IFS attractors and Cantor sets

We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R³ such that every homeomorphism f of R³ which preserves K coincides with the identity on K.     

Magnetic structures and crystal field in the heavy electron materials YbAgGe and YbPtIn

We have examined the magnetic properties of the heavy electron compounds YbAgGe and YbPtIn by ¹⁷⁰Yb M?ssbauer spectroscopy down to 0.1 K, and the crystal field properties of YbAgGe by Perturbed Angular Correlations (PAC) measurements up to 900 K. In YbAgGe, we show that each of the two magnetically ordered phases below 0.8 K involves a specific incommensurate modulation of the Yb moment. An analysis of existing low temperature specific heat data suggests the persistence of fluctuations of the correlated Yb spins down to 0.1 K. The PAC data allow to discriminate among proposed Yb³⁺ crystal field level schemes. In YbPtIn, we show that the low temperature magnetic order phase has an antiferro-para structure, where zero moment Yb ions coexist with large moment ones, and that a 90° moment reorientation occurs at 1.4 K.     

On quartics with three-divisible sets of cusps

 We study the geometry and codes of quartic surfaces with many cusps. We apply Gr?bner bases to find examples of various configurations of cusps on quartics. Received: 10 May 2002 / Revised version: 11 November 2002 Published online: 3 March 2003 Permanent address: Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland. e-mail: rams@mi.uni-erlangen.de, rams@im.uj.edu.pl Research partially supported by the Schwerpunktprogramm ``Global methods in complex geometry' of the Deutsche Forschungsgemeinschaft, and by EAGER. Mathematics Subject Classification (2000): 14J25, 14J17     

Crystal structures and magnetic properties of two low-dimensional materials constructed from [Mn(III)(salen)H2O]+ and [M(CN)8](3-/4-) (M = Mo or W) precursors

The syntheses, X-ray structures, and magnetic behaviors of two new cyano-bridged assemblies, the molecular [Mn(III)(salen)H2O]3[W(V)(CN)8].H2O (1) and one-dimensional [Mn(salen)(H2O)2]2[[Mn(salen)(H2O)][Mn(salen)]2[Mo(CN)(8)]].0.5ClO4.0.5OH.4.5H2O (2), are presented. Compound 1 crystallizes in the monoclinic system, has space group P2(1)/c, and has unit cell constants a = 13.7210(2) A, b = 20.6840(4) A, c = 20.6370(2) A, and Z = 4. Compound 2 crystallizes in the triclinic system, has space group P, and has unit cell dimensions a = 18.428(4) A, b = 18.521(3) A, c = 18.567(4) A, and Z = 2. The structure of 1 consists of the asymmetric V-shaped Mn-NC-W-NC-Mn-O(phenolate)-Mn molecules, where W(V) coordinates with [Mn(salen)H2O] and singly phenolate-bridged [Mn(salen)H2O]2 moieties through the neighboring cyano bridges. The [W(V)(CN)8]3- ion displays distorted square-antiprism geometry. The structure of 2 consists of the cyano-bridged [Mn3(III)Mo(IV)]n- repeating units linked by double phenolate bridges into one-dimensional zigzag chains. The Mn(III) centers are bound to Mo(IV) of square-antiprism geometry through the neighboring cyano bridges. The magnetic studies of 1 reveal the antiferromagnetic intramolecular interactions through the CN and phenolate bridges and the relatively weak intermolecular interactions. Compound 1 becomes antiferromagnetically ordered below TN = 4.6 K. The presence of the magnetic anisotropy is documented with the MH measurements carried out for both polycrystalline and single-crystal samples. At T = 1.9 K, the spin-flop transition is observed in the field of 18 kOe applied parallel to the bc plane, which is the easy plane of magnetization. Field dependence of magnetization of 1 shows field-induced metamagnetic behavior from the antiferromagnetic ground state of ST = 3/2 to the state of ST = 5/2. The magnetic properties of 2 indicate a weak antiferromagnetic interaction between Mn(III) centers in double-phenolate-bridged [Mn(III)(salen)]2 dinuclear subunits and a very weak ferromagnetic interaction between them through the diamagnetic [Mo(IV)(CN)8]4- spacer.     

Probing the quantum critical behavior of CeCoIn5 via Hall effect measurements

We present highly sensitive Hall effect measurements of the heavy fermion compound CeCoIn5 down to temperatures of 55 mK. A pronounced dip in the differential Hall coefficient | partial differential rho(xy)/ partial differential H| at low temperature and above the upper critical field of superconductivity, H(c2), is attributed to critical spin fluctuations associated with the departure from Landau Fermi liquid behavior. This identification is strongly supported by a systematic suppression of this feature at elevated pressures. The resulting crossover line in the field-temperature phase diagram favors a field induced quantum critical point at mu(0)H(qc) approximately 4.1 T below H(c2)(T=0) suggesting related, yet separate, critical fields.     

Characterization of LiNbO3 waveguides fabricated by proton exchange in water

Proton exchange of LiNbO₃ substrates has been achieved by immersing the samples in distilled water in sealed ampoules at temperatures between 190 °C and 300 °C. The samples have been studied by infrared spectra analysis, dark mode reflectivity and X-ray rocking curve diffraction. The results obtained show that exchange rates as high as with common acids (85%) are easily reached. The structure of the exchanged waveguides varies from the low index -phase to the high index -phases depending on the temperature and time length of the exchange process, as well as on the distilled water amount used. Optical waveguides made up of phases of high, sharp index jump (n_e0.12) as well as of low index jump and very low propagation losses (0.5 dB/cm) have been obtained and characterized. PACS 42.82.Et; 42.70.Mp     

Magnetic properties of Yb Mo O and Gd Mo O from rare earth Mössbauer measurements

Using ¹⁷⁰Yb and ¹⁵⁵Gd M?ssbauer measurements down to ∼ 0.03 K, we have examined the semiconducting pyrochlore Yb₂Mo₂O₇ where the Mo intra-sublattice interaction is anti-ferromagnetic and the metallic pyrochlore Gd₂Mo₂O₇ where this interaction is ferromagnetic. Additional information was obtained from susceptibility, magnetisation and ¹⁷²Yb perturbed angular correlation measurements. The microscopic measurements evidence lattice disorder which is important in Yb₂Mo₂O₇ and modest in Gd₂Mo₂O₇. Magnetic irreversibilities occur at 17 K in Yb₂Mo₂O₇ and at 75 K in Gd₂Mo₂O₇ and below these temperatures the rare earths carry magnetic moments which are induced through couplings with the Mo sublattice. In Gd₂Mo₂O₇, we observe the steady state Gd hyperfine populations at 0.027 K are out of thermal equilibrium, indicating that Gd and Mo spin fluctuations persist at very low temperatures. Frustration is thus operative in this essentially isotropic pyrochlore where the dominant Mo intra-sublattice interaction is ferromagnetic. Received 13 January 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: hodges@drecam.saclay.cea.fr     

Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets

A compact set is self-conformal if it is a finite union of its images by conformal contractions. It is well known that if the conformal contractions satisfy the ``open set condition' (OSC), then has positive -dimensional Hausdorff measure, where is the solution of Bowen's pressure equation. We prove that the OSC, the strong OSC, and positivity of the -dimensional Hausdorff measure are equivalent for conformal contractions; this answers a question of R. D. Mauldin. In the self-similar case, when the contractions are linear, this equivalence was proved by Schief (1994), who used a result of Bandt and Graf (1992), but the proofs in these papers do not extend to the nonlinear setting.

     

Paramagnetic fluctuations in Yb3Ga5O12 investigated with 172Yb PAC probe

¹⁷²Yb PAC measurements were carried out on Yb₃Ga₅O₁₂ at temperatures ranging from 14 to 1100 K. The time dependent hyperfine interaction is clearly evident below room temperature. It is attributed to spin fluctuations of Yb ion in the ground state of the ²F_7/2 multiplet. Above 500 K, the temperature dependence of the electric field gradient is shown to result from a varying population of the crystal electric field levels. This revised version was published online in August 2006 with corrections to the Cover Date.