the reference functions and in the spin-orbit integrals is shown to exhibit robust performance for elements across the periodic table. On the other hand, the more rigorous spinor representation shows more rapid convergence with respect to the number of correlated electrons and is the preferred choice for accurate calculations for heavy elements.

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

Parameterized model to approximate theoretical collision-induced absorption band shapes for O2-O2 and O2-N2

Collision-induced absorption from vibronic transitions of O2-O2 and O2-N2 collision complexes is an important contributor to light-matter interaction in the atmosphere with relevance to radiative heat transfer and remote sensing. Despite in-depth studies involving quantum calculations of this effect, comparisons between experiment and theory would benefit from less computationally burdensome calculations that closely approximate the temperature dependence of the theoretical band shape and intensity. Accordingly, we present a parameterized representation of recent quantum calculations for collision-induced absorption by O2-O2 and O2-N2 about the 1.27 μm monomer band of O2. This approach leverages the theoretical decomposition of the spectra into exchange and spin-orbit contributions, with each component having a distinct temperature-dependent band shape. Composite spectra are approximated as a linear combination of the theoretical profiles with seven adjustable parameters that scale the component intensities and their dependences on temperature. We demonstrate that this empirical representation can accurately simulate the theoretical calculations, and we present a global fit of the model to previously reported collision-induced absorption spectra (O2-O2, O2-N2, and O2-air) measured by cavity ring-down spectroscopy over the temperature range 271 K–332 K.

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.

Spin orbital reorientation transitions induced by magnetic field

Here we report on a new effect similar to the spin reorientation transition (SRT) that takes place at two magnetic fields of BSORT1 and BSORT2. The effect is observed in the magnetization curves of small Mn3+ magnetic clusters in the wurtzite GaN (being in a paramagnetic state) calculated using crystal field model approach. The obtained results suggest that the computed magnetic anisotropy (MA) reverses its sign on increasing B across BSORT. However, a detailed analysis shows that MA is unchanged for high magnetic fields. We show that the observed effect arises from the interplay of the crystalline environment and the spin–orbit coupling λSˆLˆ, therefore we name it spin orbital reorientation transition (SORT). The value of BSORT1 depends on the crystal field model parameters and the number of ions N in a given cluster, whereas BSORT2 is controlled mostly by the magnitude of the spin–orbit coupling λ. The explanation of SORT is given in terms of the spin MS and orbital momentum ML contributions to the total magnetization M=MS+ML. The similar effect should also be present in other materials with not completely quenched (non zero) orbital angular momentum L, a uniaxial magnetic anisotropy and the positive value of λ.

Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy.

The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

Phonon, electron, and magnon excitations in antiferromagnetic L10 -type MnPt

Antiferromagnetic $L{1}_{0}$-type MnPt is a material with relatively simple crystal and magnetic structures, recently attracting interest due to its high N\'eel temperature and wide usage as a pinning layer in magnetic devices. While it is experimentally well characterized, the theoretical understanding is much less developed, in part due to the challenging accuracy requirements dictated by the small underlying energy scales that govern magnetic ordering in antiferromagnetic metals. In this paper, we use density functional theory, the Korringa-Kohn-Rostoker formalism, and a Heisenberg model to establish a comprehensive theoretical description of antiferromagnetic $L{1}_{0}$-type MnPt, along with accuracy limits, by thoroughly comparing to available literature data. Our simulations show that the contribution of the magnetic dipole interaction to the magnetocrystalline anisotropy energy of ${K}_{1}=1.07\ifmmode\times\else\texttimes\fi{}{10}^{6}$ J/m${}^{3}$ is comparable in magnitude to the spin-orbit contribution. Using our result for the magnetic susceptibility of $5.25\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, a lowest magnon frequency of about 2.02 THz is predicted, confirming THz spin dynamics in this material. From our data for electron, phonon, and magnon dispersion, we compute the individual contributions to the total heat capacity and show that the dominant term at or above 2 K arises from phonons. From the Landau-Lifshitz-Gilbert equation, we compute a N\'eel temperature of 990--1070 K. Finally, we quantify the magnitude of the magneto-optical Kerr effect generated by applying an external magnetic field. Our results provide insight into the underlying physics, which is critical for a deep understanding of fundamental limits of the time scale of spin dynamics, stability of the magnetic ordering, and the possibility of magneto-optical detection of collective spin motion.

Role of tensor interaction as salvation of cluster structure in Ti44

Background: The $^{44}$Ti nucleus has been known to have a $^{40}$Ca+$\alpha$ cluster structure, and inversion doublet structure has been observed; however, $\alpha$ cluster structure tends to be washed out when the breaking of the $\alpha$ cluster is allowed due to the spin-orbit interaction. Nevertheless, $\alpha$ clustering in medium-heavy nuclei is quite a hot subject recently. Purpose: The tensor interaction has been known to play an essential role in the strong binding of the $^4$He nucleus, which induces the two-particle-two-hole (2p2h) excitation. Since this excitation is blocked when another nucleus approaches, it is worthwhile to show whether the tensor effect works to keep the distance between $^4$He and $^{40}$Ca and becomes the salvation of the clustering in $^{44}$Ti. Methods: The spin-orbit effect is included in the cluster model by using the antisymmetrized quasi cluster model (AQCM) developed by the authors. We have also developed an improved version of the simplified method to include the tensor contribution ($i$SMT), which allows us to estimate the tensor effect within the cluster model. The competition of these two is investigated in the medium-heavy mass region for the first time. Results: According to AQCM, the spin-orbit interaction completely breaks the $\alpha$ cluster and restores the symmetry of $jj$-coupling shell model when the $\alpha$ cluster approaches the $^{40}$Ca core. On the other hand, $i$SMT gives a large distance between $\alpha$ and $^{40}$Ca due to the tensor effect. Conclusions: In $^{44}$Ti, because of the strong spin-orbit and tensor contributions, two completely different configurations ($jj$-coupling shell model and cluster states) almost degenerate, and their mixing becomes important.

Optical and magnetic response of ultrathin film topological insulators in tilted magnetic field

Faraday’s rotation and magnetic susceptibility of an ultrathin film of topological insulator, placed in tilted magnetic field, are studied. A Hall effect analogue is studied in terms of Faraday’s rotation. It is an isotropic response and tunable with magnetic field. Susceptibility has three contributions; spin, orbital and spin–orbital. All three contributions are calculated for magnetic field tilted at an angle θ with respect to the perpendicular axis on the plane. Spin susceptibility for low temperature varies directly with Fermi energy, orbital part show diamagnetic divergence and spin orbital contribution arises as a step function at Fermi energy.

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.

Variational and parquet-diagram calculations for neutron matter. IV. Spin-orbit interactions and linear response

We develop the parquet-diagram summation method for neutron matter interacting via potentials that include spin, tensor, and spin-orbit components. For that purpose, we derive an exact expression for the sum of all ring-diagrams in terms effective local particle-hole interactions involving the above four operators. The parquet equations are closed by deriving the spin-orbit contribution to that particle-hole interaction. We show that many-body correlations screen the bare spin-orbit potential considerably, and the corrections of that screened spin-orbit potential to the other three interaction channels are quite small. We apply our method to the calculation of the response of neutron matter to density and both longitudinal and transverse spin-dependent external fields.

Magnon-phonon interaction and the underlying role of the Pauli exclusion principle

The magnon-phonon interaction is receiving growing attention due to its key role in spin caloritronics and the emerging field of acoustic spintronics. At resonance, this magnetoelastic interaction forms magnon polarons, which underpin exotic phenomena such as magnonic heat currents and phononic spin, but is mostly investigated using mesoscopic spin-lattice models. Motivated to integrate the magnon-phonon interaction into first-principles many-body electronic structure theory, we set out to derive the exchange contribution, which is subtler than the spin-orbit contribution, using Schwinger functional derivatives. To avoid having to solve the famous Hedin-Baym equations self-consistently, the phonons are treated as perturbations to the electronic structure. A formalism based on imposing a crossing-symmetric electron-electron interaction is developed in order to treat charge and spin on equal footing to respect the Pauli exclusion principle. Due to spin conservation, the magnon-phonon interaction first enters to second order through the magnon-magnon interaction, which renormalizes the magnons. We show by iteration that the magnon-magnon interaction contains a ``screened $T$ matrix'' term and an arguably more important term which, in the local-spin limit, enables first-principles phonon emission and absorption amplitudes, predicted by phenomenological magnetoelastic models. These terms are, respectively, of first and second order in the screened collective four-point interaction $\mathcal{W}$---a crossing-symmetric analog of Hedin's $W$. Proof-of-principle results are presented at varying temperatures for an isotropic magnon spectrum in three dimensions in the presence of a flat optical phonon branch.

Magnetic response of metallic nanoparticles: Geometric and weakly relativistic effects

While the large paramagnetic response measured in certain ensembles of metallic nanoparticles has been assigned to orbital effects of conduction electrons, the spin-orbit coupling has been pointed out as a possible origin of the anomalously large diamagnetic response observed in other cases. Such a relativistic effect, arising from the inhomogeneous electrostatic potential seen by the conduction electrons, might originate from the host ionic lattice, impurities, or the self-consistent confining potential. Here we theoretically investigate the effect of the spin-orbit coupling arising from the confining potential, quantifying its contribution to the zero-field magnetic susceptibility and gauging it against the ones generated by other weakly-relativistic corrections. Two ideal geometries are considered in detail, the sphere and the half-sphere, focusing on the expected increased role of the spin-orbit coupling upon a symmetry reduction, and the application of these results to actual metallic nanoparticles is discussed. The matrix elements of the different weakly-relativistic corrections are obtained and incorporated in a perturbative treatment of the magnetic field, leading to tractable semi-analytical and semiclassical expressions for the case of the sphere, while a numerical treatment becomes necessary for the half-sphere. The correction to the zero-field susceptibility arising from the spin-orbit coupling in a single sphere is quite small, and it is dominated by the weakly-relativistic kinetic energy correction, which in turn remains considerably smaller than the typical values of the nonrelativistic zero-field susceptibility. Moreover, the spin-orbit contribution to the average response for ensembles of nanoparticles with a large size dispersion is shown to vanish. The symmetry reduction in going from the single sphere to the half-sphere does not translate into a significant (...)

Electron Transport Through Two Branch Interferometer with Rashba Spin Orbit Interaction

In this paper, a theoretical model for electron transport through two branch interferometer with one quantum dot in each of its arms has been considered. Both a magnetic flux applied on the circuit and the Rashba spin orbit interaction inside the two dots are taken into account, Rashba spin-orbit interaction contribution are exhibited obviously in the double quantum dots system for the thermoelectric effect, by varying the temperature of the leads , we calculate the conductance (G) and the thermopower (S).