Theoretical aspects of dipolar interactions and their appearance in first-order reversal curves of thermally activated single-domain particles

Recently, the study of interacting particles was driven by the modeling effort undertaken to interpret first-order reversal curve (FORC) diagrams of natural rocks and sediments. Understanding the effect of magnetostatic interactions is of primary importance in rock magnetism and paleomagnetism, and FORCs can provide useful information for this purpose. However, fully quantitative theories of FORC measurements have not been formulated yet. The goal of this paper is to fill this gap for the case of interacting single-domain (SD) particles. First, a general analytical expression is obtained for the local interaction field produced by a random set of magnetic dipoles. This expression is then used to formulate a general theory that explains the effect of the local interaction field on FORCs. Exact solutions are obtained for the case of weakly interacting single-domain particles, whereby the effect of thermal activations is considered as well. These solutions show that a rigorous analysis of the FORC function and its relationship with the distributions of coercivities and interaction fields is possible.