  The development of new approaches to tuning the resonant magnetic response of
simple all-dielectric nanostructures is very important in modern nanophotonics.
Here we show that a resonant magnetic octupole (MOCT) response can be obtained
by dividing a solid rectangular silicon block to an oligomer structure with the
introduction of narrow gaps between four nanocubes. We control and tune the
spectral position of the MOCT resonance by varying the distance between the
nanocubes. We demonstrate that several magnetic hot-spots related to the MOCT
resonance can be located in the gaps creating a strong magnetic field gradient
in free space. We observe that the resonant excitation of the MOCT moment leads
to a significant enhancement of light absorption in the system at the spectral
region, where light absorption in bulk silicon is weak. The results of this
work can be applied to design new composite antennas and metamaterials based on
complex building blocks, energy harvesting devices and molecular trapping with
magnetic hot-spots.
