Thermally activated decay of magnetic vortices

The nature of the energy barrier involved in the decay of vortices is investigated through measurements of magnetic hysteresis in an array of $2\text{\ensuremath{-}}\ensuremath{\mu}\text{m}$-diameter permalloy disks. Specifically, the magnetic susceptibility of the array is measured using the ac magneto-optical Kerr effect. Comparison to a third-order analytic model of the vortex state for the disks yields excellent agreement for realistic experimental parameters and allows extraction of the switching distribution of the disks. The high signal-to-noise and concomitant efficiency of the technique allow a large number of experiments to statistically probe the annihilation behavior in the array by changing the sample temperature and magnetic field sweep rate. A N\'eel-Brown model, modified to include the temperature dependence of the saturation magnetization, accurately describes changes in both parameters for a power-law scaling of the annihilation energy barrier as a function of applied magnetic field. Additional qualitative evidence indicates that the annihilation process proceeds similarly to a domain-wall depinning event.