Energy barriers for magnetization reversal of partially exchange-coupled particles

We study the magnetization reversal of a two-particle system with partial exchange coupling. We assume that the particles are discs and that the exchange coupling occurs through one of their plane faces extending up to 5 l w into each particle ( l w=( A/ K) 1/2). The easy axis of particle 1 coincides with the direction of the applied magnetic field H and the one corresponding to particle 2 is such that both easy axis are parallel to the contact face. We assume that the spins reorientation across the contact plane is similar to that of a Bloch wall. We write the free energy E of the system in terms of the fraction β of volume affected by exchange coupling, taking into account the anisotropy and exchange energies due to the spin reorientation and to the fraction (1- β) of non-interacting particles’ volume. For a given volume V the fraction β can be varied by sliding one particle with respect to the other, changing only the contact area. We calculate the ratio E/ KV as function of H considering the easy axis of particle 2 at different angles with respect to the easy axis of particle 1. We determine magnetic moments switching paths together with the energy barrier Δ E for switching. We find a general expression of the form Δ E/ KV=(1− H/ H 0) z , with H 0= H 0( β, ω) and z= z 0+ α( ω) β, being z 0 and H 0(0, ω) equal to the values for non-interacting particles. We discuss the switching behavior as a function of ω and H.