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Magnetic vortex echoes: application to the study of arrays of magnetic nanostructures

We propose the use of the gyrotropic motion of vortex cores in nanomagnets to produce a magnetic echo, analogous to the spin echo in NMR. This echo occurs when an array of nanomagnets, e.g., nanodisks, is magnetized with an in-plane (xy) field, and after a time τa field pulse inverts the core magnetization; the echo is a peak in M_{xy} at t=2τ. Its relaxation times depend on the inhomogeneity, on the interaction between the nanodots and on the Gilbert damping constant α. Its feasibility is demonstrated using micromagnetic simulation. To illustrate an application of the echoes, we have determined the inhomogeneity and measured the magnetic interaction in an array of nanodisks separated by a distance d, finding a d^{-n} dependence, with n\approx 4.