Energy barriers for thermal reversal of interacting single domain particles

An analytic solution to the energy barriers of two interacting single domain particles is presented. Identical volumes and uniaxial anisotropies are assumed with easy axes parallel to an external magnetic field. The locations and heights of the system energy barriers are analytically determined when the line joining the two particles is either parallel or perpendicular to the easy axes and the external field. The lowest energy barriers are saddle points of the energy surface and correspond to reversal modes under thermal agitation. When dipole coupling is not strong, the mode of thermal switching is asymmetric fanning or asymmetric coherent rotation, depending upon the bond angle, rather than symmetric fanning or coherent rotation that occurs at the nucleation field. An effective volume that describes the cooperative effect is calculated and good agreement with the numerical results using the Fokker-Planck equation is obtained. The energy barriers can be used to calculate the superparamagnetic relaxation time constants in the high barrier limit.