  We calculate the dispersion relations for magnon waves on a periodic chain of
spherical or cylindrical Yttrium Iron Garnet (YIG) particles. We use the
quasistatic approximation, appropriate when $kd \ll 1$, where $k$ is the wave
number and $d$ the interparticle spacing. In this regime, because of the
magnetic dipole-dipole interaction between the localized magnetic excitations
on neighboring particles, dispersive magnon waves can propagate along the
chain. The waves are analogous to plasmonic waves generated by electric
dipole-dipole interactions between plasmons on neighboring metallic particles.
The magnon waves can be longitudinal ($L$), transverse ($T$), or elliptically
polarized. We find that a linearly polarized magnon wave undergoes a Faraday
rotation as it propagates along the chain. The amount of Faraday rotation can
be tuned by varying the off-diagonal component of the permeability tensor. We
also discuss the possibility of wireless power transmission along the chain
using these coupled magnon waves.
