  We put forward the concept of an optomagnonic crystal: a periodically
patterned structure at the microscale based on a magnetic dielectric, which can
co-localize magnon and photon modes. The co-localization in small volumes can
result in large values of the photon-magnon coupling at the single quanta
level, which opens perspectives for quantum information processing and quantum
conversion schemes with these systems. We study theoretically a simple geometry
consisting of a one-dimensional array of holes with an abrupt defect,
considering the ferrimagnet Yttrium Iron Garnet (YIG) as the basis material. We
show that both magnon and photon modes can be localized at the defect, and use
symmetry arguments to select an optimal pair of modes in order to maximize the
coupling. We show that an optomagnonic coupling in the kHz range is achievable
in this geometry, and discuss possible optimization routes in order to improve
both coupling strengths and optical losses.
