A lower bound to the spectral threshold in curved tubes

We consider the Laplacian in curved tubes of arbitrary cross-section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann conditions at the ends of the tube. We prove that the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Dirichlet Laplacian in a torus determined by the geometry of the tube.Comment: LaTeX, 13 pages; to appear in R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sc

Nanoscopic processes of Current Induced Switching in thin tunnel junctions

In magnetic nanostructures one usually uses a magnetic field to commute between two resistance (R) states. A less common but technologically more interesting alternative to achieve R-switching is to use an electrical current, preferably of low intensity. Such Current Induced Switching (CIS) was recently observed in thin magnetic tunnel junctions, and attributed to electromigration of atoms into/out of the insulator. Here we study the Current Induced Switching, electrical resistance, and magnetoresistance of thin MnIr/CoFe/AlO$_x$/CoFe tunnel junctions. The CIS effect at room temperature amounts to 6.9% R-change between the high and low states and is attributed to nanostructural rearrangements of metallic ions in the electrode/barrier interfaces. After switching to the low R-state some electro-migrated ions return to their initial sites through two different energy channels. A low (high) energy barrier of $\sim$0.13 eV ($\sim$0.85 eV) was estimated. Ionic electromigration then occurs through two microscopic processes associated with different types of ions sites/defects. Measurements under an external magnetic field showed an additional intermediate R-state due to the simultaneous conjugation of the MR (magnetic) and CIS (structural) effects.Comment: 6 pages, 4 figure