Exchange through nonmagnetic insulating matrix.

Exchange interactions between hard-magnetic particles in a nonmagnetic matrix are investigated by model calculations. A Landau-Ginzburg approach is developed to describe the net exchange interactions between spheres of arbitrary diameters. Introducing cylindrical coordinates and integrating over the surfaces of the adjacent spheres yields an exchange coupling which decreases with a decay length depending on interatomic exchange, intra-atomic exchange, and temperature. Typically, the decay length does not exceed a few interatomic distances. The decay is exponential but also contains a prefactor depending on the surface curvature of the grains. It increases with decreasing curvature, but this dependence is only a small correction to the leading exponential term. [ABSTRACT FROM AUTHOR]