  Photo-induced magnetic force between nanostructures, at optical frequencies,
is investigated theoretically. Till now optical magnetic effects are not used
in scanning probe microscopy because of the vanishing natural magnetism with
increasing frequency. On the other hand, artificial magnetism in engineered
nanostructures led to the development of measurable optical magnetism. Here,
two examples of nanoprobes that are able to generate strong magnetic dipolar
fields at optical frequency are investigated: first an ideal magnetically
polarizable nanosphere and then a circular cluster of silver nanospheres that
has a loop-like collective plasmonic resonance equivalent to a magnetic dipole.
Magnetic forces are evaluated based on nanostructure polarizabilities, i.e.
induced magnetic dipoles, and magnetic-near field evaluations. As an initial
assessment on the possibility of a magnetic nanoprobe to detect magnetic
forces, we consider two identical magnetically polarizable nanoprobes and
observe magnetic forces in the order of piconewtons thereby bringing it within
detection limits of conventional atomic force microscopes at ambient pressure
and temperature. The detection of magnetic force is a promising method in
studying optical magnetic transitions that can be the basis of innovative
spectroscopy applications.
