Imaging of Spin Dynamics in Closure Domain and Vortex Structures

Time-resolved Kerr microscopy is used to study the excitations of individual micron- scale ferromagnetic thin film elements in their remnant state. Thin (18 nm) square elements with edge dimensions between 1 and 10 $\mu$m form closure domain structures with 90 degree Neel walls between domains. We identify two classes of excitations in these systems. The first corresponds to precession of the magnetization about the local demagnetizing field in each quadrant, while the second excitation is localized in the domain walls. Two modes are also identified in ferromagnetic disks with thicknesses of 60 nm and diameters from 2 $\mu$m down to 500 nm. The equilibrium state of each disk is a vortex with a singularity at the center. As in the squares, the higher frequency mode is due to precession about the internal field, but in this case the lower frequency mode corresponds to gyrotropic motion of the entire vortex. These results demonstrate clearly the existence of well-defined excitations in inhomogeneously magnetized microstructures.Comment: PDF File (Figures at reduced resolution

Sparse linear programming subprogram

This report describes a subprogram, SPLP(), for solving linear programming problems. The package of subprogram units comprising SPLP() is written in Fortran 77. The subprogram SPLP() is intended for problems involving at most a few thousand constraints and variables. The subprograms are written to take advantage of sparsity in the constraint matrix. A very general problem statement is accepted by SPLP(). It allows upper, lower, or no bounds on the variables. Both the primal and dual solutions are returned as output parameters. The package has many optional features. Among them is the ability to save partial results and then use them to continue the computation at a later time