Magnon Waves on Chains of YIG particles: Dispersion Relations, Faraday Rotation, and Power Transmission

Abstract: 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.