Distorted vortex lattice in a tetrahedral superconductor

The equilibrium shape and the orientation of the vortex lattice are studied for an s-wave tetrahedral superconductor in the vicinity of the upper critical field. The phase diagram, which includes transitions between rhombic and rectangular lattices, is constructed in the parameter space of the Ginzburg-Landau functional. The developed theory is applied to the heavy-fermion superconductor PrOs₄Sb₁₂. In a wide range of parameters, the shape of the vortex lattice is only weakly dependent on the temperature. The neutron scattering measurements of the vortex lattice in PrOs₄Sb₁₂ can be explained by particularities of the tetrahedral symmetry group and are further supported by analysis of the appropriate band structure calculations. The text was submitted by the authors in English.     

Multiple superconducting phases in heavy fermion compounds PrOs4Sb12 and CeCoIn5

In recently discovered heavy fermion compounds, quasi-two-dimensional CeCoIn₅ and skutterudite PrOs₄Sb₁₂, multiple superconducting phases with different symmetries manifest themselves belowT _c. The angle-resolved magnetothermal transport measurements revealed that in PrOs₄Sb₁₂ a novel change in the symmetry of the superconducting gap function occurs deep inside the superconducting state. The ultrasound velocity measurements revealed that in CeCoIn5 the Fulde-Ferrel-Larkin-Ovchinikov (FFLO) phase, in which the order parameter is spatially modulated and has planar nodes aligned perpendicular to the vortices, appears at low temperature and high field. These results open up a new realm for the study of the superconductivity with multiple phases.     

Anisotropic superconductivity in PrOs4Sb12

Recently two anisotropic superconducting gap functions have been observed in the skutterudite PrOs₄Sb₁₂. These order parameters are spin-triplet. There are at least 2 distinct phases in a magnetic field, bearing some resemblance to superfluid ³He. Here we present an analysis of the thermodynamic properties in these two superconducting states within the weak-coupling BCS theory.     

Magnetic structure of the Nd5Ge3 compound

Neutron diffraction measurements of the Nd₅Ge₃ intermetallic compound with a hexagonal structure (space group P6₃/mcm) have been performed at temperatures of ～10 and 293 K. The basis functions of irreducible representations of the space group D _6h ³ (P6₃/mcm), which are calculated as a result of the symmetry analysis of possible magnetic structures with the wave vector k = μb ₁, are used to facilitate the search for a real model of the magnetic structure of the compound.     

Symmetry analysis in neutron diffraction studies of magnetic structures: 3. An example: the magnetic structure of spinels

Using the symmetry analysis technique developed in the two earlier papers of this series a study is made of the magnetic structures in spinels (space group O⁷_h). The magnetic structures with the wave vector K = 0 and those with K ≠ 0 are considered in detail. As an example, an analysis is given of the magnetic ordering in MgV₂O₄ which is characterized by the three-arm star {bdK₁₀} (in Kovalev's notation) and of that in HgCr₂S₄ where a helical structure corresponding to the star {bdK₆} has been found. For each of the three stars we have determined the composition of the magnetic representation and calculated the basis functions of the irreducible representations. For the magnetic structures determined experimentally we have specified the irreducible representations by which these structures should be described. The examples furnished illustrate the typical situations liable to occur when performing symmetry analysis of magnetic structures of crystals.     

Symmetry features of the energy bands of SiP2 with the pyrite structure

Results on the structure of silicon diphosphide are examined. The space group T _h ⁶ (Pa3) is used to derive the matrices for the irreducible representations of the symmetry groups for all types of wave vectors in the Brillouin zone. It is found that time inversion results in additional degeneracy at most points on the surface of the zone.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 92–95, December, 1973.     

The clean thermally induced W {001} (1 × 1) → (√2 × √2) R 45° surface structure transition and its crystallography

A (√2 × √2)R45° surface structure on W {001} produced only by cooling below ~370 K, first reported by Yonehara and Schmidt, has been investigated by LEED, AES, work function change, characteristic loss and low energy Auger fine structure measurements. No significant changes at any energy up to 520 eV occur in the standard Auger spectrum upon cooling to 220 K for as long as 30 min after a flash to >2 500 K. The work function of the (√2 × √2) R45° at 210 K is 20 ± 10 mV below that of the (1 × 1) surface, and a sensitive feature in the fine structure of the N₇VV AES transition shows approximately 60% attenuation. Unlike for H₂ adsorption, the “surface plasmon” loss peak exhibits little if any measurable attenuation and no measurable shift in energy as the crystal cools to form the (√2 × √2)R45°. The rate of intensity buildup in the $\text{1}\text{2}$-order LEED beams is strictly temperature dependent, and significant differences exist between the $\text{1}\text{2}$-order LEED spectra produced by cooling and those produced by H₂ adsorption. Only 2-fold symmetry was observed in the LEED beam intensities at exactly normal incidence, rather than 4-fold as expected for statistically equal numbers of rotationally equivalent domains. The LEED I-V spectra for 24 fractional order beams and 12 integral order beams, taken over large energy ranges at normal incidence, clearly establish that the beam intensities display 2 mm point group symmetry, and hence a preference of one domain orientation over the other. No beam broadening or splitting effects were apparent, implying only incoherent scattering from the various domains. The half-order beam spectra (±h/2, ±h/2) are identical in relative intensity to the (±h/2, ±h/2) spectra but different in absolute intensity by a constant factor, which can be explained only by domains with p2mg space group symmetry rather than just p2mm. Adsorption of H₂ onto the cooled (√2 × √2)R45° structure restores the 4-fold symmetry in the LEED beam intensities at normal incidence, giving a c(2 × 2) hydrogen structure, the same as when adsorbing H₂ onto the above room temperature (1 × 1) crystal. This strongly supports the observed p2mg symmetry as being a true property of the cooled (√2 × √2)R45° surface structure. These results show that the (1 × 1) → (√2 × √2) R45° transition produced by cooling is a transition involving displacement of surface W atoms, and that it apparently can be characterized as an order-order, second degree, homogeneous nucleation process, which is strongly prohibited by the presence of impurities or defects.     

Effect of CO and H adsorption on the compositional structure of binary nanoalloys via DFT modeling

Theoretical methods (DFT/B3LYP and MP2) have been used to optimize the geometries of the Al _x Sb _y (x + y = 3, 5) clusters and their anions. Single point energy computations at CCSD(T) level have also been performed using the optimized B3LYP and MP2 structures. The basis sets used for Al and Sb atoms are 6-311+G(2d) and LANL2DZdp ECP, respectively. Harmonic vibrational frequency computations were carried out to confirm the nature of the stationary points. We report the structural and spectroscopic parameters of the named clusters. We also report the relative energy of the clusters, the vertical electron detachment energy, the adiabatic electron detachment energy and the adiabatic electron affinity. The most stable structures at the CCSD(T)//MP2 level are, the D _∞h linear structure (AlSb₂) and the C _2v V-bent structure (AlSb ₂ ^? ), the C _2v V-bent structure (Al₂Sb and its anion), the C _2v edge-capped tetrahedron (Al₂Sb₃ and its anion), the C _2v trigonal bipyramidal structure (Al₃Sb₂ and its anion), the C _4v square pyramidal (AlSb₄) and a C _2v ground structure for its anion, the C _2v planar trapezoidal structure (Al₄Sb) and the C _2v edge-capped tetrahedron (Al₄Sb^?). The adiabatic electron affinities calculated at the CCSD(T)//MP2 level are 2.17 eV (AlSb₂), 2.17 eV (Al₂Sb), 2.38 eV (Al₂Sb₃), 2.76 eV (Al₃Sb₂), 2.21 eV (AlSb₄) and 2.03 eV (Al₄Sb). The findings of this research are analysed, discussed and compared with the analogous picnogenides clusters.     

Composite spin-triplet superconductivity in an symmetric lattice model

The two-channel Anderson lattice model which has SU (2) ⊗ SU (2) symmetry is of relevance to understanding of the magnetic, quadrupolar and superconducting phases in U_1-xTh_xBe₁₃ or Pr based skutterudite compounds such as PrFe₄P₁₂ or PrOs₄Sb₁₂. Possible unconventional superconducting phases of the model are explored. They are characterized by a composite order parameter comprising of a local magnetic or quadrupolar moment and a triplet conduction electron Cooper-pair. This binding of local degrees of freedom removes the entropy of the non Fermi-liquid normal state. We find superconducting transitions in the intermediate valence regime which are suppressed in the stable moment regime. The gap function is non analytic and odd in frequency: a pseudo-gap develops in the conduction electron density of states which vanishes as |ω| close to ω = 0. In the strong intermediate valent regime, the gap function acquires an additional -dependence. Received 28 February 2002 / Received in final form 18 April 2002 Published online 9 July 2002     

Raman scattering investigation of ferroelastic Sb5O7I crystals

Sb₅O₇I undergoes a displacive phase transition at 481 K where the symmetry is changed fromC _6h ² toC _2h ⁵ . In the low temperature monoclinic phase the crystal is ferroelastic. The polarized Raman spectra of Sb₅O₇I have been measured at various temperatures below and above the phase transition. The frequencies and symmetries of most of the theoretically expected Raman active phonons in the ferroelastic phase have been determined. The observation of a soft mode in the ferroelastic phase which disappears above the phase transition together with the fact that the unit cell of the ferroelastic phase is twice as large as that of the paraelastic structure permits the conclusion that the phase transition results from a phonon instability at the Brillouin zone boundaryM-point of the hexagonal phase. The temperature dependent splittings and intensity changes of several Raman lines are discussed with respect to the ferroelastic property of the crystal and the phase transition.     

X-ray absorption investigation of some high oxidation states of six-co-ordinated iron in oxides of perovskite or K2NiF4-type structures

Synchrotron radiation has been used to investigate the X-ray absorption properties (Fe K-edge and EXAFS) of oxides containing iron with a high oxidation state (+3, +4, +5) in regular (O_h) or distorted (D_4h) octahedral co-ordination. It is shown that the usual monotonic variation of the edge energy with oxidation state depends closely on the electrical properties of the material and on the symmetry of the iron site. Moreover, the main absorption line is split when the symmetry of the iron site is lowered from O_h, to D_4h. New evidence is thus given that X-ray absorption spectroscopy can provide useful information about the absorbing atom site: it could be used in principle to point out certain types of distortions of the first shell of neighbors around the absorbing atom. A full EXAFS analysis of this shell and XANES (X-ray absorption near edge structure) data are also reported and discussed.     

Spontaneous breakdown of the gauge chiral symmetry and the cabibbo angle

From the general treatment of the spontaneous breakdown of the chiral SU(3)xSU(3) group down to the electromagnetic U(l) gauge group it is conjectured that the bare Cabibbo angle isπ/4. Imposing the self-consistency condition of Cabibbo and Maiani on the weak and electromagnetic corrections to the chiral symmetry breaking Hamiltonianh=ε₀ u ₀+ +ε₃ u ₃+ε₈ u ₈ leads to the determination of the physical Cabibbo angle. The agreement with the experimental value is reached when the parametrization ofh of Brandt and Preparata is used.     

Application of symmetry groups of four-dimensional space in spectroscopy of crystals

A method of classification of many-electron states that involves symmetry groups of four-dimensional space is developed. Taking into account the spatial and temporal symmetry, the selection rules for electric and magnetic dipole transitions are investigated. The reduction relations for the irreducible representations of the orthogonal group O ₄ and the group R ₄ of pure rotations of the four-dimensional space on the groups and O _h ⁴ and O ⁴ of the four-dimensional cube and of the octahedron on the three-dimensional groups O _h and D _6h of the cubic and hexagonal systems, respectively, are obtained. The four-dimensional classification of the levels of the spin-orbit interaction of rare earth ions for the intermediate reduction on the group of the four-dimensional cube is performed. With the help of the irreducible representations of the O ₄ group, the selection rules of magnetic and forbidden electric dipole transitions, as well as of intercombination transitions, are investigated.     

Tunneling conductance in ferromagnet/Sr2RuO4 junction: Detection of the d-vector direction

When a spin-triplet superconductor is attached to a ferromagnet, the tunneling conductance depends not only on the degree of the spin polarization but also sensitively on the relative angles between the magnetic moment in ferromagnet and the d-vector in spin-triplet superconductor. We study theoretically the tunneling conductance in ferromagnet/triplet superconductors assuming three nodal unitary gap functions, which are promising candidates for the pairing symmetry of Sr₂RuO₄. Our results suggest that the d-vector direction in Sr₂RuO₄ may be detected by performing angular dependent tunneling spectroscopy in this hybrid structure. We also show that these three gap functions can be distinguished by their distinctive conductance spectra.     

Levelcrossing experiments in the first excited1 P 1 states of the alkaline earths

The hyperfine structure of the lowest¹P₁ state of²⁵Mg,⁴³Ca,⁸⁷Sr,¹³⁵Ba and¹³⁷Ba have been measured by the level-crossing and anticrossing technique. The magnetic dipole and electric quadrupole coupling constants determined by these measurements are²⁵Mg(3s3p¹P₁):A=? 7.7(5) MHz; 16 MHz>B>0 MHz,⁴³Ca(4s4p¹P₁):A=? 15.3(4) MHz; ¦B¦<12 MHz,⁸⁷Sr (5s5p¹P₁:A=? 3.4(4) MHz;B=39(4) MHz,¹³⁵Ba(6s6p¹P₁):A=? 97.5(1.0) MHz;B=31(9)MHz,¹³⁷Ba(6s6p¹P₁):A=?109.2(1.2) MHz;B=51(12)MHz. The results have been compared with the predictions of the Breit-Wills theory of the two-electron hyperfine structure using the experimental data on the³P states. Large discrepancies have been observed which are due to different radial wave functions of thes andp electron in the triplet and singlet system. This effect has been taken into account by fitting the data with the aid of two additional parameters. That this procedure is justified is shown by an analysis of the fine structure splitting, the life times, and the isotopic shifts in thesp configurations of group II elements.     

Pressure induced transitions in MnAs and MnAs0.80Sb0.20

The NiAs type phases of MnAs and MnAs_0.80Sb_0.20 were studied for at pressures up to 12 GPa using the energy dispersive X-ray diffraction technique. MnAs (at ∼ 0.1 GPa) and MnAs_0.80Sb_0.20 (at ∼4 GPa) transform from the NiAs into the MnP type structure, followed by strong volume reductions. The anomalous compressibility properties are probably correlated with changes in the electronic band structure and in this respect are related to the high to low spin conversion in MnAs₁₋xP_x.     

Modes of vibrations due to (U-center + additive cation impurities) in alkali halides

Local and resonant modes due to hydride ions in various alkali halides containing additive cation impurities have been computed by the Green function technique. Local vibrations due to U-centers in alkali halides have O_h symmetry. When one of the six nearest neighbour cations is replaced by an additive impurity, the site symmetry of the system is lowered from O_h to C_4v. The phonon Green functions matríx is analysed according to the irreducible representation of the point group symmetry pertaining to the substitutional impurity. We have considered the vibrations of the hydride ion and all its six nearest neighbours. Analytical expressions have been derived for various modes of vibrations. Using group theory the 21 × 21 matrix has been block diagonalized into various irreducible representations. The effect of mass changes and the changes in short-range force constants have been taken into account. The computed results of the localized modes have been compared with the available experimental results. Good agreement has been found. Theoretical results on resonant modes are also displayed, which will be of use in future experiments on these systems.     

Exciton absorption parameters in TlGaS2 crystals

It is shown that, because the shape of the exciton absorption curve in crystalline TlGaS₂ is described by the Fano antiresonance profile, the experimentally observed exciton peak corresponds to a modified state which is the result of the configuration interaction of a discrete state (exciton) with the quasi-continuum of conduction-band states. The oscillator strength for the transition to the discrete (“pure”) exciton state is calculated as F ₀=1.22×10^?2. The exciton transition selection rules are calculated for two assumed symmetry groups, D _2h and D _4h . An analysis of the selection rules for the dipole-allowed exciton transition permits one to conclude that the symmetry group for the TlGaS₂ crystal is D _2h .     

Influence of the symmetry on the circular dichroism in angular resolved core-level photoemission

The model for angular resolved photoemission from adsorbed atoms is extended to account for the non-axial symmetry of atoms in a crystal field. In particular, circular dichroism in the angular distribution (CDAD) is theoretically investigated. A special emphasis is put on the case when incident photons are propagating along the principal axis of an atom in C_nv symmetry. The model, although mainly developed for adsorbates, may also be used as a base for emission from solid surfaces. An extension to simple bulk symmetries, like D_6h for hexagonal or O_h for cubic crystals, is included. The CDAD for normal incidence does not vanish in the extended model and reflects the symmetry of the adsorption site. Scattering induced final state effects are discussed for alkali metal adsorption. A numerical calculation of the emission from the shallow 4p core level of Rb atoms adsorbed in a (√3×√3)−R30° structure on a Pt(111) surface is presented. In this case even the extended photoemission model predicts the absence of CDAD. The appearance of CDAD is only possible due to the scattering of photoelectrons from the neighbouring atoms of the solid.