A two‐dimensional micromagnetic model of magnetizations and fields in magnetite

Abstract

A two‐dimensional micromagnetic model is used to obtain magnetic domain structures for cubic particles of magnetite with sides 1 μm or less. We show that complex submicron structures evolve continuously with increasing particle size into recognizable classical domain structures. Two such sequences of equilibrium states are seen. The lowest energy state for particle sizes above 0.06 μm is the “vortex” state (already seen in three‐dimensional models). Another state is seen in larger particles which has angles between walls of 90°, 125°, and 145°, agreeing with domain observations of magnetite. These are usually called 71°, 109°, and 180° walls, based on the assumption that the domain moments are in the easy ([111]) directions, but we find that the domains are actually magnetized in the [100] and [110] directions. Because both states eventually become single domain in sufficiently small particles, there is no critical single domain size in a conventional sense, but there is a rapid decrease in normalized remanence over the size range 0.06 – 0.18 μm. Bloch‐like and Néel‐like walls are seen, but strong surface fields are only found over the Bloch‐like walls. Depending on the geometry of the particle observed, one may see only a partial expression of closure domains in domain observations.