  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 \tau a field pulse inverts the core magnetization;
the echo is a peak in M_{xy} at t=2\tau. Its relaxation times depend on the
inhomogeneity, on the interaction between the nanodots and on the Gilbert
damping constant \alpha. 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.
