Spin-orbit Coupling Parameter Research Articles

Fermionic Hubbard model with Rashba or Dresselhaus spin–orbit coupling

In this work, we investigate the possible dramatic effects of Rashba or Dresselhaus spin–orbit coupling (SOC) on the fermionic Hubbard model in a two-dimensional square lattice. In the strong coupling limit, it leads to the rotated antiferromagnetic Heisenberg model which is a new class of quantum spin model. For a special equivalent class, we identify a new spin–orbital entangled commensurate ground (Y-y) state subject to strong quantum fluctuations at T = 0. We evaluate the quantum fluctuations by the spin wave expansion up to order . In some SOC parameter regimes, the Y-y state supports a massive relativistic incommensurate magnon (C-IC) with its two gap minima positions continuously tuned by the SOC parameters. The C-IC magnons dominate all the low temperature thermodynamic quantities and also lead to the separation of the peak positions between the longitudinal and the transverse spin structure factors. In the weak coupling limit, any weak repulsive interaction also leads to a weak Y-y state. There is only a crossover from the weak to the strong coupling. High temperature expansions of the specific heats in both weak and strong coupling are presented. The dramatic roles to be played by these C-IC magnons at generic SOC parameters or under various external probes are hinted at. Experimental applications to both layered noncentrosymmetric materials and cold atoms are discussed.

Phase control of Goos-Hänchen shifts in a fixed structure with carbon-nanotube quantum dot nanostructure

In this article we proposed a new model based on carbon-nanotube quantum dot (CNT QD) nanostructure for controlling the Goos-Hanchen (GH) shifts in reflected and transmitted light beams. In our calculation we introduce the spin-orbit coupling parameter in the CNT QD nanostructure. Our results show that owing to the presence of spin-orbit coupling, Rabi frequency of magnetic field, coupling laser field and relative phase between applied fields, the enhanced GH shifts in reflected and transmitted light beams can be achieved. Moreover, we demonstrate that such enhanced GH shifts are simultaneously obtained for both reflected and transmitted light beams. At the end, we discuss the impact of intracavity thickness on the GH shift properties of reflected and transmitted light beams. We hope that our proposed model may be used for future developments based on CNT QD nanostructures.

Fröhlich polaron in nanowire with Rashba and Dresselhaus spin-orbit couplings

We use the Lee-Low-Pines variational method to clarify the effects of the spin-orbit couplings on the properties of the quasi-one-dimensional Fröhlich polaron in the weak and intermediate coupling limits of the electron-phonon interaction. Polaron energy and polaron shift are investigated numerically and analytic expressions for the polaron self-energy and effective mass are obtained as functions of the spin-orbit coupling parameters. We have shown that the basic parameters of the polaron in nanowire can be effectively manipulated by the Rashba and Dresselhaus spin-orbit couplings, and thus they can be used for controlling the various physical processes in nanowires.

Model spin-orbit coupling Hamiltonians for graphene systems

We present a detailed theoretical study of effective spin-orbit coupling (SOC) Hamiltonians for graphene based systems, covering global effects such as proximity to substrates and local SOC effects resulting, for example, from dilute adsorbate functionalization. Our approach combines group theory and tight-binding descriptions. We consider structures with global point group symmetries $D_{6h}$, $D_{3d}$, $D_{3h}$, $C_{6v}$, and $C_{3v}$ that represent, for example, pristine graphene, graphene mini-ripple, planar boron-nitride, graphene on a substrate and free standing graphone, respectively. The presence of certain spin-orbit coupling parameters is correlated with the absence of the specific point group symmetries. Especially in the case of $C_{6v}$---graphene on a substrate, or transverse electric field---we point out the presence of a third SOC parameter, besides the conventional intrinsic and Rashba contributions, thus far neglected in literature. For all global structures we provide effective SOC Hamiltonians both in the local atomic and Bloch forms. Dilute adsorbate coverage results in the local point group symmetries $C_{6v}$, $C_{3v}$, and $C_{2v}$ which represent the stable adsorption at hollow, top and bridge positions, respectively. For each configuration we provide effective SOC Hamiltonians in the atomic orbital basis that respect local symmetries. In addition to giving specific analytic expressions for model SOC Hamiltonians, we also present general (no-go) arguments about the absence of certain SOC terms.

Spin-orbit coupling of sp2 nanocarbons and magnetism of fullerene C60 in view of spin peculiarities of unrestricted Hartree–Fock solution

ABSTRACTThe paper presents the first application of unrestricted Hartree–Fock formalism to the consideration of spin-orbit coupling (SOC) of open-shell systems in general and sp2 nanocarbons in particular. The SOC parameters determination is exhibited on the example of stretched ethylene. g-Factor determination addresses fullerene C60 due to its peculiar “paradiamagnetic” behavior at low temperature characterized by a set of local spins with different g-factors. The approach application has allowed not only to suggest a reliable explanation of the factor variability but to supplement it by a quantitative agreement with experimental data.

Spin injection beyond the diffusive limit in the presence of spin-orbit coupling

Spin injection from epitaxial iron into InGaAs/InAs quantum wells is observed using an all-electric nonlocal setup. From the choice of material, a significant spin-orbit interaction (SOI) is expected. The contact separation of the spin-valve devices is in the order of the mean free path so that the transport is at the transition between diffusive and ballistic. With an established purely diffusive model a spin-injection efficiency of $77%$ is determined from the data. This value is very large compared to previous observations on diffusive spin-valve devices on similar material systems. Motivated by similar results on ballistic spin-valve devices in a material system with small spin-orbit coupling, a recent model was suggested in which a ballistic spin-dephasing length was pointed out to be the crucial length scale. With this model and an experimentally determined spin-orbit coupling parameter of $\ensuremath{\alpha}=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ eV m, very high spin-injection efficiencies are still determined in our quantum wells. We suggest that the spin-dephasing length to be used in the model must be larger due to the crystallographic anisotropy of the spin-orbit coupling, i.e., in our setup the SOI stabilizes the spin in the crystal direction of the spin-polarized current.

Spin-orbit coupling mediated tunable electron heat capacity of quantum wells

The heat capacity of conduction electrons obtained from the Sommerfeld expansion is shown to be tunable via the Rashba and Dresselhaus spin-orbit coupling parameters. Using AlInSb/InSb/AlInSb as a representative heterostructure with alterable well and asymmetric barrier regions, the heat capacity is higher for the spin-down electrons and suffers a reduction for wider wells. A further lowering is obtained through the application of a uniaxial strain. Finally, we suggest a method to determine the spin lifetimes for spin relaxing via the D'yakonov-Perel' mechanism from experimental estimates of thermodynamic potentials such as the Helmholtz free energy and the heat capacity.

The excited-state structure, vibrations, lifetimes, and nonradiative dynamics of jet-cooled 1-methylcytosine

We have investigated the S0 → S1 UV vibronic spectrum and time-resolved S1 state dynamics of jet-cooled amino-keto 1-methylcytosine (1MCyt) using two-color resonant two-photon ionization, UV/UV holeburning and depletion spectroscopies, as well as nanosecond and picosecond time-resolved pump/delayed ionization measurements. The experimental study is complemented with spin-component-scaled second-order coupled-cluster and multistate complete active space second order perturbation ab initio calculations. Above the weak electronic origin of 1MCyt at 31 852 cm-1 about 20 intense vibronic bands are observed. These are interpreted as methyl group torsional transitions coupled to out-of-plane ring vibrations, in agreement with the methyl group rotation and out-of-plane distortions upon 1ππ∗ excitation predicted by the calculations. The methyl torsion and ν1' (butterfly) vibrations are strongly coupled, in the S1 state. The S0 → S1 vibronic spectrum breaks off at a vibrational excess energy Eexc ∼ 500 cm-1, indicating that a barrier in front of the ethylene-type S1⇝S0 conical intersection is exceeded, which is calculated to lie at Eexc = 366 cm-1. The S1⇝S0 internal conversion rate constant increases from kIC = 2 ⋅ 109 s-1 near the S1(v = 0) level to 1 ⋅ 1011 s-1 at Eexc = 516 cm-1. The 1ππ∗ state of 1MCyt also relaxes into the lower-lying triplet T1 (3ππ∗) state by intersystem crossing (ISC); the calculated spin-orbit coupling (SOC) value is 2.4 cm-1. The ISC rate constant is 10-100 times lower than kIC; it increases from kISC = 2 ⋅ 108 s-1 near S1(v = 0) to kISC = 2 ⋅ 109 s-1 at Eexc = 516 cm-1. The T1 state energy is determined from the onset of the time-delayed photoionization efficiency curve as 25 600 ± 500 cm-1. The T2 (3nπ∗) state lies >1500 cm-1 above S1(v = 0), so S1⇝T2 ISC cannot occur, despite the large SOC parameter of 10.6 cm-1. An upper limit to the adiabatic ionization energy of 1MCyt is determined as 8.41 ± 0.02 eV. Compared to cytosine, methyl substitution at N1 lowers the adiabatic ionization energy by ≥0.32 eV and leads to a much higher density of vibronic bands in the S0 → S1 spectrum. The effect of methylation on the radiationless decay to S0 and ISC to T1 is small, as shown by the similar break-off of the spectrum and the similar computed mechanisms.

Characterization of spin-orbit coupling in gated wire structures using Al2O3/In0.75Ga0.25As/In0.75Al0.25As inverted heterojunctions

Gated parallel wire structures obtained from inverted-modulation-doped heterojunctions made of high-In-content metamorphic InGaAs/InAlAs were investigated. The narrowest wire width was found to be ∼190 nm made using electron beam lithography and reactive ion etching. Magneto-transport was measured at low temperatures. Weak anti-localization and suppression with applied negative gate voltages were observed in low-mobility wide wires (1360 nm), which were considered for a two-dimensional system. The dependence on the gate voltage of spin-orbit coupling parameters was also obtained by fitting. The parameters decreased as the negative gate voltages increased. The trend might originate not from the electron system at the InGaAs/InAlAs interface but from the other electron system accumulated at the Al2O3/InGaAs interface, which can also contribute to conductivity. In high-mobility narrow wires (190 nm), which are close to a one-dimensional system, weak anti-localization peaks were still observed, indicating strong spin-orbit coupling. In addition, the critical widths of wires corresponding to zero conductance were estimated to be <100 nm. Therefore, our metamorphic modulation doped heterojunctions seem suitable for smaller spin-FETs.

Resonances in the rotational constants of Cs2 levels analysed by an improved-Bv-formula associated to a 2-channel model

Spin-orbit coupling in long-range molecular levels of Cs2 assigned to resonances in the rotational constant spectrum (Lignier L. et al., Phys. Chem. Chem. Phys., 13 (2011) 18910; Pichler M. et al., J. Chem. Phys., 121 (2004) 1796) has been analyzed with a model which associates an improved-Bv-formula (established here) and a 2-channel model. The approach explains the Lorentzian shape of the observed resonances superimposing a non-horizontal background and the fit of the Bv-spectrum allows us to deduce the spin-orbit coupling parameters. We compare this approach with an analysis of the binding energies using the vibrational quantum defect (VQD). The good agreement between the methods lets one conclude that the improved-Bv-formula associated with a 2-channel model provides a pertinent approach for analyzing coupled molecular series.

Effect of Rashba spin–orbit coupling on the electronic, thermodynamic, magnetic and transport properties of GaAs, InAs and InSb quantum dots with Gaussian confinement

The effect of Rashba spin–orbit interaction on the electronic, thermodynamic, magnetic and transport properties of a one-electron Gaussian quantum dot is investigated in the presence of a magnetic field and its interaction with the electron spin using the canonical ensemble approach. The temperature-dependent energy, magnetization, susceptibility, specific heat and the persistent current are calculated as a function of the spin–orbit coupling parameter. The results are applied to GaAs, InAs and InSb quantum dots.

Properties of spin–orbit-coupled Bose–Einstein condensates

The experimental and theoretical research of spin–orbit-coupled ultracold atomic gases has advanced and expanded rapidly in recent years. Here, we review some of the progress that either was pioneered by our own work, has helped to lay the foundation, or has developed new and relevant techniques. After examining the experimental accessibility of all relevant spin–orbit coupling parameters, we discuss the fundamental properties and general applications of spin–orbit-coupled Bose–Einstein condensates (BECs) over a wide range of physical situations. For the harmonically trapped case, we show that the ground state phase transition is a Dicke-type process and that spin–orbit-coupled BECs provide a unique platform to simulate and study the Dicke model and Dicke phase transitions. For a homogeneous BEC, we discuss the collective excitations, which have been observed experimentally using Bragg spectroscopy. They feature a roton-like minimum, the softening of which provides a potential mechanism to understand the ground state phase transition. On the other hand, if the collective dynamics are excited by a sudden quenching of the spin–orbit coupling parameters, we show that the resulting collective dynamics can be related to the famous Zitterbewegung in the relativistic realm. Finally, we discuss the case of a BEC loaded into a periodic optical potential. Here, the spin–orbit coupling generates isolated flat bands within the lowest Bloch bands whereas the nonlinearity of the system leads to dynamical instabilities of these Bloch waves. The experimental verification of this instability illustrates the lack of Galilean invariance in the system.

Theory of electronic and spin-orbit proximity effects in graphene on Cu(111)

We study orbital and spin-orbit proximity effects in graphene adsorbed to the Cu(111) surface by means of density functional theory (DFT). The proximity effects are caused mainly by the hybridization of graphene $\ensuremath{\pi}$ and copper $d$ orbitals. Our electronic structure calculations agree well with the experimentally observed features. We carry out a graphene-Cu(111) distance dependent study to obtain proximity orbital and spin-orbit coupling parameters, by fitting the DFT results to a robust low energy model Hamiltonian. We find a strong distance dependence of the Rashba and intrinsic proximity induced spin-orbit coupling parameters, which are in the meV and hundreds of $\ensuremath{\mu}\mathrm{eV}$ range, respectively, for experimentally relevant distances. The Dirac spectrum of graphene also exhibits a proximity orbital gap, of about 20 meV. Furthermore, we find a band inversion within the graphene states accompanied by a reordering of spin and pseudospin states, when graphene is pressed towards copper.

Judd–Ofelt analysis of β-NaGdF4: Yb3+, Tm3+ and β-NaGdF4:Er3+ single crystals

Hexagonal β-NaGdF4 single crystals were grown by the Bridgman technique, one doped with 5% Yb3+, 0.5% Tm3+ and the other with 1% Er3+. Based on polarized absorption spectra a Judd–Ofelt analysis was performed using the software RELIC. The energy barycenters of the room temperature absorption bands were used to refine the 4f wavefunctions in the intermediate coupling approximation, and obtain the Slater integrals F(2), (4), (6) and the spin–orbit coupling parameter ζ. The experimental oscillator strengths were fitted, using calculated matrix elements, to the three Judd–Ofelt parameters Ω2,4,6. The radiative lifetimes and branching ratios were determined and compared to experimental data. The oscillator strengths of selected transitions relevant to upconversion processes are discussed.

Periodic Trends in Lanthanide Compounds through the Eyes of Multireference ab Initio Theory.

Regularities among electronic configurations for common oxidation states in lanthanide complexes and the low involvement of f orbitals in bonding result in the appearance of several periodic trends along the lanthanide series. These trends can be observed on relatively different properties, such as bonding distances or ionization potentials. Well-known concepts like the lanthanide contraction, the double-double (tetrad) effect, and the similar chemistry along the lanthanide series stem from these regularities. Periodic trends on structural and spectroscopic properties are examined through complete active space self-consistent field (CASSCF) followed by second-order N-electron valence perturbation theory (NEVPT2) including both scalar relativistic and spin-orbit coupling effects. Energies and wave functions from electronic structure calculations are further analyzed in terms of ab initio ligand field theory (AILFT), which allows one to rigorously extract angular overlap model ligand field, Racah, and spin-orbit coupling parameters directly from high-level ab initio calculations. We investigated the elpasolite Cs2NaLn(III)Cl6 (Ln(III) = Ce-Nd, Sm-Eu, Tb-Yb) crystals because these compounds have been synthesized for most Ln(III) ions. Cs2NaLn(III)Cl6 elpasolites have been also thoroughly characterized with respect to their spectroscopic properties, providing an exceptionally vast and systematic experimental database allowing one to analyze the periodic trends across the lanthanide series. Particular attention was devoted to the apparent discrepancy in metal-ligand covalency trends between theory and spectroscopy described in the literature. Consistent with earlier studies, natural population analysis indicates an increase in covalency along the series, while a decrease in both the nephelauxetic (Racah) and relativistic nephelauxetic (spin-orbit coupling) reduction with increasing atomic number is calculated. These apparently conflicting results are discussed on the basis of AILFT parameters. The AILFT derived parameters faithfully reproduce the underlying multireference electronic structure calculations. The remaining discrepancies with respect to experimentally derived data are mostly due to underestimation of the ligand field splittings, while the dynamic correlation and nephelauxetic effects appears to be adequately covered by CASSCF/NEVPT2.

Influence of spin-orbit interaction on magnetic properties of fullerenes

The current paper is devoted to the consideration of s p 2-carbonaceous fullerenes molecules in a homogeneous magnetic field. Due to a reduction system symmetry in the magnetic field, the energy splitting gives rise dominant atomic structures in fullerene molecules with local symmetries. Spin-orbit interaction plays a crucial role in this phenomenon. The current paper is aimed at determine spin-orbit coupling parameters, as an energy E SO and a constant a SO as well as a Lande g-factor for the C60-based compounds in the magnetic field.

The Role of Spin-Orbit Coupling in the Double-Ionization Photoelectron Spectra of XCN(2+) (X = Cl, Br, and I).

The photoelectron spectra of XCN(2+) (X = Cl, Br, and I) were calculated employing ab initio electronic structure methods with high-level electron correlation and explicit treatment of spin-orbit coupling. Twelve scalar-relativistic excited states of the dicationic systems, calculated from state-averaged CASSCF/MRCI calculations, were used as the electronic basis to evaluate spin-orbit eigenstates. While the spin-orbit effects in ClCN(2+) are found to be negligible, the electronic spectroscopy of BrCN(2+) and ICN(2+) is significantly influenced by interstate spin-orbit coupling. Several electronic degeneracies are lifted, and many unexpected accidental degeneracies occurred due to the spin-orbit coupling. In particular, the spin-orbit interactions between X̃ (3)Σ(-)-b̃ (1)Σ(+), Ã (3)Π-c̃ (1)Π, B̃ (3)Δ-ã (1)Δ, and C̃ (3)Σ(+)-d̃ (1)Σ(-) are found to be strong in BrCN(2+) and ICN(2+). By careful analysis of the effect of spin-orbit coupling parameters and the spin-orbit eigenstate composition, an assignment of the hitherto unidentified experimental photoelectron bands of BrCN(2+) and ICN(2+) is presented.

Improved Segmented All-Electron Relativistically Contracted Basis Sets for the Lanthanides.

Improved versions of the segmented all-electron relativistically contracted (SARC) basis sets for the lanthanides are presented. The second-generation SARC2 basis sets maintain efficient construction of their predecessors and their individual adaptation to the DKH2 and ZORA Hamiltonians, but feature exponents optimized with a completely new orbital shape fitting procedure and a slightly expanded f space that results in sizable improvement in CASSCF energies and in significantly more accurate prediction of spin-orbit coupling parameters. Additionally, an extended set of polarization/correlation functions is constructed that is appropriate for multireference correlated calculations and new auxiliary basis sets for use in resolution-of-identity (density-fitting) approximations in combination with both DFT and wave function based treatments. Thus, the SARC2 basis sets extend the applicability of the first-generation DFT-oriented basis sets to routine all-electron wave function-based treatments of lanthanide complexes. The new basis sets are benchmarked with respect to excitation energies, radial distribution functions, optimized geometries, orbital eigenvalues, ionization potentials, and spin-orbit coupling parameters of lanthanide systems and are shown to be suitable for the description of magnetic and spectroscopic properties using both DFT and multireference wave function-based methods.

Dispersion laws of the two-dimensional cavity magnetoexciton-polaritons

The energy spectrum of the 2D cavity magnetoexciton-polaritons has been investigated previously, using exact solutions for the Landau quantization of conduction electrons and heavy holes provided by the Rashba method [1]. Two lowest Landau quantization levels for electrons and three lowest Landau levels for heavy-holes, lead to the construction of the six lowest magnetoexciton sates. They consist of two dipole-active, two quadrupole-active, and the two forbidden quantum transitions from the ground state of the crystal to the magnetoexciton states. The interaction of the four optical-active magnetoexciton states with the cavity mode photons with a given circular polarization and with well-defined incidence direction leads to the creation of five magnetoexciton-polariton branches. The fifth order dispersion equation is examined by using numerical calculations and the second order dispersion equation is solved analytically, taking into account only one dipole-active magnetoexciton state. The effective polariton mass on the lower polariton branch, the Rabi frequency and the corresponding Hopfield coefficients are determined in dependence on the magnetic field strength, the Rashba spin-orbit coupling parameters and the electron and hole g-factors.

Spin-orbit coupling and operation of multivalley spin qubits

Spin qubits composed of either one or three electrons are realized in a quantum dot formed at a Si/SiO_2-interface in isotopically enriched silicon. Using pulsed electron spin resonance, we perform coherent control of both types of qubits, addressing them via an electric field dependent g-factor. We perform randomized benchmarking and find that both qubits can be operated with high fidelity. Surprisingly, we find that the g-factors of the one-electron and three-electron qubits have an approximately linear but opposite dependence as a function of the applied dc electric field. We develop a theory to explain this g-factor behavior based on the spin-valley coupling that results from the sharp interface. The outer "shell" electron in the three-electron qubit exists in the higher of the two available conduction-band valley states, in contrast with the one-electron case, where the electron is in the lower valley. We formulate a modified effective mass theory and propose that inter-valley spin-flip tunneling dominates over intra-valley spin-flips in this system, leading to a direct correlation between the spin-orbit coupling parameters and the g-factors in the two valleys. In addition to offering all-electrical tuning for single-qubit gates, the g-factor physics revealed here for one-electron and three-electron qubits offers potential opportunities for new qubit control approaches.