Vortex dynamics in patterned nanomagnets

Abstract

Magnetic vortices in restricted geometries, characterized by a circulating in-plane magnetization and an out-of-plane vortex core, exhibit a rich excitation spectrum, of which the fundamental mode is a non-degenerate translational excitation that corresponds to circular motion of its core at a characteristic frequency. Recently there has been considerable interest in the unique dynamics of these vortices, motivated in part by the potential applications of field- and current-driven core polarization reversals. Here we investigate the dynamics of magnetic vortices confined in lithographically defined, micron-sized Permalloy disks with circular and elliptical symmetry. The resonance frequencies are detected experimentally using a microwave reflection technique where an r.f. current in a coplanar waveguide generates an oscillating magnetic field that is absorbed preferentially at the eigenfrequencies of the magnetic disks patterned on its central strip. The eigenfrequency of a single vortex depends primarily on the magnetostatic energy profile and, consequently, can be tuned by varying the geometry of the disk or through effective confinement by shifting the vortex to an energetically distinct position using a static magnetic field [1], with frequencies typically in the range of 50 MHz to 1 GHz. In single vortex systems the out-of-plane magnetic core defines the direction that the core circulates around its equilibrium position. For dynamically interacting vortex pairs, the relative polarizations of the two cores leads to four modes with distinct eigenfrequencies and motion patterns, three of which can be excited by a spatially uniform magnetic field [2]. For small amplitude perturbations the energy profile is harmonic in form but for larger perturbations, micromagnetic simulations show that higher order terms are necessary to describe the energy profile, suggesting that nonlinearities in the excitation mode should emerge. Experimentally we find that as the amplitude of the r.f. driving field is increased, the translational-mode peak first takes on a distorted shape and then splits into two well-defined peaks that differ in frequency by up to 25 % as the field is increased [3]. Although the translational mode frequency increases substantially as a function of an in-plane dc field H applied along the ellipse minor axis, the critical driving field and the magnitude of the splitting change little with H. The thickness and field dependence of this mode-splitting phenomenon are examined via measurements of lithographically patterned micron-sized Permalloy ellipses with thicknesses of 20, 40, and 60 nm. The experimental results compare well with numerical calculations that incorporate a critical velocity parameter, providing new insight into the origin of the observed vortex dynamic mode splitting.