THEORY OF THE CURIE-WEISS BEHAVIOR OF AN AGGREGATED MAGNETIC SUSPENSION

We develop the aggregate mechanism of interaction between particles in a ferrofluid. As the mechanism of Curie-Weiss behavior of a magnetic liquid seems to be the formation of aggregates of magnetic particles, further information on the formation of aggregates can be obtained by measuring the toroidal susceptibility of the aggregate suspension. We consider the model of rigid (unchangeable in form) aggregates consisting of superparamagnetic particles. It is assumed that the magnetic structure of dipoles inside the aggregate arises owing to their interactions with each other when the temperature is sufficiently reduced. A general expression is derived for initial susceptibilities of the suspension (magnetic, toroidal and cross) for a rigid aggregate of arbitrary form, and it is shown that the temperature dependence of the susceptibilities is of a more general form than in the simple Curie-Weiss law. These susceptibilities are calculated for the best known aggregates, two-particle aggregates. It is shown that the main contribution of these aggregates to the magnetic susceptibilities is ferromagnetic in nature, which corresponds to the type of the ordered state of these aggregates. We also present the results of a numerical calculation of the temperature dependence of the susceptibilities for certain types of aggregate including densely packed ones.