Spin-orbit Coupling Parameter Research Articles

Temperature effect and Rashba effect of polaron in a parabolic quantum well

Using Tokuda’s improved linear combination operator method and variational technique, the expression of the polaron effective mass in an parabolic quantum well is derived. Due to the spin-orbit interaction, the effective mass of polaron splits into two branches. The dependence of effective mass on temperature and mean number phonons is discussed by numerical calculation. The effective mass of polaron is an increasing function of temperature and mean number phonons. The absolute value of total spin splitting effective mass increases with the increase in temperature and spin-orbit coupling parameter, and decreases with the increase in velocity. Due to the heavy hole characteristic, the spin splitting effective mass is negative.

EPR parameters and optical spectrum of α-Al2O3:Ti3+ with dynamic Jahn-Teller effect

The quenching phenomenon of trigonal crystal field (CF), spin–orbit (SO) coupling operators, and orbital operators reflected in electron paramagnetic resonance (EPR) parameters and energy splitting intervals observed in experiments of α-Al2O3:Ti3+ is theoretically investigated by the calculation of EPR g factors and the energy differences of the lowest three levers E3/2, 1E1/2 and 2E1/2 with the formulas derived with high-order perturbation method. In the calculation, the coupling of 2T2g and 2Eg with e vibrational model of dynamic Jahn-Teller effect are considered. The calculated results are in agreement with the experimental values. The local defect structure around Ti3+ ions (bond lengths and angles of [TiO6]9-) and trigonal CF parameters ν and v′ are determinedand the covalence effects on SO coupling parameters ζ, ζ’ and orbital reduction parameters k、k’ are determined also.

Spin and charge persistent currents in a Kane Mele α-T 3 quantum ring

We conduct a thorough study of different persistent currents in a spin-orbit coupled α-T 3 (pseudospin-1) fermionic quantum ring (QR) that smoothly interpolates between graphene (α = 0, pseudospin-1/2) and a dice lattice (α = 1, pseudospin-1) in presence of an external perpendicular magnetic field. In particular, we have considered effects of intrinsic (ISOC) and Rashba spin-orbit couplings (RSOC) that are both inherent to two dimensional quantum structures and yield interesting consequences. The energy levels of the system comprise of the conduction bands, valence bands, and flat bands which show non-monotonic dependencies on the radius, R of the QR, in the sense that, for small R, the energy levels vary as 1/R , while the variation is linear for large R. The dispersion spectra corresponding to zero magnetic field are benchmarked with those for finite fields to enumerate the role played by the spin–orbit coupling terms therein. Further, it is noted that the flat bands demonstrate dispersive behavior, and hence is able to contribute to the transport properties only for finite ISOC. Moreover, RSOC yields spin-split bands, thereby contributing to the spin-resolved currents. The charge and the spin-polarized persistent currents are hence computed in presence of these spin-orbit couplings. The persistent currents in both the charge and spin sectors oscillate as a function of the magnetic field with a period equal to the flux quantum, as they should be; although they now depend upon the spin–orbit coupling parameters. Interestingly, the ISOC distorts the current profiles, owing to the distribution of the flat band caused by it, whereas RSOC alone preserves the flat band and hence a perfect periodicity of the current characteristic is maintained. Further, we have explored the role played by the parameter α in our entire analysis to enable studies while interpolating from graphene to a dice lattice.

Exchange-correlation effects on the structural, electronic, and optical properties of Sr2RuO4 using DFT calculations

We perform a first principle study on the electronic, structural, and optical properties of Sr2RuO4 by various functionals: LSDA, GGA, GGA-mBJ, PBE-D3, optB88-vdW, vdW-DF2 and HSE06 using the plane-wave method of density functional theory (DFT) in the presence of the spin-orbit coupling (SOC) and Coulomb interaction parameter, U. The dynamical stability and the thermal stability are calculated via phonon dispersions and ab initio molecular dynamics simulations, respectively. The band structure calculation and the orbital-resolved density of states of LSDA and the schemes of GGA reveal different ground state. For GGA-mBJ and the hybrid functional, there is an indirect gap in the band structure. In the case of vdW functionals, our findings are in agreement with GGA. We compute a variety of optical responses and compare them with existing experimental studies. The results of the dielectric function suggest that GGA-mBJ (LSDA and GGA) may better account for the experimental findings in the presence (absence) of SOC at the infrared spectral region (infrared and visible spectral regions). We observe that the optical responses are strongly influenced by SOC and intraband transitions. Among the optical spectra, we focus more on the electron energy loss spectrum, which depends on the excitations, the exchange-correlation effects, and the multiorbital nature of Sr2RuO4.

The dynamical stripes in spin–orbit coupled Bose–Einstein condensates with Josephson junctions

The Josephson dynamics of the Bose–Einstein condensation with Raman-induced spin–orbit coupling is investigated. A quasi-1D trap is divided into two reservoirs by an optical barrier. Before the tunneling between the reservoirs is turned on, the system stays in its equilibrium ground state, which displays a rich phase diagram for different spin–orbit coupling parameters and interaction strengths. In this work we focus on the plane wave phase and the stripe phase. Our calculation shows that, when the tunneling is turned on, the plane wave phase evolves into a dynamical stripe phase, that is, the density of the particle changes from uniform to periodically modulated. Basically, this stripe is described by a sine function and the wave length, the amplitude and the initial phase of the function are all varying with time. If the system stays in stripe phase initially, the stripes become “sliding” when the tunneling is turned on, which reflects the running of one of the phases of the wave function.

The Synthesis, Crystal Structure, and Magnetic Properties of Mono-Scorpionate Eu(III) Complexes

Three Eu3+ complexes containing a neutral tripodal ligand possessing a predictable coordination mode have been obtained and studied. The trispyrazolylmethane complexes have an aqua ligand in the coordination sphere, forming both the mononuclear species [Eu(HCPz3)H2O(NO3)3] and the dimer [Eu(HCPz3)H2O(CF3SO3)3]2, having a Chinese lantern structure, whereas the use of the methylated tripod leads to the water-free complex, [Eu(HC(PzMe2)3)(NO3)3]. A qualitative analysis of the magnetic susceptibility of polycrystalline samples demonstrated that the magnetic properties can be described using a simple Van Vleck formula with spin–orbit coupling parameter (λ = 383 ÷ 406 cm−1) close to the values for free Eu3+ ions. The stereochemical analysis of the coordination environment of [Ln(HC(PzMe2)3)(NO3)3] has shown that these complexes can be used as diamagnetic model systems to obtain information on the crystal field effects in the paramagnetic monoradical complexes, [LnRad(NO3)3], since both types of compounds have the same type of coordination polyhedron (symmetry point group D3h) and very close Ln–donor atom distances.

Luminescence of isoelectronic lanthanide pairs (Ln2+/Ln3+): A relative compression factor for isoelectronic Ln 4fn levels

Luminescent trivalent lanthanides (Ln3+) are utilised extensively in photonic and optoelectronic devices. Luminescent divalent lanthanides (Ln2+) are less frequently applied, despite their desirable 5d electronic properties and similar 4f electronic properties. We report on the luminescence of several isoelectronic lanthanide pairs (Ln3+/Ln2+) that possess the same 4fn configurations but different nuclear charges. The intraconfigurational and interconfigurational transitions of divalent Nd, Sm, Eu, Dy, Ho, Tm and Yb in NaMgF3 are compared to those transitions of trivalent counterparts in NaMgF3 and similar hosts. The 4fn(2S+1LJ) levels of Ln2+ ions are compressed by a factor ξ, relative to the isoelectronic Ln3+. The factor varies within each 4fn configuration with the energy of excited 2S’+1LJ’ states. We define an alternative factor ξ′ that corrects for the intra-ion dependence by introducing a power law dependence on the excited state energies. The inter-ion dependence correlates with the spin-orbit coupling parameters of the isoelectronic ions.

Twist-angle dependent proximity induced spin-orbit coupling in graphene/topological insulator heterostructures

The proximity-induced spin-orbit coupling (SOC) in heterostructures of twisted graphene and topological insulators (TIs) Bi$_2$Se$_3$ and Bi$_2$Te$_3$ is investigated from first principles. To build commensurate supercells, we strain graphene and correct thus resulting band offsets by applying a transverse electric field. We then fit the low-energy electronic spectrum to an effective Hamiltonian that comprises orbital and spin-orbit terms. For twist angles 0$^\circ\leq\Theta \lessapprox 20^\circ$, we find the dominant spin-orbit couplings to be of the valley-Zeeman and Rashba types, both a few meV strong. We also observe a sign change in the induced valley-Zeeman SOC at $\Theta\approx 10^\circ$. Additionally, the in-plane spin structure resulting from the Rashba SOC acquires a non-zero radial component, except at $0^\circ$ or $30^\circ$. At $30^\circ$ the graphene Dirac cone interacts directly with the TI surface state. We therefore explore this twist angle in more detail, studying the effects of gating, TI thicknesses, and lateral shifts on the SOC parameters. We find, in agreement with previous results, the emergence of the proximitized Kane-Mele SOC, with a change in sign possible by electrically tuning the Dirac cone within the TI bulk band gap.

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.

Unraveling the T1 formation in mono-arm styrylbenzene heteroanalogues

We present a theoretical investigation of the nonradiative relaxation dynamics associated with the low-lying excited electronic states of mono-arm styrylbenzene heteroanalogues. These molecules possess near-degenerate S 1 (bright π π ∗ ) and S 2 (dark n π ∗ ) states, enabling intersystem crossing via both states upon photoexcitation to S 1 . Singlet-triplet energy gaps and associated spin–orbit coupling parameters suggest favorable intersystem crossing via S 2 → T 5 . The nuclear wavepacket initiated at the Franck–Condon point of the receiver triplet state (T 5 ) decays rapidly to lower triplet states via accessible multiple conical intersections, indicating the ultrafast formation of T 1 in these molecules. Our findings show that these molecules would transfer energy to molecular oxygen via T 1 . • T 1 formation pathways of mono-arm styrylbenzene heteroanalogues are investigated. • TD-DFT calculations and SOC values reveal S 2 -T 5 as the triplet generating channel. • Conical intersections in the triplet manifold lead to ultrafast internal conversion.

Probing details of spin-orbit coupling through Pauli spin blockade

Spin-orbit interaction (SOI) plays a fundamental role in many low-dimensional semiconductor and hybrid quantum devices. In the rapidly evolving field of semiconductor spin qubits, SOI is an essential ingredient that can allow for ultrafast qubit control. The exact manifestation of SOI in a given device is, however, often both hard to predict theoretically and probe experimentally. Here, we develop a detailed theoretical connection between the leakage current through a double quantum dot in Pauli spin blockade and the underlying SOI in the system. We present a general analytic expression for the leakage current, which allows to connect experimentally observable features to both the magnitude and orientation of an effective spin-orbit field acting on the moving carriers. Motivated by the large recent interest in hole-based quantum devices, we further zoom in on the case of Pauli blockade of hole spins, assuming a strong transverse confinement potential. In this limit we also find an analytic expression for the current at low external magnetic field, that includes the effect of hyperfine coupling of the hole spins to randomly fluctuating nuclear spin baths. This result can be used to extract information about both hyperfine and spin-orbit coupling parameters for hole spins in devices with a significant fraction of nonzero nuclear spins.

Magnetic Toroidal Moment under Partial Magnetic Order in Hexagonal Zigzag-Chain Compound Ce3TiBi5

We theoretically investigate an antiferromagnetic structure in a hexagonal zigzag-chain compound Ce$_3$TiBi$_5$, which shows a linear magnetoelectric effect in metals and an unfamiliar temperature dependence of magnetic susceptibility. We find a partial magnetic order as a coexistence of a nonmagnetic zigzag chain and staggered antiferromagnetic zigzag chains. The latter accompany in-plane magnetic toroidal dipole moments which are responsible for the observed behaviors. We show that magnetic frustration arising from competing exchange interactions plays an important role to realize such a partial magnetic order. Furthermore, we present the important spin-orbit coupling parameters to induce the physical phenomena driven by the magnetic toroidal dipole moment, such as the linear magnetoelectric effect and nonlinear transport.

Detailed structural and topological analysis of SnBi2Te4 single crystal

We report herein the successful synthesis of the topological material SnBi2Te4 in single-crystal form. Phase purity and unidirectional growth are evident from X-ray diffraction (XRD) patterns acquired from a powdered sample and a crystal flake. The crystalline morphology has also been visualized by acquiring a field-emission scanning electron microscope (FESEM) image. The crystal has been thoroughly characterized by means of Raman spectroscopy and X-ray photoelectron spectroscopy (XPS) measurements. The topological properties of SnBi2Te4 have been probed through magneto-transport measurements. SnBi2Te4 has been found to exhibit a small but non-saturating magneto-resistance (MR) up to ±12 T. The low-field magnetoconductivity (MC) of SnBi2Te4 at 2 K can be well explained through the Hikami–Larkin–Nagaoka (HLN) formalism, which confirms the presence of a weak anti-localization (WAL) effect in its crystal. Moreover, the non-trivial topological character has been evidenced through first-principles calculations using density functional theory (DFT), with and without spin-orbit coupling (SOC) protocols. A significant change in the bulk electronic band structure is observed upon the inclusion of SOC parameters, signifying topological properties of SnBi2Te4. Its topological non-trivial character has also been verified through calculation of Z2 invariants and the surface states spectrum in the (111) plane.

Full-zone persistent spin textures with giant spin splitting in two-dimensional group IV–V compounds

Persistent spin texture (PST), a property of solid-state materials maintaining unidirectional spin polarization in the momentum k-space, offers a route to deliver the necessary long carrier spin lifetimes through the persistent spin helix (PSH) mechanism. However, most of the discovered PST locally occurred in the small part around certain high symmetry k-points or lines in the first Brillouin zone (FBZ), thus limiting the stability of the PSH state. Herein, by symmetry analysis and first-principles calculations, we report the emergence of full-zone PST (FZPST), a phenomenon displaying the PST in the whole FBZ, in the two-dimensional group IV–V (A = Si, Sn, Ge; B = Bi, Sb) compounds. Due to the existence of the in-plane mirror symmetry operation in the wave vector point group symmetry for the arbitrary in the whole FBZ, fully out-of-plane spin polarization is observed in the k-space, thus maintaining the FZPST. Importantly, we observed giant spin splitting in which the PST sustains, supporting large spin–orbit coupling parameters and small wavelengths of the PSH states. Our analysis demonstrated that the FZPST is robust for the non-degenerate bands, which can be effectively controlled by the application of an external electric field, thus offering a promising platform for future spintronic applications.

Elementary excitations in a spin–orbit-coupled spin-1 Bose–Einstein condensate

While a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC) has been experimentally observed, its elementary excitations remain unclear in the stripe phase. Here, we systematically study the elementary excitations in three distinct phases of a spin–orbit-coupled spin-1 BEC. We find that the excitation spectrum as well as the corresponding static response function and structure factor depend strongly on spin–orbit coupling parameters such as the quadratic Zeeman field and the Rabi frequency. In the stripe phase, besides two gapless Goldstone modes, we show the existence of roton excitations. Finally, we demonstrate that quantum phase transitions between these different phases including the zero-momentum, plane wave and stripe phases are characterized by the sound velocities and the quantum depletion.

DFTB Parameters for the Periodic Table: Part III, Spin-Orbit Coupling

Spin-orbit coupling (SOC) is crucially important for the correct description of the electronic structure and transport properties of inorganic semiconductors, and for assessing topological properties as in topological insulators. We present a consistent set of SOC parameters for the density-functional based tight-binding (DFTB) method covering the elements throughout the periodic table. The parameters are based on atomic SOC data calculated at the level of density-functional theory (DFT). We tested these parameters for representative systems with significant SOC, including transition metal dichalcogenide two-dimensional crystals, III-V bulk semiconductors, and topological insulators. Our parameterization opens the door for DFTB-based electronic structure and transport calculations of very large systems, such as twisted van der Waals heterostructures.

Synthesis and Magnetic Properties of Antimony-Ligated Co(II) Complexes: Stibines versus Phosphines

Herein, we test the hypothesis that neutral, heavy-atom stibine donors can increase the extent of spin-orbit coupling on light, 3d transition metal. To this end, we developed a novel synthetic route toward coordinating a paramagnetic 3d metal ion─cobalt(II)─with neutral stibine ligands. Such complexes have not been reported in the literature due to the weak σ donor strength of stibines and the hard-soft mismatch between a 3d metal and a 5p ligand─which herein has been overcome using alkylated Sb donors. Magnetometry of [(SbiPr2Ph)2Co(I)2] (1) reveals that the stibine complex 1 exhibits a higher magnitude D value (D = |24.96| cm-1) than the spectroscopically derived value for the corresponding phosphine complex 3 (D = -13.13 cm-1), indicative of large zero-field splitting. CASSCF/NEVPT2 calculations corroborate the experimental D values for 1 and 3, predicting D = -31.9 and -8.9 cm-1, respectively. A re-examination of magnetic parameters across the entire series [(ER3)2Co(X)2] (E = P → Sb; X = Cl → I) reveals that (i) increasingly heavy pnictogens lead to an increased X-Co-X bond angle, which is correlated with larger magnitude D values, and (ii) for a given X-Co-X bond angle, the D value is always higher in the presence of a heavy pnictogen as compared with a heavy halide. Ab initio ligand field theory calculations for 1 (stibine complex) and 3 (phosphine complex) reveal no substantial differences in spin-orbit coupling (ζ = 479.2, 480.2 cm-1) or Racah parameter (B = 947.5, 943.9 cm-1), an indicator of covalency. Thus, some "heavy atom effect" on the D value beyond geometric perturbation is operative, but its precise mechanism(s) of action remains obscure.

Optical conductivity and far-field radiation of silicene

Silicene is a silicon analogue of graphene. From symmetry considerations, we develop the matrix of Hamiltonian, including spin-orbit coupling in silicene. This work analyzes the heat and angular momentum radiation from silicene through the theory of far-field radiation and optical conductivity. We discuss the relation between the radiation and spin-orbit coupling parameters. Our results show the effects of different parameters, such as temperature and sublattice potential, on optical conductivity and radiation of silicene. In particular, the threshold frequency of optical conductivity causes the appearance of the second peak in energy radiation spectrum. We also find that the ratio of the perpendicular electric field to the intrinsic spin-orbit coupling is related to the strength of angular momentum radiation, which may promote the application of silicene.

Intrinsic magnon Nernst effect in pyrochlore iridate thin films

We theoretically study the magnon spin thermal transport using a strong coupling approach in pyrochlore iridate trilayer thin films grown along the [111] direction. As a result of the Dzyaloshinskii-Moriya interaction (DMI), the spin configuration of the ground state is an all-in/all-out ordering on neighboring tetrahedra of the pyrochlore lattice. In such a state, the system has an inversion symmetry and a Nernst-type thermal spin current response is well defined. We calculate the temperature dependence of the magnon Nernst response with respect to the magnon band topology controlled by the spin-orbit coupling parameters and observe topologically protected chiral edge modes over a range of parameters. Our study complements prior work on the magnon thermal Hall effect in thin-film pyrochlore iridates and suggests that the [111] grown thin-film pyrochlore iridates are a promising candidate for thermal spin transport and spin caloritronic devices.

Comparing the effective enhancement of local and nonlocal spin-orbit couplings on honeycomb lattices due to strong electronic correlations

We investigate the interplay of electronic correlations and spin-orbit coupling (SOC) for a one-band and a two-band honeycomb lattice model. The main difference between the two models concerning SOC is that in the one-band case the SOC is a purely non-local term in the basis of the $p_z$ orbitals, whereas in the two-band case with $p_x$ and $p_y$ as basis functions it is purely local. In order to grasp the correlation effects on non-local spin-orbit coupling, we apply the TRILEX approach that allows to calculate non-local contributions to the self-energy approximatively. For the two-band case we apply dynamical mean-field theory. In agreement with previous studies, we find that for all parameter values in our study, the effect of correlations on the spin-orbit coupling strength is that the bare effective SOC parameter is increased. However, this increase is much weaker in the non-local than in the local SOC case. Concerning the TRILEX method, we introduce the necessary formulas for calculations with broken SU(2) symmetry.