  Anisotropic magnetic interactions become the origins of intriguing magnetic
structures, such as helical and skyrmion structures by the
Dzyaloshinskii-Moriya interaction. In general, possible anisotropic exchange
interactions are restricted by crystal symmetry. Meanwhile, by lowering the
crystal symmetry with light, additional anisotropic magnetic interactions are
expected according to its polarization and frequency. In this study, we clarify
a relationship between anisotropic magnetic interactions and symmetry lowering
in insulating magnets irradiated by light. Based on the Floquet formalism, we
find that a variety of anisotropic two-spin and three-spin interactions are
induced via spin-dependent electric polarizations activated by light
irrespective of the presence/absence of the spatial inversion symmetry; we
systematically classify them in the hexagonal point group, tetragonal point
group, and their subgroups. Our symmetry analyses show that the light-induced
two-spin (three-spin) interaction is owing to the reduction of the point group
to a chiral point group (black and white magnetic point group). We also
demonstrate the effect of the light-induced magnetic interactions on the
magnetic structures in a triangular unit. Our results will be a symmetry-based
reference for the Floquet engineering of magnetic structures.
