Large Spin-orbit Splitting Research Articles

Long magnetic relaxation time of Fe–Bi spin-glass system

Bi and Fe are mutually insoluble either in the solid or liquid states. However, metastable Fe–Bi alloys can be made using the rapidly quenching method. We have successfully prepared metastable Fe x Bi 1− x alloys over a wide composition range by DC magnetron co-sputtering. The X-ray diffraction results indicate that the magnetic Fe atoms are gradually replacing the Bi atoms in a rhombohedral structure for x<0.6. The magnetic measurements show that a spin-glass results with the freezing temperature increasing with x. In addition, a long relaxation characteristic time τ is observed which is about 20 h at room temperature. The slow relaxation behavior of the Fe–Bi system can be qualitatively explained from the picture that Bi has a large spin–orbit splitting.

Radiative properties of Zeeman components of atomic multiplets: Dependence of line intensities on the magnetic field

Analytical expressions for the dependence of the intensity of Zeeman components of doublet lines on the magnetic field are obtained. Sharp changes of these function on passing from the anomalous Zeeman effect to the Paschen-Back effect lead to the disappearance of marginal lines and the equalization of intensities of remaining lines. In the region of the complete Paschen-Back effect, a strong influence on these dependences is produced by the dynamic atom-field interaction, which weakens the paramagnetic effect in the states with a positive magnetic quantum number m and enhances the effect in the states with a negative m. Simple analytical expressions are obtained that take into account the effect of the diamagnetic interaction on line intensities. The role of the diamagnetic interaction increases in Rydberg atomic states with a large spin-orbit splitting. For the states with m > 0, it can lead to the “diamagnetic reversal” of the Paschen-Back effect, i.e., the recovery of the anomalous Zeeman effect.

Negative-ion photoelectron spectroscopy of CH3S−

A 364-nm negative-ion photoelectron spectrum of CH 3 S − has been recorded. The electron affinity is 1.867±0.004 eV. Well-resolved vibrational structure has been observed such that the C–S symmetric stretch and the C–H symmetric stretch have been measured at 725±15 cm −1 and 1260±30 cm −1 , respectively. The spin–orbit splitting is reported at 265±15 cm −1 . The large spin–orbit splitting quenches the Jahn–Teller modes seen in the analogous radicals, CH 3 O and CF 3 S.

Optical transitions in broken gap heterostructures

We have used an eight-band model to investigate the electronic structures and to calculate the optical matrix elements of InAs-GaSb broken gap semiconductor heterostructures. The unusual hybridization of the conduction band states in the InAs layers with the valence band states in the GaSb layers has been analyzed in detail. We have studied the dependence of the optical matrix elements on the degree of conduction-valence hybridization, the tuning of the hybridization by varying the width of the GaSb layers and/or InAs layers, and the sensitivity of quantized levels to this tuning. Large spin-orbit splitting in the energy bands has been demonstrated. Our calculation can serve as a theoretical model for infrared lasers based on broken gap quantum well heterostructures.

Photoreflectance spectroscopy of CdTe(001) around E1 and E1+Δ1: linear electro-optic spectrum

We report on the measurement of the linear electro-optic (LEO) reflectance spectrum of CdTe (001) in an energy range around the E1 and E1+Δ1 interband transitions. This spectrum shows a sharp peak localized in energy around E1 and a second shorter peak around E1+Δ1. We show that the theoretical model developed in an earlier article for the LEO line shape of GaAs (001) gives an accurate description of the experimental LEO CdTe spectrum as well. This model includes two contributions to the LEO line shape, a first one proportional to the normalized energy derivative of the reflectance spectrum and a second one associated to the sample reflectance. The large spin-orbit splitting energy of CdTe, (Δ1≈0.6 eV) allows for a neat separation of the contributions to the LEO spectrum of the E1 and E1+Δ1 critical points, providing a critical test for the LEO line shape model. From the fitting we obtain d′/d=1.5 for the conduction band to valence band deformation potential ratio and E2=9.1 eV for the interband deformation potential in the Brooks notation.

Shell structure of superheavy nuclei in self-consistent mean-field models

We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models -- the Skyrme-Hartree-Fock approach and the relativistic mean-field model -- using a large number of parameterizations. Results obtained with the Folded-Yukawa potential are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. While all relativistic models give a reasonable description of spin-orbit splittings, all non-relativistic models show a wrong trend with mass number. The spin-orbit splitting of heavy nuclei might be overestimated by 40%-80%. Spherical doubly-magic superheavy nuclei are found at (Z=114,N=184), (Z=120,N=172) or (Z=126,N=184) depending on the parameterization. The Z=114 proton shell closure, which is related to a large spin-orbit splitting of proton 2f states, is predicted only by forces which by far overestimate the proton spin-orbit splitting in Pb208. The Z=120 and N=172 shell closures predicted by the relativistic models and some Skyrme interactions are found to be related to a central depression of the nuclear density distribution. This effect cannot appear in macroscopic-microscopic models which have a limited freedom for the density distribution only. In summary, our findings give a strong argument for (Z=120,N=172) to be the next spherical doubly-magic superheavy nucleus.

First-principles calculations of the magneto-optical Kerr effect in L1 0-type ordered alloys TM–X [formula omitted

The magneto-optical polar Kerr effect of L1 0(CuAu)-type ordered alloys TM–X ( TM= Mn, Fe, Co ; X= Pt, Au ) was calculated from the electronic structures given by the first-principles LMTO-ASA method. The calculated results agreed reasonably well with the experimental results. The important optical transitions were identified by detailed analysis of the electronic structures and transition matrix elements. As an example, it was found that the peak structure at 4 eV in the Kerr spectra of L1 0-FeAu mainly originated from the d ↓±2→f ↓±3 transitions on Au, in which the strength of the d ↓−2→f ↓−3 transition was much larger than the d ↓+2→f ↓+3 transition due to the large spin-orbit splitting in Au(5d ↓±2)-band. In this transition, the final state Au(5f ↓±3) is a small tail state hybridized with the unoccupied Fe(3d ↓) state. Thus, the transition can simply be described as the Au(5d ↓)→Fe(3d ↓) transition as predicted by Sato et al. [J. Magn. Soc. Japan 20 (S1) (1996) 35]. Another type of transition p ↓±1→d ↓±2 on Pt was found to be very strong and plays an important role in the Kerr spectra of TM–Pt, since there are many final states (Pt(5d ↓)) in the transition due to the spin polarization in Pt(5d)-bands.

Effects of the spin-orbit interaction in Heusler compounds: Electronic structures and Fermi surfaces of NiMnSb and PtMnSb.

Electronic structures of the Heusler compounds, NiMnSb and PtMnSb, are investigated by using the linearized-muffin-tin-orbital band method. Equilibrium properties such as lattice constants and bulk moduli are obtained from total energy calculations and effects of the spin-orbit interaction on electronic structures and Fermi surfaces are explored. In the semirelativistic band calculations, NiMnSb is half-metallic, i.e., metallic for majority spin while semiconducting for minority spin bands, but PtMnSb is normal metallic at the experimental lattice constant. PtMnSb becomes a half metal if we take into account the spin-orbit interaction explicitly in the calculation. Equilibrium lattice constants obtained in the ferromagnetic band calculations agree very well with experimental values. The magnitudes of the energy gap in the minority spin bands are found to be sensitive to the variation of the lattice constants for NiMnSb and PtMnSb. The effect of the spin-orbit interaction is substantial in PtMnSb, in contrast to NiMnSb in which it is negligible. A large spin-orbit splitting at \ensuremath{\Gamma} in PtMnSb is due to Pt 6p states near ${\mathit{E}}_{\mathit{F}}$, which may be involved in optical transitions to generate a large magneto-optical Kerr effect. Further, the itinerant electrons that mediate the Ruderman-Kittel-Kasuya-Yosida interaction between Mn magnetic moments in NiMnSb and PtMnSb are identified as those on the nearly spherical hole Fermi surfaces of the 12th majority spin bands centered at \ensuremath{\Gamma}.

Differences between L 3 and L 2 X-ray absorption spectra

The L 3 and L 2 edges of transition metals show differences in their spectral shape. Also the ratio between the L 3 and L 2 edges is found to deviate from 2:1. The interactions responsible for these effects are: the multiplet effects and the 3d (4d) spin-orbit coupling. The electronic interactions and spin- and orbital polarizations of the valence electrons determine the ground state (symmetry) and determine the shape itself. For 4d systems the L 3 and L 2 are separated by a large core spin-orbit splitting of about 100 eV. Differences between their L 3 and L 2 edge originate from the weight transfer between the t 2g and e g peaks due to the multiplet effects. Because this weight transfer is larger for L 3 edge, it is better to use the L 2 edge for a comparison to single particle calculations. The only interaction which can affect their branching ratio is the 4d spin-orbit coupling. For 3d systems the multiplet effects dominate all other interactions and the L 3 and L 2 are completely different and show their characteristic multiplet structure. The multiplet effects are large enough to affect also the branching ratio.

A comparison of photoelectron spectroscopy and two-photon ionization spectroscopy: Excited states of Au2, Au3, and Au4

Photoelectron spectra of Au−n with n=2–4 are reported. Due to the relatively high photon energy used in our experiment (hν=6.424 eV) and the energy resolution of about 50 meV, various transitions into excited states of the neutral clusters are resolved. It is demonstrated that photoelectron spectra can serve as a map of the electronic states of a cluster, while the high resolution of the resonant two-photon ionization (R2PI) method gains information about the symmetry of the states. The comparison with similar data of Ag−n clusters indicates the influence of relativistic effects and the large spin–orbit splitting for Au.

Optical and magneto-optical properties of Fe0.28TaS2

Ellipsometry and polar magneto-optical Kerr effect measurements were performed on Fe0.28TaS2 in the photon energy region 0.6-5 eV. The complex dielectric tensor was calculated from the measured data. Strong anisotropy was found in the diagonal elements of the dielectric tensor. Strong absorption bands at 1.6 and 3.8 eV for light polarized perpendicular to the c-axis were attributed to transitions between Ta 5d bands. In the off-diagonal element of the dielectric tensor five transitions with diamagnetic line shapes were observed. These transitions are between Fe 3d and Ta 5d states. The large magneto-optical contribution results from the large exchange splitting of the Fe 3d states combined with the large spin-orbit splitting of Ta 5d states.

Photoelectron spectroscopy of krypton and xenon clusters

Ultraviolet photoelectron spectra have been measured for pulsed supersonic beams of krypton and xenon as dilute mixtures in helium. The spectra exhibit broad bands which are located at lower ionization energies relative to the monomer ion states, 2P3/2 and 2P1/2, with which they correlate. The structural features of the spectra, particularly in the first band group, become more complex with increasing condensation, apparently relating to the mean cluster size associated with each spectrum. The spectra are interpreted using the cluster-size dependent core-ion model developed to explain the analogous spectra of the argon clusters. The argon clusters spectra were interpreted as showing the presence of Ar+3, Ar+7, and Ar+13 core ions, with Ar+3 involved in the ionization of small neutral clusters, and Ar+13 produced by the dominant ionization mechanism in large clusters as well as in solid argon. The krypton and xenon clusters show variations of this behavior. The relatively large spin-orbit splitting of the Kr+ and Xe+ p-hole states is reflected in the two band groups observed in the respective Kr and Xe clusters spectra. The lower ionization energy band group in each case exhibits structural features similar to those observed for the argon clusters spectra. The krypton spectra indicate, that for the largest clusters, all three core-ion mechanisms are operative; whereas, for xenon, the largest clusters show only the triatomic core ion, Xe+3, as involved in the ionization mechanism. The high pressure clusters spectra of argon, krypton, and xenon are effectively identical with those reported for their respective condensed thin films, indicating that these variations in the core-ion mechanism of ionization are also responsible for the differences observed in the ultraviolet photoemission spectra of the rare-gas solids.

Piezoreflectivity Studies of the Exciton and the Step in Potassium Iodide

Piezoreflectivity spectra of KI were measured and energy shifts due to the cubic, tetragonal and trigonal deformations were obtained on the lowest energy exciton and the step which has been identified with the onset of a band to band transition. Energy shifts of the exciton were found similar to those of the step in the case of the uniaxial deformations. The similarity was reduced to the similarity of the electronic state, because of the large spin-orbit splitting of the 5 p state of an I - ion. Difference in shift energy of the exciton and the step in the case of the cubic deformation was accounted for by changes of the effective mass and the high frequency dielectric constant. In addition, energy shifts determined directly from the piezoreflectivity were shown to be the same as those determined from the deformation induced changes of dielectric constants.

Eight-band k

Second-order L\owdin perturbation theory is used to calculate the interaction matrices for an eight-band k\ensuremath{\cdot}p model (near the \ensuremath{\Gamma} point) of zinc-blende crystals under a uniform strain. The model treats the ${\mathrm{\ensuremath{\Gamma}}}_{6}$ conduction bands, ${\mathrm{\ensuremath{\Gamma}}}_{8}$ valence bands, and ${\mathrm{\ensuremath{\Gamma}}}_{7}$ spin-orbit split-off bands. The model includes strain interactions arising from both the orbital and spin-orbit terms of the Hamiltonian. In addition to the usual Pikus-Bir deformation-potential constants, a, b, and d, which describe the coupling of the valence band to strain, two new deformation-potential constants arise, a' and b', which describe the coupling of the conduction band to strain. The constant a' couples the conduction band to hydrostatic deformations and the constant b', which results from a lack of inversion symmetry, couples the conduction band to shear deformations. The strain also introduces a k-dependent conduction-band--valence-band mixing that is linear in strain, in wave vector, and in the momentum matrix element between the conduction and valence bands. In the absence of strain, the eight-band Kane model is recovered. Under a finite strain, in the limit of a large conduction-band--valence-band gap and large spin-orbit splitting, the four-band Luttinger model with strain is recovered.

QCD sum rule analysis of spin-orbit splitting in baryons

A determination of spin-orbit splitting in N and Λ using the QCD sum rule technique of Shifman, Vainshtein, and Zakharov is presented. The QCD sum rules coupling to J P = 1 2 − nucleons, first considered by Belyaev and Ioffe are shown to provide a consistent description of N 1 2 − (1535) . The QCD sum rules coupling to the low-lying Δ 1 2 + , Λ 1 2 − , and Λ 3 2 − , are presented as these sum rules have not been previously considered in the literature. The non-perturbative calculations of spin-orbit splitting and odd parity excitation energies in the low-lying states of N and Λ are in agreement with experimental data. This is in contrast to conventional quark models. The large spin-orbit splitting in Λ resonances arises without invoking coupling to the KN scattering channel. The reduction of the strange quark condensate relative to the u or d quark condensate acts to increase the spin-orbit splitting in the low-lying Λ resonances. The results do not exclude coupling of Λ(1405) to the KN channel provided any additional spin-orbit splitting arising from the coupling is of the order of 30 MeV. Finally the Δ 1 2 + sum rules cast doubt on the existence of the unconfirmed (one ∗) Δ 1 2 + (1550) resonance.

The Role of off-Diagonal Disorder on Alloy Phase Stability: An Application To The Ni-Pt System

The occurrence of ordering in the Ni-Pt alloy system seems to violate theoretical predictions based on a tight-binding description of the electronic structure [1,2,3]. In these descriptions of transition metal alloys, ordering is predicted if the d-band is about half filled, and phase separation is predicted if the d-band is almost empty or almost full. This so-called bandfilling argument clearly fails in the case of Ni-Pt alloys, which order despite an almost filled d-band. The band filling rule is derived under the assumption that off-diagonal disorder (ODD), that is, the difference in d-bandwidths of the constituents, can be ignored. In Ni-Pt that is not the case, the d-bandwidths of the pure elements Ni and Pt are 0.32 Ry and 0.57 Ry, respectively [4]. However, it has been argued that taking ODD into account would result in an even stronger phase separation tendency in the theoretical prediction [2]. Magnetism is not a factor in equiatomic Ni-Pt alloys, and thus can not be invoked to correct the erroneous prediction. Other factors, such as spin orbit coupling in the relativistic description of Pt can change the prediction only if very large spin orbit splitting is assumed on the Pt atom [5].

Strong coupling expansions in pure lattice gauge theory mixed actions: Carles Ayala and Marià Baig. Grup de Física Teòrica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

A determination of spin-orbit splitting in N and Λ using the QCD sum rule technique of Shifman, Vainshtein, and Zakharov is presented. The QCD sum rules coupling to JP = 12− nucleons, first considered by Belyaev and Ioffe are shown to provide a consistent description of N12−(1535). The QCD sum rules coupling to the low-lying Δ12+, Λ12−, and Λ32−, are presented as these sum rules have not been previously considered in the literature. The non-perturbative calculations of spin-orbit splitting and odd parity excitation energies in the low-lying states of N and Λ are in agreement with experimental data. This is in contrast to conventional quark models. The large spin-orbit splitting in Λ resonances arises without invoking coupling to the KN scattering channel. The reduction of the strange quark condensate relative to the u or d quark condensate acts to increase the spin-orbit splitting in the low-lying Λ resonances. The results do not exclude coupling of Λ(1405) to the KN channel provided any additional spin-orbit splitting arising from the coupling is of the order of 30 MeV. Finally the Δ12+ sum rules cast doubt on the existence of the unconfirmed (one ∗) Δ12+(1550) resonance.

Stepwise enhancement of bound dipoles in strongly coupled plasma: C. Deutsch. L.P.G.P., Bât. 212, Université Paris XI, 91405 Orsay, France and Department of Applied Physics, Stanford University, Stanford, California 94305; G. Naouri. L.P.G.P., Bât. 212, Université Paris XI, 91405 Orsay, France

A determination of spin-orbit splitting in N and Λ using the QCD sum rule technique of Shifman, Vainshtein, and Zakharov is presented. The QCD sum rules coupling to JP = 12− nucleons, first considered by Belyaev and Ioffe are shown to provide a consistent description of N12−(1535). The QCD sum rules coupling to the low-lying Δ12+, Λ12−, and Λ32−, are presented as these sum rules have not been previously considered in the literature. The non-perturbative calculations of spin-orbit splitting and odd parity excitation energies in the low-lying states of N and Λ are in agreement with experimental data. This is in contrast to conventional quark models. The large spin-orbit splitting in Λ resonances arises without invoking coupling to the KN scattering channel. The reduction of the strange quark condensate relative to the u or d quark condensate acts to increase the spin-orbit splitting in the low-lying Λ resonances. The results do not exclude coupling of Λ(1405) to the KN channel provided any additional spin-orbit splitting arising from the coupling is of the order of 30 MeV. Finally the Δ12+ sum rules cast doubt on the existence of the unconfirmed (one ∗) Δ12+(1550) resonance.

Nuclear ground-state properties and nuclear forces in the unitary-model-operator approach: Application to 16O.

A formulation is given to derive an effective interaction in the framework of the unitary-model-operator approach. A unitary transformation is introduced to describe two-body correlations and is determined from the condition that the effective interaction should be decoupled between the low- and high-momentum spaces. A unitary transformation of the Hamiltonian is made and the transformed Hamiltonian is represented in a cluster-expansion form. The effective interaction thus defined is E independent and Hermitian. The contributions of one-, two-, and three-body-cluster terms are taken into consideration. The self-consistent single-particle potential is considered sym- metrically for both occupied (hole) and unoccupied (particle) states. The theory is applied to the calculation of the ground-state properties of $^{16}\mathrm{O}$ using three potentials, namely, the Paris, Reid soft-core, and supersoft-core potentials. A large gain in the binding energy is obtained. Final results for the gound-state energy and the charge radius are as follows: -119.2 MeV and 2.62 fm for the Paris, -115.1 MeV and 2.60 fm for the Reid soft core, and -121.7 MeV and 2.62 fm for the supersoft core. The single-particle energies of the occupied orbits are also calculated. Good agreement between the calculated and experimental energies is obtained. In particular, a large spin-orbit splitting of the 0p orbits is reproduced with the results 5.6 MeV for the Paris, 5.1 MeV for the Reid soft core, and 5.4 MeV for the supersoft core, which should be compared with the experimental value 6.1 MeV.

Spin-orbit splitting in σ-hypernuclei

The shell model analysis of experimental 0+, 2+ spectra of\(_{\Sigma ^ - } {}^{12}Be\) and\(_{\Sigma ^ - } {}^{16}C\) as obtained from (K−,π+) in-flight and stoppedK− reactions, is performed. It suggests a large (twice that for nucleons) spin-orbit splitting of Σ hyperon levelsp3/2 andp1/2. Certain constraints on effective central ΣN interaction arise, as well. Some experiments are put forward to further test this value and to extend it to Ξ hypernuclei.