Spin-orbit Space Research Articles

Spin susceptibility for orbital-singlet Cooper pair in the three-dimensional Sr2RuO4 superconductor

We study the spin susceptibility of the orbital-singlet pairings, including the spin-triplet/orbital-singlet/$s$-wave $E_g$ representation proposed by Suh \textit{et al}., [H.\ G.\ Suh \textit{et al}., Phys.\ Rev.\ Research \textbf{2}, 032023 (2020)], for a three-orbital model of superconducting Sr$_2$RuO$_4$ in three dimensions. For the pseudospin-singlet states represented in the band basis, the spin susceptibility decreases when reducing the temperature, irrespective of the direction of the applied magnetic fields, even if they are spin-triplet/orbital-singlet pairings in the spin-orbital space. However, because the pseudospin-triplet \textbf{d}-vector in the band basis is not completely aligned in the $xy$-plane (along $z$-axis) owing to the strong atomic spin-orbit coupling, the spin susceptibility for spin-singlet/orbital-singlet/odd-parity pairings is reduced around $5$-$10$ percent with the decrease of the temperature along the $z$ ($x$) axis. We can determine the symmetry of the pseudospin structure of the Cooper pair by the temperature dependence of the spin susceptibility measured by nuclear magnetic resonance experiments. Our obtained results serve as a guide to determine the pairing symmetry of Sr$_2$RuO$_4$.

Optical holonomic single quantum gates with a geometric spin under a zero field

Realization of fast fault-tolerant quantum gates on a single spin is the core requirement for solid-state quantum-information processing. As polarized light shows geometric interference, spin coherence is also geometrically controlled with light via the spin-orbit interaction. Here, we show that a geometric spin in a degenerate subspace of a spin-1 electronic system under a zero field in a nitrogen vacancy center in diamond allows implementation of optical non-adiabatic holonomic quantum gates. The geometric spin under quasi-resonant light exposure undergoes a cyclic evolution in the spin-orbit space, and acquires a geometric phase or holonomy that results in rotations about an arbitrary axis by any angle defined by the light polarization and detuning. This enables universal holonomic quantum gates with a single operation. We demonstrate a complete set of Pauli quantum gates using the geometric spin preparation and readout techniques. The new scheme opens a path to holonomic quantum computers and repeaters.

Extended parametrization scheme of f-spectra

The standard one particle parametrization scheme of f-spectra which is based on the second-order Judd–Ofelt theory of electric dipole f ⟷ f transitions in lanthanides is extended by new terms. The extended scheme, although still one particle in origin, is defined in terms of double tensor operators that act within the spin–orbital space. In addition to the discussion of the physical mechanisms, which give rise to the new parameters, the results of numerical calculations performed for the Eu 3 + ion in acetate crystal are presented as an illustration. In the discussion of the accuracy of the reproduction of the intensities of observed transitions, the problem of the theoretical description of the hypersensitive transitions is also addressed.

Spin-orbital fluctuations and a large mass enhancement inLiV2O4

We present a scenario that the multi-component fluctuations, especially those of the spin-orbital coupled modes, lead to the mass enhancement observed in LiV_2O_4. This phenomena is possible because all these modes are fluctuating due to the geometrical frustration. To illustrate this mechanism, the t_{2g}-orbital Hubbard model on the pyrochlore lattice is studied based on the random-phase approximation. We derive the generalized susceptibility in the SU(6) spin-orbital space and calculate the free energy by using a coupling-constant integration. The estimated specific heat coefficient is of the correct order of magnitude to explain the experiment.

Judd—Ofelt theory: past, present and future

The original Judd-Ofelt theory is briefly presented in the terms of effective operators defined in the traditional form that has been used for many years for the interpretation of the f spectra of rare earths. The semi-empirical approach of the Judd-Ofelt theory that defines the one-particle parametrization scheme is modified here. The unit tensor operators that act within the orbital space are replaced by double tensor operators acting within the spin-orbital space. This extension enables one to include the impact of the relativistic effects upon the transition amplitude. At the same time it leads to a generalization of the theoretical approach to f ↔ f transitions, especially in the case of those that are not described by the standard scheme.

Judd–Ofelt theory in a new light on its (almost) 40th anniversary

The standard Judd–Ofelt theory of one photon electric dipole transitions in f N systems is discussed in the language of the one particle parametrization scheme. An overview of various physical mechanisms that contribute to the Judd–Ofelt intensity parameters is performed. The analysis of the morphology of these parameters is based on the static model of their original derivation, dynamic model, electron correlation third order approach, spin–orbit interaction influence, and an exotic perturbation caused by a specific mass shift. As a new aspect of the investigations on the physical nature of f↔f transitions, a transformation of the Judd–Ofelt effective operators to their relativistic version is presented. In this approach the transition amplitude is expressed by the effective double tensor operators, acting within the 4f N shell, and effectively representing relativistic contributions. In particular, the relativistic form of the crystal field potential is employed, and in addition, the interactions through the crystal field potential within the spin–orbital space are included.

A relativistic crystal field for S-state f electron ions

In order to improve the theoretical reproduction of thesplitting of the energy levels for S-state f electron ions, amodel in which the relativistic effects are included in aneffective way is used. Although the effective operators actwithin the spin-orbital space, and the radial integrals involvethe large and small components of therelativistic theory, all the required matrix elements areevaluated within the intermediate coupling scheme. The approachis illustrated by the results of numerical calculationsperformed for the representative ions: Gd3+, Cm3+, and Bk4+. The results of the analysissupport the expectation that for such large systems therelativistic effects indeed play an important role. Inaddition, it is concluded that the fitting procedure appliedfor the determination of the crystal field parameters has tobe performed within the parametrization scheme that includesthe relativistic weights for the various parameters.

Mixed-symmetry solutions of generalized three-particle Bargmann-Wigner equations in the strong-coupling limit

Starting from a nonlinear isospinor-spinor field equation, generalized three-particle Bargmann-Wigner equations are derived. In the strong-coupling limit, a special class of spin 1/2 bound-states are calculated. These solutions which are antisymmetric with respect to all indices, have mixed symmetries in isospin-superspin space and in spin orbit space. As a consequence of this mixed symmetry, we get three solution manifolds. In appendix \ref{b}, table 2, these solution manifolds are interpreted as the three generations of leptons and quarks. This interpretation will be justified in a forthcoming paper.

Complete set of orthogonal scalar operators for the configuration ƒ^3

When Coulomb interactions between f3 and other electronic configurations are taken to third and higher orders of perturbation theory, it becomes necessary to augment the standard set of thirteen electrostatic parameters with eight more. The operators associated with these eight parameters are orthogonalized to the standard set of operators, and a complete set of the matrix elements of all 21 orthogonalized operators is given for f3. The group-theoretical properties of these operators are examined. Each operator corresponds to a unique pair of irreducible representations of R7 (the rotation group in the seven-dimensional orbital space of an f electron) and of G2 (Cartan’s first exceptional group), but the associated quasispin ranks and irreducible representations of Sp14 (the symplectic group in the 14-dimensional spin–orbital space of an f electron) are sometimes mixed. The combinations of quasispin ranks are odd for the three-electron operators t and even for the two-electron operators e.

General linear group approach to bivariational problems

AbstractA bivariational scheme based on the general linear group of spin orbital space is presented, with the aim of obtaining approximations to the spectra of complex rotated Hamiltonians.

Self-consistent molecular orbital methods. XVI. Numerically stable direct energy minimization procedures for solution of Hartree–Fock equations

Direct energy minimization methods are examined for solution of the Hartree–Fock equations in a basis expansion. Given a set of trial spin– orbitals, an initial direction for a univariate search of spin–orbital space is specified using general energy-weighted coordinates. The first energy minimum in such a search then provides an initial point for the next iterative step. Techniques are proposed for the maintenance of spin–orbital continuity during this process. Comparison of various energy-weighted coordinates indicates that most effective convergence is achieved if the search path is chosen to pass through the point corresponding to the classical procedure involving the construction of successive approximations to the Fock matrix. The utility of the new method is illustrated by the completion of a previous systematic study of Hartree–Fock energies for small organic species.

The Use of Tensor Operators in Nuclear Collision Problems

The consequences of the invariance under rotations and reflections of the collision matrix are expressed as a relationship between the expectation values of initial-state and final-state irreducible tensor operators in spin-orbit space. This relationship is used to give a proof of the Eisner-Sachs theorem on the complexity of angular distributions of nuclear reactions and some extensions of this theorem.