  We study the interplay between collective and individual optically-induced
magnetic responses in quadrumers made of identical dielectric nanoparticles.
Unlike their plasmonic counterparts, all-dielectric nanoparticle clusters are
shown to exhibit multiple dimensions of resonant magnetic responses that can be
employed for the realization of anomalous scattering signatures. We focus our
analysis on symmetric quadrumers made from silicon nanoparticles and verify our
theoretical results in proof-of-concept radio frequency experiments
demonstrating the existence of a novel type of magnetic Fano resonance in
nanophotonics.
