We show that non-reciprocal bands can be formed in a magnetized periodic chain of spherical plasmonic particles with two particles per unit cell. Simplified form of symmetry operators in dipole approximations are used to demonstrate explicitly the relation between spectral non-reciprocity and broken spatial-temporal symmetries. Due to hybridization among plasmon modes and free photon modes, strong spectral non-reciprocity appears in region slightly below the lightline, where highly directed guiding of energy can be supported. The results may provide a clear guidance on the design of one-way waveguides.
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