Frequencies of Radially Symmetric Excitations in Vortex State Disks

Abstract

Submicron ferromagnetic disks with a vortex ground state exhibit interesting and potentially useful dynamic properties arising from excitations on the ground state. In particular, a magnetic pulse applied perpendicular to the vortex plane will excite radially symmetric modes. Previous calculations of the frequencies of these modes based on the linearized Landau-Lifschitz equation and the magnetostatic Green's function give eigenfrequencies proportional to the square root of the aspect ratio radic( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L/R)</i> , where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> is the disk thickness and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> is the disk radius. However, experimental frequency data show significant deviation from the square root dependence. An improved calculation of the frequency is done through a collective variable approach by exploiting the high symmetry of these modes. In the linear approximation, this approach gives the main contribution to the frequency proportional to radic(( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L/R</i> )ln( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R/L</i> )), which is closer to the observed aspect ratio dependence.