  In this article, we propose a concise theoretical framework based on mixed
field-susceptibilities to describe the decay of magnetic dipoles induced by
non--magnetic nanostructures. This approach is first illustrated in simple
cases in which analytical expressions of the decay rate can be obtained. We
then show that a more refined numerical implementation of this formalism
involving a volume discretization and the computation of a generalized
propagator can predict the dynamics of magnetic dipoles in the vicinity of
nanostructures of arbitrary geometries. We finally demonstrate the versatility
of this numerical method by coupling it to an evolutionary optimization
algorithm. In this way we predict a structure geometry which maximally promotes
the decay of magnetic transitions with respect to electric emitters.
