Spin Part Research Articles

The spin and orbital contributions to magnetic dipole transitions

In previous works, we examined the systematics of magnetic dipole transitions in a single j shell. We here extend the study to large space calculations. We consider the nuclei [Formula: see text]Ti, [Formula: see text]Ti and [Formula: see text]Cr. Of particular interest are the contributions to [Formula: see text] of the spin and orbital parts of the magnetic dipole operator. Whereas usual scissors mode analyses have as an initial state the [Formula: see text] ground state (of an even-even nucleus), we here start with the lowest [Formula: see text] state. This enables us to reach many more states, e.g., [Formula: see text] 1, and 2 and thus get a better picture of the collectivity of this state.

Interconversion between the orbital and spin angular momentum of light beams in three-wave mixing processes in the bulk of an isotropic chiral medium.

A phenomenological description of nondegenerate and degenerate three-wave mixing in the bulk of an isotropic chiral medium is given for the wide class of fundamental light beams with nonuniform polarization distribution and multimode transverse structure. Special attention is paid to the classical and quantum interpretation of interconversion between spin and orbital parts of the angular momentum of the input and output beams.

Schottky specific heat of the lightly Mn-substituted electron-doped SrTiO3

Large changes in the low-temperature specific heat (low-T C) by applying magnetic fields up to 9 Tesla were found in the lightly Mn-substituted electron-doped perovskites Sr1−xLaxTiO3. The changes in the low-T C are qualitatively well explained by the Schottky specific heat (CSch) of localized spins of the Mn 3d electrons in weak internal magnetic fields via itinerant electrons. According to the analysis by using the conventional model, the doped Mn ions are apparently not Mn4+ (S = 3/2) ions, but are Jahn-Teller active Mn3+ (S = 2) ions or mixtures of Mn3+ and Mn2+ ions. However, the actual numbers of localized spins estimated from CSch are about 30% smaller than the expected values. Part of the localized spins of the Mn 3d electrons may disappear due to Kondo coupling with the itinerant electrons, leading to the observed enhancement of the electronic specific heat coefficients.

Interatomic orbital magnetism: The case of 3d adatoms deposited on the Pt(111) surface

The orbital magnetic moment is still surprisingly not well understood, in contrast to the spin part. Its description in finite systems, such as isolated atoms and molecules, is not problematic, but it was only recently that a rigorous picture was provided for extended systems. Here we focus on an intermediate class of systems: magnetic adatoms placed on a non-magnetic surface. We show that the essential quantity is the ground-state charge current density, in the presence of spin-orbit coupling, and set out its first-principles description. This is illustrated by studying the magnetism of the surface Pt electrons, induced by the presence of Cr, Mn, Fe, Co and Ni adatoms. A physically appealing partition of the charge current is introduced. This reveals that there is an important nonlocal contribution to the orbital moments of the Pt atoms, extending three times as far from each magnetic adatom as the induced spin and local orbital moments. We find that it is as sizable as the latter, and attribute its origin to a spin-orbital susceptibility of the Pt surface, different from the one responsible for the formation of the local orbital moments.

Electrically tunable entanglement of an interacting electron pair in a spin-active double quantum dot

Finding efficient methods for controlling entanglement is an important issue in quantum information processing. Here, we inspect theoretically possible ways for tuning orbital and spin entanglement of two interacting particles confined to a double quantum dot with spin-orbit coupling (SOC) which renders possible the coupling of spin to an external electric field. The entanglement in the spin part is sensitive to a transverse electric field. We show that through the field-induced SOC the entanglement of the spin subsystem can be slightly increased; the effect of a longitudinal electric field is more subtle: For a small interdot distance, a longitudinal electric field enhances substantially the entanglement of spins, while for a large interdot distance it has no impact. An external longitudinal electric field has a minor effect on the entanglement in the orbital part irrespective of the interdot distance. We trace back this observed phenomenon to a combined effect of the applied external electric field and the overlap of wave functions which is enhanced for decreasing interdot distances. As a result, at large interdot separation, the concurrence of the two-electron states turns insensitive to the applied electric field.

Investigations of half-metallic ferromagnetism and thermoelectric properties of cubic XCrO3 (X = Ca,Sr,Ba) compounds via first-principles approaches

In this paper, the physical aspects of the cubic phase XCrO3 (X=Ca,Sr,Ba) perovskites are studied by employing full-potential linearized augmented plane wave plus local orbital (FP-LAPW+lo) method. These compounds have been found stable in ferromagnetic (FM) phase since they possess lower energy in FM phase compared to non-FM phase and their stability is also confirmed by calculating the enthalpy of formation (ΔH). The electronic structures of these compounds are analyzed with Trans and Blaha modified Becke–Johnson potential (TB-mBJ) for both spin up and spin down channels, which indicate their half-metallic characters. Analysis of density of states (DOS) shows major contributions of O-2p states in the valence band and Cr 3d-state in conduction band. A comparative analysis of crystal field effect (ΔEcrystal) and the exchange energies (direct Δx(d) and indirect Δx(pd)) tells about the main part of electronic spin in ferromagnetic character. The calculated magnetic moments make these compounds favorable for spintronic applications. In the end, thermoelectric parameters are computed for 200 K–800 K temperature range to explore potential of these compounds for applications in renewable energy devices.

Proton Spin Puzzle and Confinement of Quarks

It is shown that the confinement effect that is significant at great distances from the nucleon center is capable of inducing the appreciable quark helicity flip. A simultaneous change in projections of the orbital angular momentum of quarks on the direction of their motion, which follows from the Dirac equation, ensures the conservation of the total angular momentum of the system. Thus, a part of the proton spin, measured in experiments with deep inelastic scattering of leptons, may be hidden in the orbital angular momentum of quarks.

Controlled spin of a nonbirefringent droplet trapped in an optical vortex beam

The spin part of the angular momentum of light can cause a birefringent particle to spin around its axis, while having no effect on a nonbirefringent particle. The orbital part of light’s angular momentum, on the other hand, can cause both birefringent and nonbirefringent particles to orbit around the axis of a light beam. In this paper, we demonstrate that nonbirefringent particles can also be made to spin around their axis when trapped in an optical vortex beam. The rotation of the particle depends on the ratio of the size of the particle and the diameter of the laser beam in which the particle is trapped. It can therefore be controlled by varying the position of the particle with respect to the focal point of the laser beam. The rotational frequency can also be controlled by changing the polarization state of the beam, since spin–orbit coupling affects the total angular momentum experienced by the trapped particle. The motion of the trapped particle is detected by a photodiode and a high-speed camera. Most microparticles found in nature are nonbirefringent, and the method presented in this paper will therefore open up new applications for optically induced rotations.

Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams

Light beams may carry optical spin or orbital angular momentum, or both. The spin and orbital parts manifest themselves by the ellipticity of the state of polarization and the vortex structure of phase of light beams, separately. Optical spin and orbit interaction, arising from the interaction between the polarization and the spatial structure of light beams, has attracted enormous interest recently. The optical spin-to-orbital angular momentum conversion under strong focusing is well known, while the converse process, orbital-to-spin conversion, has not been reported so far. In this paper, we predict in theory that the orbital angular momentum can induce a localized spin angular momentum in strong focusing of a spin-free azimuthal polarization vortex beam. This localized longitudinal spin of the focused field can drive the trapped particle to spin around its own axis. This investigation provides a new degree of freedom for spinning particles by using a vortex phase, which may have considerable potentials in optical spin and orbit interaction, light-beam shaping, or optical manipulation.

Angular momentum of phonons and its application to single-spin relaxation

We reexamine the relaxation process of a single spin embedded in an elastic medium, a problem studied recently by Garanin and Chudnovsky (GC) [Phys. Rev. B 92, 024421 (2015)] from the viewpoint of angular-momentum transfer. Using Noether's theorem, we identify two distinct angular momenta of the medium, one Newtonian discussed by GC and the other field-theoretical, both of which consist of an orbital part and a spin part. For both angular momenta, we found that the orbital part is as essential as the spin part in the relaxation process. In particular, the angular-momentum transfer from the (real) spin to the Newtonian orbital part may be considered as an incipient rotation that leads to the Einstein--de Haas effect.

Relativistic spin-orbit interactions of photons and electrons

Laboratory optics, typically dealing with monochromatic light beams in a single reference frame, exhibits numerous spin-orbit interaction phenomena due to the coupling between the spin and orbital degrees of freedom of light. Similar phenomena appear for electrons and other spinning particles. Here we examine transformations of paraxial photon and relativistic-electron states carrying the spin and orbital angular momenta (AM) under the Lorentz boosts between different reference frames. We show that transverse boosts inevitably produce a rather nontrivial conversion from spin to orbital AM. The converted part is then separated between the intrinsic (vortex) and extrinsic (transverse shift or Hall effect) contributions. Although the spin, intrinsic-orbital, and extrinsic-orbital parts all point in different directions, such complex behavior is necessary for the proper Lorentz transformation of the total AM of the particle. Relativistic spin-orbit interactions can be important in scattering processes involving photons, electrons, and other relativistic spinning particles, as well as when studying light emitted by fast-moving bodies.

Magnetic Exchange Interaction in Nitronyl Nitroxide Radical-Based Single Crystals of 3d Metal Complexes: A Combined Experimental and Theoretical Study.

Two stable nitronyl nitroxide free radicals {R1 = 4′-methoxy-phenyl-4,4,5,5,-tetramethylimidazoline-1-oxyl-3-oxide (NNPhOMe) and R2 = 2-(2′-thienyl)-4,4,5,5-tetramethylimidazoline 3-oxide 1-oxyl (NNT)} are successfully synthesized using Ullmann condensation. The reactions of these two radicals with 3d transition metal ions, in the form of M(hfac)2 (where M = Co or Mn, hfac: hexafluoroacetylacetone), result in four metal–organic complexes Co(hfac)2(NNPhOMe)2, 1; Co(hfac)2(NNT)2·(H2O), 2; Mn(hfac)2(NNPhOMe)·x(C7H16), 3; and Mn(hfac)2(NNT)2, 4. The crystal structure and magnetic properties of these complexes are investigated by single-crystal X-ray diffraction, dc magnetization, infrared, and electron paramagnetic resonance spectroscopies. The compounds 1 and 4 crystallize in the triclinic, P1̅, space group, whereas complex 3 crystallizes in the monoclinic structure with the C2/c space group and forms chain-like structure along the c direction. The complex 2 crystallizes in the monoclinic symmetry with the P21/c space group in which the N–O unit of the radical coordinates with the Co ion through hydrogen bonding of a water molecule. All compounds exhibit antiferromagnetic interactions between the transition metal ions and nitronyl nitroxide radicals. The magnetic exchange interactions (J/KB) are derived using isotropic spin Hamiltonian H = −2J∑(SmetalSradical) for the model fitting to the magnetic susceptibility data for 1, 2, 3, and 4. The exchange interaction strengths are found to be −328, −1.25, −248, and −256 K, for the 1, 2, 3, and 4 metal–organic complexes, respectively. Quantum chemical density functional theory (DFT) computations are carried out on several models of the metal–radical complexes to elucidate the magnetic interactions at the molecular level. The calculations show that a small part of the inorganic spins are delocalized over the oxygens from hfac {∼0.03 for Co(II) and ∼0.015 for Mn(II)}, whereas a more significant fraction {∼0.24 for Mn(II) and ∼0.13 for Co(II)} of delocalized spins from the metal ion is transferred to the coordinated oxygen atom(s) of nitronyl nitroxide.

Computations of the chirality-sensitive effect induced by an antisymmetric indirect spin–spin coupling

ABSTRACTResults of quantum mechanical computations of the antisymmetric part of the indirect spin–spin coupling tensor, , performed using the coupled-cluster method, the second-order polarisation propagator approximation, and the density functional theory for 25 molecules and nearly 100 spin–spin couplings are reported. These results are used for an estimation of the magnitude of the recently proposed liquid-state nuclear magnetic resonance chirality-sensitive effect, which allows to determine the molecular chirality directly, i.e. without the need for the application of any chiral agent. The following were found: (i) the antisymmetry J⋆ is usually larger for the coupling between spins separated by two chemical bonds in comparison with the coupling through one bond, (ii) promising samples are those which contain fluorine, and (iii) the antisymmetry of the spin–spin coupling tensor is of the order of a few hertz for commercially available chemical compounds. Therefore, the relevant property of the experiment, the pseudoscalar Jc, for them is of the order of 1 nHz m/V.

Orbital and spin parts of energy currents for electromagnetic waves through spatially inhomogeneous media

We investigate electromagnetic waves propagating through non-magnetic and loss-free dielectric media, but with spatially inhomogeneous refractive indices. We derive hence a set of analytic formulae for conservation laws and energy-current (Poynting) vector. As a result, we deduce that the energy-current vector cannot be neatly separated into its orbital and spin parts in contrast to the cases with spatially homogeneous media. In addition, we present physical interpretations of the two additional terms due to spatial material inhomogeneity.

Spin force and torque in non-relativistic Dirac oscillator on a sphere

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin–orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.

NMR study on anomalous superconducting phase diagram in UBe13

In order to clarify unusual superconducting properties in a heavy fermion superconductor UBe13, we have carried out 9Be NMR measurements using a single crystal with Tc≅0.85K. The NMR spectra under the magnetic field H=3T parallel to [111] crystal axis show no change between Tc(H=3T)=0.64K and Ta(H=3T)=0.55K. Below Ta, however, the Knight shift for Be(II) decreased. The reduction of the Knight shift of Be(II) is amount to ∼0.01%, which is much smaller than spin part of the Knight shift, Ks∼0.1% estimated from Clogston Jaccarino plot. The origin of reduction of the Knight shift cannot be explained by spin singlet superconductivity.

Two and three particles entanglement; helicity and spin with momentum

Construction of the reduced spin and helicity density matrix for systems of two and three particles are described by a wave packet with sharp and Gaussian momentum distribution. The entropy for the spin and helicity part of the systems is calculated from the viewpoint of moving observers.

Higher-order modes of vacuum-clad ultrathin optical fibers

We present a systematic treatment of higher-order modes of vacuum-clad ultrathin optical fibers. We show that, for a given fiber, the higher-order modes have larger penetration lengths, larger effective mode radii, and larger fractional powers outside the fiber than the fundamental mode. We calculate, both analytically and numerically, the Poynting vector, propagating power, energy, angular momentum, and helicity (or chirality) of the guided light. The axial and azimuthal components of the Poynting vector can be negative with respect to the direction of propagation and the direction of phase circulation, respectively, depending on the position, the mode type, and the fiber parameters. The orbital and spin parts of the Poynting vector may also have opposite signs in some regions of space. We show that the angular momentum per photon decreases with increasing fiber radius and increases with increasing azimuthal mode order. The orbital part of angular momentum of guided light depends not only on the phase gradient but also on the field polarization, and is positive with respect to the direction of the phase circulation axis. Meanwhile, depending on the mode type, the spin and surface parts of angular momentum and the helicity of the field can be negative with respect to the direction of the phase circulation axis.

Comparison of nitrogen-vacancy complexes in diamond and cubic SiC: dose dependencies and spin-Hamiltonian parameters

At present the nitrogen-vacancy (NV) complex in diamond is the most promising defect for application in the area of quantum computing. This provides a stimulus for an extensive search of other defects in semiconductors with similar properties. Recently it was shown that the NCVSi defect complex in SiC is perspectively appropriate for this goal as well. In the present work we perform comparative ab initio studies of NV complexes in diamond and 3C-SiC. We focus both on radiospectroscopic characterization of these defects and on the calculation of the equilibrium concentration of complexes in irradiated crystals. In particular a full set of spin-Hamiltonian parameters including g-tensors, hyperfine tensors and the spin–spin part of zero-field splitting constant Dss were calculated for both negative and neutral charge states as well as for excited quartet states of neutral complexes. Comparison of calculated values with the available experimental data and results of other calculations show good agreement, especially in the case when hybrid and meta-hybrid functionals were used. This makes the unambiguous identification of negative NV complexes in both materials possible. Our calculations reveal that the ground states of neutral complexes are a difficult case for both DFT calculations and experimental observations. This is caused by multi-determinantal behavior of wave function for such complexes, which leads to a large amount of spin contamination and to the broken symmetry solution which appeared for single Slater determinant DFT calculations. Based on the calculated minimum of free energy of neutral and negative complexes in SiC and diamond we obtained the equilibrium concentrations of these complexes depending on the vacancy concentration produced by irradiation. We show that in some dose regions both negative and neutral complexes coexist, while in other regions only one charge state prevails. Comparison of the calculated and experimental dose dependencies for diamond shows good qualitative agreement.

Transfer efficiency of angular momentum in sum-frequency generation and control of its spin and orbital parts by varying polarization and frequency of fundamental beams

Considering sum-frequency generation in an isotropic chiral nonlinear medium, we analyze the transfer of the spin angular momentum of fundamental elliptically polarized Gaussian light beams to the signal beam, which appears as the superposition of two Laguerre–Gaussian modes with both spin and orbital angular momentum. Only for the circular polarization of the fundamental radiation is its angular momentum fully transferred to the sum-frequency beam; otherwise, part of it can be transferred to the medium. Its value, as well as the ratio of spin and orbital contributions in the signal beam, depends on the fundamental frequency ratio and the polarization of the incident beams. Higher energy conversion efficiency in sum-frequency generation does not always correspond to higher angular momentum conversion efficiency.