Geometric signature of reversal modes in ferromagnetic nanowires

Magnetic nanowires are a good platform to study fundamental processes in Magnetism and have many attractive applications in recording such as perpendicular storage and in spintronics such as non-volatile magnetic memory devices (MRAM) and magnetic logic devices. In this work, nanowires are used to study magnetization reversal processes through a novel geometric approach. Reversal modes imprint a definite signature on a parametric curve representing the locus of the critical switching field. We show how the different modes affect the geometry of this curve depending on the nature of the anisotropy (uniaxial or cubic anisotropy), demagnetization and exchange effects. The samples we use are electrochemically grown Nickel and Cobalt nanowires.Comment: 11 pages, 21 figures to submit to Europhysics Letter

Parametric Regression on the Grassmannian

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in Euclidean spaces and generalize this concept to general nonflat Riemannian manifolds, following an optimal-control point of view. We then specialize this idea to the Grassmann manifold and demonstrate that it yields a simple, extensible and easy-to-implement solution to the parametric regression problem. In fact, it allows us to extend the basic geodesic model to (1) a time-warped variant and (2) cubic splines. We demonstrate the utility of the proposed solution on different vision problems, such as shape regression as a function of age, traffic-speed estimation and crowd-counting from surveillance video clips. Most notably, these problems can be conveniently solved within the same framework without any specifically-tailored steps along the processing pipeline.Comment: 14 pages, 11 figure