Spin-orbit Hamiltonian Research Articles

Tight-binding electronic spectra on graphs with spherical topology: II. The effect ofspin–orbit interaction

This is the second of two papers devoted to tight-binding electronic spectra on graphs withthe topology of the sphere. We investigate the problem of an electron subject to aspin–orbit interaction generated by the radial electric field of a static point chargesitting at the center of the sphere. The tight-binding Hamiltonian considered is adiscretization on polyhedral graphs of the familiar form of the spin–orbit Hamiltonian. It involvesSU(2) hopping matrices of the form living on the oriented links of the graph. For a given structure, the dimensionless coupling constantμ is the only parameter of the model. An analysis of the energy spectrum is carried out for thefive Platonic solids (tetrahedron, cube, octahedron, dodecahedron and icosahedron) and theC60 fullerene. Exceptfor the latter, the μ-dependence of all the energy levels is obtained analytically in closed form. Ratherunexpectedly, the spectra are symmetric under the exchange , where Θ is the common arc length of the links. For the symmetric pointμ = Θ/2,the problem can be exactly mapped onto a tight-binding model in the presence of the magnetic fieldgenerated by a Dirac monopole, studied recently. The dependence of the total energy at half-fillingon μ is investigated in all examples.

Erratum: “Theoretical transition probabilities for the OH Meinel system” [J. Chem. Phys. 126, 114314 (2007)

about 2.5% or 1.4 ms. Furthermore, we found a phase difference in the basis sets used to implement the rotational Hamiltonian of Eq. 2 and the lambda-doubling Hamiltonian of Eqs. 8–10. Finally, we found an inconsistency in the implementation of the spin-orbit Hamiltonian. The equations in the paper are consistent. In the new calculations we also replace the re = 1.8342a0 value by a more recent value 3 of re = 1.8324a0. The new calculations affect the numbers in Tables IV and V, which are reproduced here in Tables I and II. Our electric dipole moment function yields slightly higher values for the expectation values of the dipole moment than experimentally observed. Therefore, in Table II, we also include a lifetime based on our dipole moment function scaled with a factor of 0.9966. This is the average ratio between the experimentally observed v =0,1,2 dipole moment and our ab initio values. Finally, we make available a new EPAPS document 4 based on the corrected calculations. The line strengths are computed using the partition function QT = 296 = 80.362 from the HITRAN database. The changes reported here do not significantly alter our conclusions.

Theoretical study of the electronic states of hollandite vanadateK2V8O16

We consider electronic properties of hollandite vanadate ${\mathrm{K}}_{2}{\mathrm{V}}_{8}{\mathrm{O}}_{16}$, a one-dimensional zigzag-chain system of ${t}_{2g}$ orbitals in a mixed valent state. We first calculate the Madelung energy and obtain the relative stability of several charge-ordering patterns to determine the most stable one that is consistent with the observed superlattice structure. We then develop the strong-coupling perturbation theory to derive the effective spin-orbit Hamiltonian, starting from the triply degenerate ${t}_{2g}$ orbitals in the $\mathrm{V}{\mathrm{O}}_{6}$ octahedral structure. We apply an exact-diagonalization technique on small clusters of this Hamiltonian and obtain the orbital-ordering pattern and spin structures in the ground state. We thereby discuss the electronic and magnetic properties of ${\mathrm{K}}_{2}{\mathrm{V}}_{8}{\mathrm{O}}_{16}$, including predictions on the outcome of future experimental studies.

Bosonic quasideterminants and eigenvalue problems of generalized spin-orbit operators

This paper deals with an extension of the applications of the paper by Gelfand and Retakh [Funct. Anal. Appl. 25, 91 (1991)] on quasideterminant (QsD) algebraic method to eigenvalue problems in quantum mechanics. Using relevant identities on the free 1-mode bosonic algebra, we build characteristic QsDs associated with generalized spin-orbit Hamiltonians with a well defined representation which allows us to explicitly and straightforwardly compute analytical expressions of eigenenergies. Specific instances are provided on f-deformed generalized Jaynes–Cummings models and other Hamiltonian classes widely used in condensed matter physics.

Ab initio study on the ground and low-lying excited states of cesium iodide (CsI)

Potential energy curves (PECs) for the ground and low-lying excited states of the cesium iodide (CsI) molecule have been calculated using the internally contracted multireference configuration interaction calculation with single and double excitation method with the relativistic pseudopotentials. PECs for seven Lambda-S states, X 1Sigma+, 2 1Sigma+, 3Sigma+, 1Pi, and 3Pi are first calculated and then those for 13 Omega states are obtained by diagonalizing the matrix of the electronic Hamiltonian H(el) plus the effective one-electron spin-orbit (SO) Hamiltonian H(SO). Spectroscopic constants for the calculated ground X 0+-state PEC with the Davidson correction are found to agree well with the experiment. Transition dipole moments (TDMs) between X 0 and the other Omega states are also obtained and the TDM between X 0+ and A 0+ is predicted to be the largest and that between X 0+ and B 0+ is the second largest around the equilibrium internuclear distance. The TDMs between X 0+ and the Omega=1 states are estimated to be nonzero, but they are notably small as compared with those between the 0+ states. Finally, vibrational levels of the X 0+ PEC for the two isotopic analogs, (133)CsI and (135)CsI, are numerically obtained to investigate the isotope effect on the vibrational-level shift. It has been found that the maximized available isotope shift is approximately 30 cm(-1) around nu=136.

On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

We give a variational proof of the existence of infinitely many bound states placed below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials, thus extending results of J. Brüning, V. Geyler, K. Pankrashkin, J. Phys. A: Math. Theor. 40 F113–F117 (2007).

Jahn–Teller effect in the 4T 2g excited state of Cr 3+ ion in Cs 2NaYF 6 crystal

Calculations of the fine structure of Cr 3+ energy levels in Cs 2NaYF 6 accompanied by estimations of the Jahn–Teller (JT) stabilization energy in the first excited 4T 2g state of Cr 3+ ion are presented. Two independent approaches—effective second-order spin–orbit Hamiltonian and analysis of the potential energy surfaces—are used. The JT energy was estimated to be 216 and 257 cm –1 in the first and the second models, respectively. It is shown that the octahedral [CrF 6] 3− complex undergoes an equatorial expansion by 0.09 Å and an axial elongation by 0.02 Å due to the combined effect of the a 1g and e g normal modes.

Effect of the Spin-Orbit Interaction on the Thermodynamic Properties of Crystals: Specific Heat of Bismuth

We discuss measurements and ab initio calculations of the specific heat for crystalline bismuth, strictly speaking, a semimetal but in the temperature region accessible to us (T>2 K) acting as a semiconductor. We extend experimental data available in the literature and notice that the ab initio calculations without spin-orbit interaction exhibit a maximum at approximately 8 K, about 20% lower than the measured one. Inclusion of spin-orbit interaction decreases the discrepancy markedly: the maximum of C(T) is now only 7% larger than the measured one. Exact agreement is obtained if the strength of the spin-orbit Hamiltonian is reduced by a factor of approximately 0.9. We also discuss the dependence of the lattice parameter and the cohesive energy on spin-orbit interaction.

Semiconductor spintronics

Semiconductor spintronicsSpintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. While metal spintronics has already found its niche in the computer industry—giant magnetoresistance systems are used as hard disk read heads—semiconductor spintronics is yet to demonstrate its full potential. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spin-dependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent interaction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In view of the importance of ferromagnetic semiconductor materials, a brief discussion of diluted magnetic semiconductors is included. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field.

Frequency dependence of induced spin polarization and spin current in quantum wells

Dynamic response of two-dimensional electron systems with spin-orbit interaction is studied theoretically on the basis of quantum kinetic equation, taking into account elastic scattering of electrons. The spin polarization and spin current induced by the applied electric field are calculated for the whole class of electron systems described by $\mathbf{p}$-linear spin-orbit Hamiltonians. The absence of nonequilibrium intrinsic static spin currents is confirmed for these systems with arbitrary (nonparabolic) electron energy spectrum. Relations between the spin polarization, spin current, and electric current are established. The general results are applied to the quantum wells grown in [001] and [110] crystallographic directions, with both Rashba and Dresselhaus types of spin-orbit coupling. It is shown that the existence of the fixed (momentum-independent) precession axes in [001]-grown wells with equal Rashba and Dresselhaus spin velocities or in symmetric [110]-grown wells leads to vanishing spin polarizability at arbitrary frequency $\ensuremath{\omega}$ of the applied electric field. This property is explained by the absence of Dyakonov-Perel-Kachorovskii spin relaxation for the spins polarized along these precession axes. As a result, a considerable frequency dispersion of spin polarization at very low $\ensuremath{\omega}$ in the vicinity of the fixed precession axes is predicted. Possible effects of extrinsic spin-orbit coupling on the obtained results are discussed.

The ground state phases of orbitally degenerate spinel oxides

I review the microscopic spin–orbital Hamiltonian and ground state properties of spin one-half spinel oxides with threefold t 2 g orbital degeneracy. It is shown that for any orbital configuration a ground state of corresponding spin only Hamiltonian is infinitely degenerate in the classical limit. The extensive classical degeneracy is lifted by the quantum nature of the spins, an effect similar to order-out-of-disorder phenomenon by quantum fluctuations. This drives the system to a non-magnetic spin-singlet dimer manifold with a residual degeneracy due to relative orientation of dimers. The magneto-elastic mechanism of lifting the “orientational” degeneracy is also briefly reviewed.

Tunneling currents in ferromagnetic systems with multiple broken symmetries

SHORTENED ABSTRACT: A system exhibiting multiple simultaneously broken symmetries offers the opportunity to influence physical phenomena such as tunneling currents by means of external control parameters. In this paper, we consider the broken SU(2) (internal spin) symmetry of ferromagnetic systems coexisting with \textit{i)} the broken U(1) symmetry of superconductors and \textit{ii)} the broken spatial inversion symmetry induced by a Rashba term in a spin-orbit coupling Hamiltonian. In order to study the effect of these broken symmetries, we consider tunneling currents that arise in two different systems; tunneling junctions consisting of non-unitary spin-triplet ferromagnetic superconductors and junctions consisting of ferromagnets with spin-orbit coupling.

SPOCK.CI: A multireference spin-orbit configuration interaction method for large molecules

We present SPOCK.CI, a selecting direct multireference spin-orbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spin-free density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] and includes spin-orbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective one-electron spin-orbit atomic mean-field Hamiltonian, the application of a resolution-of-the-identity approximation to computationally expensive spin-free four-index integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spin-dependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Second-order properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sum-over-state approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on 4H-pyran-4-thione, dithiosuccinimide, and free-base porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of free-base porphin, MRSOCI calculations can easily be run on a single-processor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.

Effect of spin-orbit interaction on the quenching of the acoustoelectric current in a quasi-one-dimensional channel

We investigate the effect that the Rashba spin-orbit (SO) coupling has on the quenching of the acoustoelectric current in a narrow channel. For an electrostatic potential $V(\mathbf{r},t)$, the SO Hamiltonian is given by ${H}_{SO}=[\ensuremath{\hbar}∕{(2{m}^{*}c)}^{2}]\mathbf{\ensuremath{\nabla}}V∙(\mathbf{\ensuremath{\sigma}}\ifmmode\times\else\texttimes\fi{}\mathbf{p})$. Here, $\mathbf{p}$ is the particle momentum and $\mathbf{\ensuremath{\sigma}}$ is the vector of Pauli matrices. The confining potential $V(\mathbf{r},t)$ arises from the electrostatic potential within the channel due to a powerful surface acoustic wave (SAW) launched in a piezoelectric material, plus the two-dimensional confinement at the heterojunction as well as the potential defining the narrow channel between split metal gates. Working in the adiabatic approximation, we demonstrate that the SO interaction increases the confinement of a captured electron in a moving SAW quantum dot and may consequently improve the quenching of the quantized acoustoelectric current.

Vibronic absorption, fluorescence, and phosphorescence spectra of psoralen: a quantum chemical investigation

Excited state potential energy hypersurfaces of 7H-furo[3,2-g][1]benzopyran-7-one (psoralen) have been explored employing (time-dependent) Kohn-Sham density functional theory. At selected points, we have determined electronic excitation energies and electric dipole (transition) moments utilizing a combined density functional/multireference configuration interaction method. Spin-orbit coupling has been taken into account employing an efficient, non-empirical spin-orbit mean-field Hamiltonian. Franck-Condon factors have been computed for vibrational modes with large displacements in the respective Dushinsky transformations. The simulated band spectra closely resemble experimental band shapes and thus validate the theoretically determined nuclear structures at the S(0), S(1), and T(1) minima. In the S(1) (pi(HOMO)-->pi*(LUMO)) state, the lactone bond of the pyrone ring is significantly elongated. From excited vibrational levels of the S(1) state a conical intersection between a (pi-->sigma*) excited state and the electronic ground state may be energetically accessible. Fast non-radiative decay via this relaxation pathway could explain the low fluorescence quantum yield of psoralen. The T(1) (pi(HOMO-1)-->pi*(LUMO)) exhibits a diradicaloid electronic structure with a broken C(5)-C(6) double bond in the pyrone ring. A variational multireference spin-orbit configuration interaction procedure yields a phosphorescence lifetime of 3 s, in excellent agreement with experimental estimates.

Effective quantum dimer model for trimerized kagomé antiferromagnet

An effective spin-orbit Hamiltonian is derived for a spin-1/2 trimerized kagome antiferromagnet in the second-order of perturbation theory in the ratio of two coupling constants. Low-energy singlet states of the obtained model are mapped to a quantum dimer model on a triangular lattice. The quantum dimer model is dominated by dimer resonances on a few shortest loops of the triangular lattice. Characteristic energy scale for the dimer model constitutes only a small fraction of the weaker exchange coupling constant.

Orbital and spin physics in LiNiO2 and NaNiO2

We derive a spin–orbital Hamiltonian for a triangular lattice of eg orbital degenerate (Ni3+) transition-metal ions interacting via 90° superexchange involving (O2−) anions, taking into account the onsite Coulomb interactions on both the anions and the transition metal ions. The derived interactions in the spin–orbital model are strongly frustrated, with the strongest orbital interactions selecting different orbitals for pairs of Ni ions along the three different lattice directions. In the orbital-ordered phase, favoured in mean field theory, the spin–orbital interaction can play an important role by breaking the U(1) symmetry generated by the much stronger orbital interaction and restoring the three-fold symmetry of the lattice. As a result, the effective magnetic exchange is non-uniform and includes both ferromagnetic and antiferromagnetic spin interactions. Since ferromagnetic interactions still dominate, this offers yet insufficient explanation for the absence of magnetic order and the low-temperature behaviour of the magnetic susceptibility of stoichiometric LiNiO2. The scenario proposed to explain the observed difference in the physical properties of LiNiO2 and NaNiO2 includes small covalency of Ni–O–Li–O–Ni bonds inducing weaker interplane superexchange in LiNiO2, insufficient to stabilize orbital long-range order in the presence of stronger intraplane competition between superexchange and Jahn–Teller coupling.

Assessment of theoretical prediction of the NMR shielding tensor of195PtClxBr6−x2−complexes by DFT calculations: experimental and computational results

In the present work, the ZORA spin-orbit Hamiltonian, in conjunction with the gauge including orbital (GIAO) method based on DFT theory has been used to calculate 195Pt chemical shift of 195PtClxBr(6-x)(2-) complexes. Excellent agreement with experiments has been obtained for calculations bearing on optimized geometries and all electrons triple zeta + polarization (TZP) STO basis sets: the relative error with respect to experiment amounts to <1.5%. It is found that the Pt chemical shift is dominated by the paramagnetic and the spin orbit contribution, whereas the diamagnetic term remains negligible. The influence of the quality of the basis sets has been studied and found to be small, provided a basis set like TZP is used. Several calculations have been performed in order to establish the sensitivity of the chemical shift to a variation in the bond lengths. A strong dependence has been found, with an increase of the chemical shift amounting to 150 ppm pm(-1) for a distance decrease. Large sensitivity to the solvation, leading to changes in the structure, is then expected. Different tests using conductor-like screening models have been performed in order to establish the sensitivity of the chemical shift to solvation. It has been observed that the changes in the geometry are more important than charge transfers. Finally, the sensitivity of the system to the exchange-correlation functional is found rather weak, at least among the GGA functionals.

Orbital–Peierls transition in the spin chains of [formula omitted

The distinguishing feature of the pyroxene compound NaTiSi2O6 is the presence of quasi-one-dimensional arrays of edge sharing TiO6 octahedra. Besides its spin (s=12), each Ti3+ ion has an additional orbital degree of freedom. We determine the properties of the microscopic spin–orbital Hamiltonian for this compound by finite temperature Monte Carlo simulations. We show that for the spin and orbital ordering to occur at the same temperature, the orbital crystal field splitting should be smaller than or comparable to the inter-site superexchange integral. The simulations strongly indicate that in NaTiSi2O6 there is an orbital–Peierls transition, which is an orbital ordering transition that is accompanied by a lattice dimerization. Magnetically, in this case, the system goes from a high temperature quasi-one-dimensional antiferromagnet to a low-temperature valence bond solid. The experimentally observed spin gap and lattice anomalies are strong evidence for the presence of an orbital–Peierls transition in NaTiSi2O6.

The Rashba effect on a double-barrier spin polarizer

The Rashba effect on a double-barrier spin polarizer is considered using a formalism that produces accurate results with little computational effort. In previous articles, we proposed a spin polarizer consisting of a well made of a dilute magnetic semiconductor (DMS) enclosed by two non-magnetic barriers. In the absence of Rashba effect, the magnetization of the well produces totally polarized electronic levels separated by 0.15 eV. The highest steady magnetic field obtained in a laboratory could not produce a Zeeman splitting so big. As a consequence the calculated currents are almost totally polarized. The Rashba spin–orbit Hamiltonian produces a spin flip. Therefore, the levels at the well have not well-defined spin polarization and the currents are less polarized. The device presented here would be useful for spintronics because there are DMS ferromagnetic at room temperature. Our tight-binding Hamiltonian, including the Rashba term, is H = H K + H P + H E + H M + H h - i + H h - h + H R . The first term is the kinetic energy. H P describes the double-barrier profile and the third term represent the electric field due to the applied bias. The magnetic H M , the hole-impurity H h - i and the hole–hole H h - h terms are included in the mean field approximation. The profile and the charge distribution are calculated self-consistently. By using a decimation formalism, all these terms are treated exactly. Finally, the Rashba term H R is very small. Therefore, it is treated using second order perturbation theory. The calculation confirm that the Rashba effect on the currents is of second order. Consequently, the resulting depolarization is very small.