Micromagnetic study of the influence of crystal defects on coercivity in magnetite

Abstract

A one-dimensional micromagnetic model is used to calculate the thermal dependence of microcoercivity (hc) produced by the unpinning of a domain wall (DW) from various types of defects in magnetite. Equilibrium solutions are found that minimize the magnetoelastic, anisotropy, exchange, magnetostatic, and external field energies with respect to the wall width (w) and position of the wall relative to the defect. The defect may be a single dislocation, dislocation dipole, planar defect, or planar defect bounded by two parallel dislocations. Wall pinning is produced by (1) microstress fields of dislocations, (2) local changes in exchange and anisotropy constants within a planar defect region, or (3) a combination of both effects. The calculations, using temperature-dependent parameters, predict the thermal dependence of hc (T) as a function of grain size, domain wall width, defect spacing, and type of defect. Results show that, for grain sizes between 1 and 100 μm, hc(T) is usually a function of the wall width raised to some power n. The particular value of n is found to be a function of the DW-defect interaction spacing (d/w), type of defect, and grain size. Also, within this size range, the wall width expands with temperature more gradually than classical theory predicts. The microcoercivity results are used with the theory of Xu and Merrill (1990) to predict the thermal dependence of the macroscopic coercivity Hc in magnetite. For grains with low defect densities, such as recrystallized magnetites, negative dislocation dipoles with d/w≈0.1–1 produce a thermal dependence of coercivity that agrees with experimental results. In the high defect density limit, a population of positive and negative dislocation dipoles with a distribution of dipole widths produce an Hc (T) dependence consistent with experimental data from crushed and glass ceramic magnetites.