An investigation of multi-domain hysteresis mechanisms using FORC diagrams

Abstract

First-order reversal curve (FORC) diagrams provide a sensitive means of probing subtle variations in hysteresis behaviour, and can help advance our understanding of the mechanisms that give rise to hysteresis. In this paper, we use FORC diagrams to study hysteresis mechanisms in multi-domain (MD) particles. The classical domain wall (DW) pinning model due to Néel [Adv. Phys. 4 (1955) 191] is a phenomenological one-dimensional model in which a pinning function represents the interactions of a DW with the surrounding medium. Bertotti et al. [J. Appl. Phys. 85 (1999a) 4355] modelled this pinning function as a random Wiener–Lévy (WL) process, where particle boundaries are neglected. The results of Bertotti et al. [J. Appl. Phys. 85 (1999a) 4355] predict a FORC diagram that consists of perfectly vertical contours, where the FORC distribution decreases with increasing microcoercivity. This prediction is consistent with our experimental results for transformer steel and for annealed MD magnetite grains, but it is not consistent with results for our MD grains that have not been annealed. Here, we extend the DW pinning model to include particle boundaries and an Ornstein–Uhlenbeck (OU) random process, which is more realistic that a WL process. However, this does not help to account for the hysteresis behaviour of the unannealed MD grains. We conclude that MD hysteresis is more complicated than the physical picture provided by the classical one-dimensional pinning model. It is not known what physical mechanism is responsible for the breakdown of the classical DW pinning model, but possibilities include DW interactions, DW nucleation and annihilation, and DW curvature.