Domain structure of titanomagnetite grains with closure domains

Abstract

Abstract Theoretical domain structure parameters and their temperature dependence have been calculated for 1–100-μm magnetite and intermediate titanomagnetite grains, on the basis of a simple model which incorporates closure domains. The model includes the effects of magneto elastic energy due to incompatible magnetostriction of main domains and closure domains and the reduction of magnetostatic energy of surface poles owing to the μ∗ effect. Refinements of the model incorporate the magneto elastic energy and the magnetostatic energy of domain walls. Grains in the form of cubes and rhombohedral prisms can be treated using the model. Comparison with analogous calculations for an open domain structure model reveals that the predicted magnitudes of domain width are significantly larger, by a factor of ∼ 5, for the closed domain structure model. The calculated domain widths are slightly greater for cubic grains than for grains with rhombohedral prismatic shape. The theoretical temperature variation for the closed domain structure model exhibits relatively stable domain structure at low to moderate temperatures, with an increase in domain width as the Curie temperature is approached, in contrast to the open domain structure model, which predicts a decrease in domain width at high temperatures, given realistic assumptions about the temperature dependence of the magnetostriction constant. The total magnetic free energy of the closed domain structure is substantially lower than that of the open domain structure, at all temperatures and for all grain sizes. This implies that closed domain structure should be preferred over open domain structure in magnetite and titanomagnetite. The theoretical predictions of domain width and its temperature dependence for the closed domain structure are in much better agreement with experimental observations than for the open domain structure.