  Based on a linearized Landau-Lifshitz equation, we show that two-dimensional
periodic allay of ferromagnetic particles coupled with magnetic dipole-dipole
interactions supports chiral spin-wave edge modes, when subjected under the
magnetic field applied perpendicular to the plane. The mode propagates along a
one-dimensional boundary of the system in a unidirectional way and it always
has a chiral dispersion within a band gap for spin-wave volume modes. Contrary
to the well-known Damon-Eshbach surface mode, the sense of the rotation depends
not only on the direction of the field but also on the strength of the field;
its chiral direction is generally determined by the sum of the so-called Chern
integers defined for spin-wave volume modes below the band gap. Using simple
tight-binding descriptions, we explain how the magnetic dipolar interaction
endows spin-wave volume modes with non-zero Chern integers and how their values
will be changed by the field.
