  Interacting magnetic nanoobjects constitute one key component for many
proposed spintronic devices, from microwave nano-oscillators to magnetic memory
elements. For this reason, the mechanism of this interaction and its dependence
with distance $d$ between these nanoobjects has been the subject of several
recent studies. In the present work, the problem of the interaction between
magnetic nanodisks with magnetic vortex structures is treated both analytically
and through micromagnetic simulation. The coupling of two magnetic nanodisks is
obtained, in the case of nanodisks with different gyrotropic frequencies. The
motion of the two vortex cores, and consequently the time dependence of the
total magnetization $M(t)$ is derived using Thiele's equation and by
simulation. The magnetic coupling strength as a function of the distance
between the disks of each pair is computed with a recently developed method,
using the magnetic vortex echoes, analogous to the NMR spin echoes. The results
of the two approaches differ by approximately $10\%$ and can be fitted with a
multipolar expansion of odd negative powers of $d$; using one single term, a
dependence with distance found is broadly in agreement with studies employing
other techniques. The coupling frequencies as a function of distance for the
pair of nonidentical disks are also obtained.
