Abstract

We formulate the theory of the collective spin wave modes of arrays of spherical particles of ferromagnetic material, under the assumption that each sphere in the array is magnetized uniformly. In addition, the intersphere interactions have their origin in the magnetic fields generated by the precessing moments, appropriate to the case where there is no direct physical contact between the spheres. The formulation is a real space analysis, and thus can be applied in principle to disordered arrangements of spheres. While our formulation is quite general, and is directly applicable to the case where both exchange and dipolar interactions influence spin motions within an individual sphere, explicit calculations are presented for the case where exchange is absent. The numerical calculations we discuss explore the collective spin wave modes of square planar arrays of spheres, and consider the case where the spheres are magnetized both perpendicular and parallel to the plane.