State Property Systems and Closure Spaces: A Study of Categorical Equivalence

We show that the natural mathematical structureto describe a physical entity by means of its states andits properties within the Geneva–Brussels approachis that of a state property system. We prove that the category of state property systems (andmorphisms) SP is equivalent to the category ofclosure spaces (and continuous maps) Cls. We showthe equivalence of the state determinationaxiom for state property systems with the T₀separation axiom for closure spaces. We alsoprove that the category SP ₀ ofstate-determined state property systems is equivalent tothe category L ₀ of based completelattices. In this sense the equivalence of SP andCls generalizes the equivalence ofCls ₀ (T₀ closure spaces)and L ₀ proven by Erne(1984).     

Luminescence characteristics of ultraviolet upconversion from Er 3 + :YAG crystal by Ar + laser (488 nm) excitation

Ultraviolet and violet upconversion signals at 271 nm, 317 nm, 381 nm and 407 nm were observed when an erbium-doped YAG crystal was pumped by an Ar⁺ laser (488 nm). The dependence of intensity of luminescence emitting from the ⁴S _3/2 state and the ²P _3/2 state on pump power (I) was experimentally investigated. Changes from I¹ down to I ^1/2 for the ⁴S _3/2 state and from I² down to I¹ for the ²P _3/2 state were observed. The upconversion mechanism was discussed by means of the rate equations. It appears that energy-transfer upconversion (ETU) is a dominant process for the Er³⁺:YAG crystal used in our experiment. Received 20 March 2001 and Received in final form 11 July 2001     

Coexistence of superconductivity and spin density wave orderings in the organic superconductor (TMTSF) 2 PF 6

The phase diagram of the organic superconductor (TMTSF)₂PF₆has been revisited using transport measurements with an improved control of the applied pressure. We have found a 0.8 kbar wide pressure domain below the critical point (9.43 kbar, 1.2 K) for the stabilisation of the superconducting ground state featuring a coexistence regime between spin density wave (SDW) and superconductivity (SC). The inhomogeneous character of the said pressure domain is supported by the analysis of the resistivity between T _SDW and T _SC and the superconducting critical current. The onset temperature T _SC is practically constant ( 1.20±0.01 K) in this region where only the SC/SDW domain proportion below T _SC is increasing under pressure. An homogeneous superconducting state is recovered above the critical pressure with T _SC falling at increasing pressure. We propose a model comparing the free energy of a phase exhibiting a segregation between SDW and SC domains and the free energy of homogeneous phases which explains fairly well our experimental findings. Received 3 September 2001 and Received in final form 9 November 2001     

Dual model for magnetic excitations and superconductivity in UPd 2 Al 3

The Heavy Fermion state in UPd₂Al₃ may be approximately described by a dual model where two of the three U-5 f electrons are in a localized state split by the crystalline electric field into two low lying singlets with a splitting energy Δ≃ 6 meV. The third 5 f electron has itinerant character and forms the Heavy Electron bands. Inelastic neutron scattering and tunneling experiments suggest that magnetic excitons, the collective propagating crystal field excitations of the localized 5 f electrons, mediate superconducting (sc) pairing in UPd₂Al₃. A theory for this novel mechanism is developed within a nonretarded approach. A model for the magnetic exciton bands is analyzed and compared with experiment. The sc pair potential which they mediate is derived and the gap equations are solved. It is shown that this mechanism favors an odd parity state which is nondegenerate due to the combined symmetry breaking by the crystalline electric field and the AF order parameter. A hybrid model including the spin fluctuation contribution to the pairing is also discussed. Received 22 October 2001 and Received in final form 28 February 2002     

On the evolution of the ground state in the system U x La 1 - x S: Polarized neutron diffraction and X-ray magnetic circular dichroism study

In the U_xLa_1-xS system there is an abrupt loss of the long-range ferromagnetic ordering found in pure US at a critical concentration x _c ∼ 0.57, which is far above the percolation limit. As the magnetic ground state in such a system can be strongly affected by small variations of the 5f localization, we have investigated a set of samples with different x by polarized neutron diffraction and X-ray magnetic circular dichroism (XMCD). The neutron results are consistent with early measurements performed on pure US. Even at the lowest U content (x = 0.15, below x _c ) the shape of the induced form factor (f ( Q )) is comparable with that found for x = 1 and is well reproduced by either a U⁴⁺ or a U³⁺ state. The ratio between the orbital and the effective spin moments in the XMCD measurements confirms this result, but the evolution of the shape at the M₅ edge suggests an abrupt change in the distribution of the electrons (holes) in the 5 f density of states around x _c . Received 31 January 2001     

Thermal conductivity and thermal Hall effect in Bi- and Y-based high-T c superconductors

Measurements of the thermal conductivity (k_xx) and the thermal Hall effect (k_xy) in high magnetic fields in Y- and Bi-based high-T _c superconductors are presented. We describe the experimental technique and test measurements on a simple metal (niobium). In the high-T _c superconductors k_xx and k_xy increase below T _c and show a maximum in their temperature dependence. k_xx has contributions from phonons and quasiparticle (QP) excitations, whereas k_xy is purely electronic. The strong increase of k_xy below T _c gives direct evidence for a strong enhancement of the QP contribution to the heat current and thus for a strong increase of the QP mean free path. Using k_xy and the magnetic field dependence of k_xx we separate the electronic thermal conductivity ( k _xx ^el ) of the CuO ₂ -planes from the phononic thermal conductivity ( k _xx ^ph ). In YBa₂Cu₃O _{7 - δ} k _xx ^el shows a pronounced maximum in the superconducting state. This maximum is much weaker in Bi₂Sr₂CaCu₂O _{8 + δ} , due to stronger impurity scattering. The maximum of k _xx ^el is strongly suppressed by a magnetic field, which we attribute to the scattering of QPs on vortices. An additional magnetic field independent contribution to the maximum of k_xx occurs in YBa₂Cu₃O _{7 - δ} , reminiscent of the contribution of the CuO-chains, as determined from the anisotropy in untwined single crystals. Our data analysis reveals that below T _c as in the normal state a transport (τ) and a Hall ( ) relaxation time must be distinguished: The inelastic (i.e. temperature dependent) contribution to τ is strongly enhanced in the superconducting state, whereas displays the same temperature dependence as above T _c . We determine also the electronic thermal conductivity in the normal state from k_xy and the electrical Hall angle. It shows an unusual linear increase with temperature. Received 23 August 2000     

Kinematically complete final state investigations of molecular photodissociation: two- and three-body decay of laser-prepared H 3 3 s ? 2 A 1 '

We have performed kinematically complete investigations of molecular photodissociation of triatomic hydrogen in a fast beam translational spectrometer recently built in Freiburg. The apparatus allows us to investigate laser-induced dissociation of neutral molecules into two, three, or more neutral products. The fragments are detected in coincidence and their vectorial momenta in the center-of-mass frame are determined. We demonstrate the potential of the method at the fragmentation of the 3 s ² A ₁ ^′ ( N = 1, K = 0) state of triatomic hydrogen. In this state, three-body decay into ground state hydrogen atoms H+H+H, two-body predissociation into H+H ₂ (v , J), and photoemission to the H ₃ ground state surface with subsequent two-body decay are competing channels. In the case of two-body predissociation, we determine the rovibrational population in the H ₂ (v , J) fragment. The vibrational distribution of H ₂ is compared with approximate theoretical predictions. For three-body decay, we measure the six-fold differential photodissociation cross-section. To determine accurate final state distributions, the geometric collection efficiency of the apparatus is calculated by a Monte Carlo simulation, and the raw data are corrected for apparatus efficiency. The final state momentum distribution shows pronounced correlation patterns which are characteristic for the dissociation mechanism. For a three-body decay process with a discrete kinetic energy release we have developed a novel data reduction procedure based on the detection of two fragments. The final state distribution determined by this independent method agrees extremely well with that observed in the triple-coincidence data. In addition, this method allows us to fully explore the phase space of the final state and to determine the branching ratios between the two- and three-body decay processes. Received 29 March 2001     

Formation of cold Cs ground state molecules through photoassociation in the pure long-range state

We report on the formation of translationally cold Cs₂ ground state molecules through photoassociation in the 1_u attractive molecular state below the 6 s _1/2 +6 p _3/2 dissociation limit. The cold molecules are obtained after spontaneous decay of photoassociated molecules in a MOT and in a dark SPOT. We also used polarized atoms, in the f =3, m f =+3Zeeman ground state. Purely asymptotic and adiabatic calculations including hyperfine interaction and rotation are in excellent agreement with observed structures. As expected, the 1_u state is actually a pure long-range state, consisting of paired atoms, uniquely linked by the first terms of the multipole expansion of the electrostatic interaction. A temperature of 20 K has been measured for the molecular cloud. Received 19 July 1999     

Interplay of structural, magnetic and transport properties in thelayered Co-based perovskite LnBaCo 2 O 5 (Ln = Tb, Dy, Ho)

The oxygen deficient cobaltites LnBaCo₂O₅ (Ln = Tb, Dy, Ho) exhibit two successive crystallographic transitions at T _N ∼340 K and at T _CO ∼210 K. Whereas the first transition (P4/mmm to Pmmm) is related to the long-range antiferromagnetic ordering of the Co ions (spin ordering), the second transition (Pmmm to Pmmb) corresponds to the long-range ordering of the Co²⁺ and Co³⁺ species (charge ordering) occurring in 1:1 ratio in the structure. The charge ordered (CO) state was directly evidenced by the observation of additional superstructure peaks using neutron and electron diffraction techniques. The CO state was also confirmed indirectly from refinement of high resolution neutron diffraction data as well as from resistivity and DSC measurements. From the refined saturated magnetic moment values only, ∼3.7 and ∼2.7 , the electronic configuration of the Co ions in LnBaCo₂O₅ remains conjectural. Two pictures, with Co³⁺ ions either in intermediate spin state ( t ⁵ _2g e ¹ _g ) or in high spin state ( t ⁴ _2g e ² _g ), describe equally well our experimental data. In both cases, the observed magnetic structure can be explained using the qualitative Goodenough-Kanamori rules for superexchange. Finally, in contrast to the parent Ln = Y compound [Vogt et al. , Phys. Rev. Lett. 84, 2969 (2000)], we do not report any spin transition in LnBaCo₂O₅ (Ln = Tb, Dy, Ho). Received 13 December 2000     

Electron spin resonance and magnetic susceptibility suggest superconductivity in Na doped WO3samples

In WO₃ doped with Na (WO₃:Na) an Electron Spin Resonance (ESR) signal with unresolved fine and/or hyperfine structure is detected and used as a probe for the state of the carriers. Using the saturation method we determined the spin-lattice relaxation rate 1/ T ₁ of these paramagnetic centers. Upon cooling below 100 K, 1/ T ₁ decreases markedly, as known to occur in NMR when a gap opens in the superconducting state. At low temperatures, 1/ T ₁ quantitatively follows BCS behavior with a gap K or 2 . The magnetic susceptibility exhibits a strong difference between magnetic-field cooled and zero-field cooled regimes below which also supports a so far unknown superconducting phase resulting from Na doping. Received 14 April 1999 and Received in final form 6 September 1999     

Microscopic interactions in CuGeO 3 and organic Spin-Peierls systems deduced from their pretransitional lattice fluctuations

CuGeO₃ exhibits a Spin-Peierls (SP) transition, at T _SP = 14.3 K, which is announced above 19 K by an important regime of one-dimensional (1D) pretransitional lattice fluctuations which can be detected until about 40 K using X-ray diffuse scattering investigations. A quantitative analysis of this scattering shows that in this 1D direction the correlation length follows the “universal” behaviour expected for the thermal fluctuations of a real order parameter which characterizes the lattice dimerization. This allows to define a 1D mean-field temperature, T _SP ^MF , of about 60 K and invalidates any mean field scenario for the SP transition of CuGeO₃. As T _SP ^MF is as high as 4 T _SP we propose that the 3D-SP order is achieved by the interchain coupling between 1D solitons which form below about 16-20 K. CuGeO₃ being in the non-adiabatic regime, it is also suggested that the observed pretransitional fluctuations of CuGeO₃ originate from the X-ray scattering on a very broad damped critical response of lower frequency than the “critical” phonon modes. From the quantitative analysis of the 1D fluctuations we also estimate the microscopic parameters of the SP chain. These parameters allow to locate CuGeO₃ close to the quantum critical boundary separating the gapped SP ground state to the ungapped anti-ferromagnetic ground state. The vicinity of a quantum critical point emphasizes the role of the quantum and non-adiabatic fluctuations and the importance of the interchain coupling in the physics of CuGeO₃. Finally we compare these findings with those obtained for the organic SP systems (BCPTTF)₂PF₆, (TMTTF)₂PF₆ and MEM(TCNQ)₂. From a similar analysis of the pretransitional lattice fluctuations it is found that (BCPTTF)₂PF₆ and (TMTTF)₂PF₆ are located on the SP gapped classical-quantum boundary and are in the adiabatic regime where the fluctuations lead to the formation of a pseudo-gap in the spin degrees of freedom. Differently, we place MEM(TCNQ)₂ inside the SP quantum phase around the crossover line between the adiabatic and non-adiabatic regimes. Received 13 September 2000 and Received in final form 6 February 2001     

Photoassociative spectroscopy of the long-range state

The photoassociative spectroscopy of the Cs₂ 0 g ^- long-range molecular state dissociating into the asymptote is performed, using cold cesium atoms in a vapor-cell magneto-optical trap (MOT). Vibrational levels from v =0 to v =132 are identified, and their rotational structure is well resolved up J =8 for levels below v =74. These data are analyzed in terms of the Rydberg-Klein-Rees (RKR) procedure, and correspond to 99.6% of an effective potential curve with a minimum at ? and a cm^-1 depth. Both ab initio calculations and simple model estimations predict a double-well structure for this potential curve, which cannot be reproduced presently by the RKR approach but which is confirmed by the presence of giant structures in the spectrum. The 1_u()long-range state is also observed for the first time in Cs₂.     

Appearance of anisotropic non s-wave superconductivity above the critical pressure of antiferromagnetic CeRhIn5

We have carried out ¹¹⁵In nuclear quadrupole resonance (NQR) measurements in CeRhIn₅. At ambient pressure, CeRhIn₅ undergoes an antiferromagnetic AF phase transition at K. The ¹¹⁵In NQR spectrum has shown the appearance of a small internal field in the direction perpendicular to the tetragonal c-axis. With application of a hydrostatic pressure, the AF state is suppressed and the superconductivity appears just above the critical pressure (P = 17 kbar). The nuclear spin lattice relaxation rate 1/T₁ of ¹¹⁵In measured at P = 27 kbar indicates the occurrence of the superconductivity in the nearly AF region. In the superconducting state, 1/T₁ has no Hebel-Slichter coherence peak just below of 2 K and has a power law T-dependence (T³) down to 300 mK. This is consistent with anisotropic superconductivity, with line nodes in the superconducting energy gap: non-s-wave superconductivity occurs in CeRhIn₅. Received 5 July 2000     

Magnetic contributions to the low-temperature specific heat of the ferromagnetic insulator Pr 0.8 Ca 0.2 MnO 3

The Pr _1-x Ca_xMnO₃ system exhibits a ferromagnetic insulating state for the composition range x ? 0.25. A metallic ferromagnetic state is never realized because of the low hole concentration and the very small averaged A-site cation radius. In the present study, the nature of the magnetic excitations at low temperature has been investigated by specific heat measurements on a Pr _0.8 Ca_0.2MnO₃ single crystal. The decrease of the specific heat under magnetic field is qualitatively consistent with a suppression of ferromagnetic spin waves in a magnetic field. However, at low temperature, the qualitative agreement with the ferromagnetic spin waves picture is poor. It appears that the large reduction of the specific heat due to the spin waves is compensated by a Schottky-like contribution possibly arising from a Zeeman splitting of the ground state multiplet of the Pr³⁺ ions. Received 21 May 2001 and Received in final form 14 December 2001     

Study of the positive muon Knight shift in : Evidence for a tetravalent -state and crystalline electric field splitting

We report on transverse field (TF) Muon Spin Rotation (μSR) measurements on a single crystal of the hexagonal heavy fermion superconductor UNi₂Al₃ between 5 K and 300 K. From the measured muon Knight shift (KS) in the easy ( a , b )-plane and along the c-axis we extracted the local magnetic susceptibility tensor [0pt] , which arises from the nearest U-neighbors. By comparison with the bulk susceptibility [0pt] it is found that [0pt] and [0pt] agree well above 150 K but deviate considerably in the basal plane below 150 K, due to the disturbance introduced by the . We succeed in reproducing both [0pt] and [0pt] on the basis of a crystalline electric field (CEF)-approach assuming U to be in the tetravalent state. The disturbance introduced by the affects the CEF-Hamiltonian in an expected manner, suggesting strongly that a CEF-picture implying a rather local 5 f-electron wave function is indeed valid. Reanalyzing older data on UPd₂Al₃ we arrive at the same conclusion. A necessary condition for extracting the local susceptibility was the knowledge of the -site, this information was derived from the analysis of the TF-relaxation rates. At low temperatures we found about 30% of the implanted at the d-site and none at this site above 200 K. The majority fraction was found to be in a tunneling state over six m (or k)-sites around the b-site. No long range diffusion was seen up to room temperature. Received 20 April 1999     

The normal state scattering rate in high- cuprates

A detailed phenomenological model is developed for the normal state transport properties of optimal and overdoped high-T_c cuprates. In particular, an explicit form of scattering rate is identified that may account, qualitatively and quantitatively, for the normal state (magneto)-transport properties of Tl₂Ba₂CuO _{6 + δ} and Bi₂Sr₂CaCu₂O _{8 + δ} across the overdoped side of the phase diagram. The proscribed form of the scattering rate is consistent also with features seen in the photoemission spectroscopy of Bi₂Sr₂CaCu₂O _{8 + δ} and offers a new and intuitive way to understand the evolution of the temperature dependence of the inverse Hall angle in Bi-based cuprates with carrier concentration. Received 5 June 2002 / Received in final form 17 December 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: n.e.hussey@bristol.ac.uk     

Orbital-selective Mott-insulator transition in Ca 2 - x Sr x RuO 4

The electronic structures of the metallic and insulating phases of the alloy series Ca_2-xSr_xRuO₄ ( 0 ? x ? 2) are calculated using LDA, LDA+U and Dynamical Mean-Field Approximation methods. In the end members the groundstate respectively is an orbitally non-degenerate antiferromagnetic insulator (x = 0) and a good metal (x = 2). For x > 0.5 the observed Curie-Weiss paramagnetic metallic state which possesses a local moment with the unexpected spin S = 1/2, is explained by the coexistence of localized and itinerant Ru-4d-orbitals. For 0.2 < x < 0.5 we propose a state with partial orbital and spin ordering. An effective model for the localized orbital and spin degrees of freedom is discussed. The metal-insulator transition at x = 0.2 is attributed to a switch in the orbital occupation associated with a structural change of the crystal. Received 27 July 2001     

Phase transitions in Sr 0.61 Ba 0.39 Nb 2 O 6 :Ce 3+ : I. Susceptibility of clusters and domains

The complex dielectric susceptibility of Sr _0.61 Ba _0.39 Nb ₂ O ₆ :Ce ³⁺ (SBN61:Ce) has been measured at frequencies and temperatures before and after poling. The relaxor behaviour with large polydispersivity observed above the ferroelectric phase transition temperature, T _c = 360 and 340 K for x (Ce) = 0 and 0.0066, respectively, is perfectly modeled within the framework of Chamberlin's dynamically correlated domain approach. Below T _c the dynamic nanodomain state crosses over into a ferroelectric state with polydispersive domain wall dynamics at very low frequencies. Presumably SBN61:Ce belongs to the three-dimensional random field Ising rather than to the dipole glass universality class. Received 1 October 1999     

Phase diagram and equations of state of BaSO4

Abstract

The phase diagram and equations of state of BaSO₄, were determined up to 29 GPa and 1000 K in a resistance-heating type diamond anvil cell. At room temperature, barite is the stable form of BaSO₄ which undergoes a reversible phase transition at 10 GPa. The high-pressure form is tentatively determined to be triclinic. At high temperature, a similar phase transition takes place in BaSO₄, but at a pressure higher than that at room temperature. Our results indicate that the phase boundary of the two polymorphs in BasO₄ has a positive slope (dT/dP) of 90 K/GPa. The equations of state for both barite and its high-pressure phase are reported.     

ESR study of calix[4]arene by spin-trapping method

Electron spin resonance (ESR) measurements are introduced to investigate the interaction between 5,11,17,23-tetrabromo-25,26,27,28-tetramethoxycalix[4]arene (II ₄) and 2-methyl-2-nitrosopropane (MNP) or nitrosodurene (ND) which are used as spin-trapping reagents under ultraviolet irradiation. In most cases, the complicated ESR spectra were observed because of the overlap of ESR signals attributed to several spin adducts in different conformations or in an inclusion state. However, after the optimum amount of ND was added into theII ₄ solution, the ESR spectrum showed that each nitrogen hyperfine line was further split to 1:2:1 triplet lines, and this is a typical spectrum ascribed to the spin adduct of ND at one para position ofII ₄.