Switching field of partially exchange-coupled particles

Abstract

The magnetization reversal of partially exchange-coupled particles is studied in detail. The starting point is the observation of a complicated phenomenology in the irreversible susceptibility and FORC distribution functions of Ba hexaferrite samples obtained by means of different sintering conditions. Several peaks in the first-order reversal curve (FORC) distribution functions were identified and associated with clusters with different number of particles. The switching fields of these clusters were related to an effective anisotropy constant K eff that depends on the number of particles in the cluster. K eff is linked to the exchange-coupled volume between two neighboring particles and as a weighted mean between the anisotropy constants of the coupled and uncoupled volumes. By using the modified Brown's equation α ex = 0.322 is obtained. In order to interpret these results, the switching field of a two-particle system with partial exchange coupling is studied. It is assumed that the spins reorientation across the contact plane between the particles is like a Bloch wall. The energy of the system is written in terms of the fraction of volume affected by exchange coupling and the switching fields for both particles are calculated. At small interaction volume fraction each particle inverts its magnetization independently from the other. As the fraction of exchange-coupled volume increases, cooperative effects appear and the two particles invert their magnetization in a cooperative way. The proposed model allows to interpret for the first time the empirical factor α ex in terms of physical arguments and also explain the details observed in the FORC distribution function.