Asymptotic Dimension

The asymptotic dimension theory was founded by Gromov in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups.Comment: Added some remarks about coarse equivalence of finitely generated groups

Sudden Critical Current Drops Induced in S/F Structures

In the search for new physical properties of S/F structures, we have found that the superconductor critical current can be controlled by the domain state of the neighboring ferromagnet. The superconductor is a thin wire of thickness d_{s} ~ 2 xi_{S}. Nb/Co and Nb/Py (Permalloy Ni_{80}Fe_{20}) bilayer structures were grown with a significant magnetic anisotropy. Critical current measurements of Nb/Co structures with ferromagnet thickness d_{F} > 30nm show sudden drops in two very defined steps when the measurements are made along the hard axes direction (i.e. current track parallel to hard anisotropy axes direction). These drops disappear when they are made along the easy axis direction or when the ferromagnet thickness is below 30nm. The drops are accompanied by vortex flux flow. In addition magnetorestistance measurements close to Tc show a sharp increase near saturation fields of the ferromagnet. Similar results are reproduced in Nb/Py bilayer structure with the ferromagnet thickness d_{F} ~ 50nm along the easy anisotropy axes. These results are explained as being due to spontaneous vortex formation and flow induced by Bloch domain walls of the ferromagnet underneath. We argue these Bloch domain walls produce a 2D vortex-antivortex lattice structure.Comment: 6 pages, 6 figure