Eliashberg-type equations for correlated superconductors

The derivation of the Eliashberg -- type equations for a superconductor with strong correlations and electron--phonon interaction has been presented. The proper account of short range Coulomb interactions results in a strongly anisotropic equations. Possible symmetries of the order parameter include s, p and d wave. We found the carrier concentration dependence of the coupling constants corresponding to these symmetries. At low hole doping the d-wave component is the largest one.Comment: RevTeX, 18 pages, 5 ps figures added at the end of source file, to be published in Phys.Rev. B, contact: [email protected]

Paramagnetic Meissner Effect in Nb Disks

Further details of the zero-field-cooled-magnetization and field-cooled-magnetization results on Nb disks exhibiting the paramagnetic Meissner effect (PME) are described. These studies indicate that two well-defined temperatures can be associated with features in the magnetization results. The higher characteristic temperature Tu is correlated with appearance of the paramagnetic moment and is strongly dependent upon the process used in forming the disk-shaped geometry of these Nb samples. The lower temperature Tp is associated with the “intrinsic coupling” of the interior Nb platelets. These latest results are shown to be consistent with the flux compression model for the appearance of the PME

Fabrication and Characterization of Co1−xFex Alloy Nanowires

Co1−xFex alloy nanowires with 40 nm diam and x=0–1.0 were fabricated by electrodeposition in nanopores of alumina templates. The crystalline structure of the nanowires is concentration dependent and shows a transition from the cobalt hexagonal-closed-packed structure (hcp) to a face-centered-cubic structure (fcc) in the concentration range

Modeling of Hysteresis and Magnetization Curves for Hexagonally Ordered Electrodeposited Nanowires

A computational model has been developed to investigate how the magnetostatic interactions affect the hysteresis and magnetization curves for hexagonal arrays of magnetic nanowires. The magnetization coupling between nanowires arises from the stray fields produced by the other nanowires composing the array such that the field at each nanowire is the sum of the external field and the interaction field with the other nanowires. Using only two adjustable parameters: the interaction between nearest neighbors and the width of the Gaussian distribution in switching fields centered around the measuredcoercivity, simulations are compared with the experimentally measuredhysteresis and magnetization curves for electrodepositedCo0.45 Fe0.55 alloy nanowires with diameters from 12 to 48 nm. Excellent agreement is found for all nanowire systems except for the largest diameter arrays where deviations from the Gaussian distribution of switching fields need to be considered

Zero Magnetization States in Electrodeposited Co0.45Fe0.55 Nanowire Arrays

Co0.45Fe0.55 alloy nanowires with 12 to 35 nm diameter and 12 μm length were fabricated by electrodeposition in porous anodic alumina templates. The initial magnetization curves reveal that the zero magnetization state is not unique and is determined by the field history (acdemagnetization process) leading to the zero average moment state. For acdemagnetization processes with the field applied parallel to the nanowire axis, the subsequent magnetization curves suggest that an individual nanowire behaves as a single domain with neighboring nanowires being antiparallel to each other in the zero magnetization state. However, for a demagnetization process with the field applied perpendicular to the nanowires, a different zero magnetization state is created in which the individual nanowires consist of multidomains having opposite axial orientations. These results are consistent with the asymmetric (symmetric) behavior found in the minor hysteresis loops measured after perpendicular (parallel) acdemagnetization on these nanowire arrays

Fabrication and Characterization of Co1−xFex Alloy Nanowires

Co1−xFex alloy nanowires with 40 nm diam and x=0–1.0 were fabricated by electrodeposition in nanopores of alumina templates. The crystalline structure of the nanowires is concentration dependent and shows a transition from the cobalt hexagonal-closed-packed structure (hcp) to a face-centered-cubic structure (fcc) in the concentration range

Prescribing the Jacobian in critical spaces

International audienceWe consider the Sobolev space $X=W^{s,p}({\mathbb S}^m ; {\mathbb S}^{k-1})$. We prove the existence of a robust distributional Jacobian $Ju$ for $u\in X$ provided $sp\ge k-1$. This generalizes a result of Bourgain, Brezis and the second author (Comm. Pure Appl. Math. 2005), where the case $m=k$ is considered. In the critical case where $sp=k-1$, we identify the image of the map $X\ni u\mapsto Ju$. This extends a result of Alberti, Baldo and Orlandi (J. Eur. Math. Soc. 2003) for $s=1$ and $p=k-1$. We also present a new, analytical, dipole construction method