Exchange/dipole collective spin-wave modes of ferromagnetic nanosphere arrays

We present theoretical studies of the spin-wave collective modes of square two-dimensional lattices of ferromagnetic nanospheres. In our description of the individual spheres in the array, we include the influence of both exchange interactions between the spins and dipolar fields generated by the spin motions. Intersphere interactions have their origin in magnetic dipole fields generated by the dynamic magnetization of the excited spheres. We explore the nature of the collective spin-wave spectrum of lattices magnetized perpendicular to the plane, and also parallel to the plane. Issues examined are the dependence of collective spin-wave mode bandwidths on the lattice constant of the array, orientation of the magnetization, propagation direction, and the size of the spheres. The last mentioned property controls the mode spectrum of the individual spheres through the influence of exchange.