  We examine the far-field optical response, under-plane wave excitation in the
presence of a static magnetic field, of core-shell nanoparticles involving a
gyroelectric component, either as the inner or the outer layer, through
analytic calculations based on appropriately extended Mie theory. We focus on
absorption and scattering of light by bismuth-substituted yttrium iron garnet
(Bi:YIG) nanospheres and nanoshells, combined with excitonic materials such as
organic-molecule aggregates or two-dimensional transition-metal
dichalcogenides, and discuss the hybrid character of the modes emerging from
the coupling of the two constituents. We observe the excitation of strong
magneto-optic phenomena and explore, in particular, the response and tunability
of a magneto-transverse light current, indicative of the photonic Hall effect.
We show how interaction between the Bi:YIG and excitonic layers leads to a pair
of narrow bands of highly directional scattering, emerging from the
aforementioned hybridization, which can be tuned at will by adjusting the
geometrical or optical parameters of the system. Our theoretical study
introduces optically anisotropic media as promising templates for strong
coupling in nanophotonics, offering a means to combine tunable magnetic and
optical properties, with potential implications both in the design of
all-dielectric photonic devices but also in novel clinical applications.
