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.
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