Temperature dependence of critical sizes, wall widths and moments in two-domain magnetite grains

We use a one-dimensional micromagnetic model with temperature-dependent parameters for the mineral magnetite to calculate the critical sizes dSDmax, above which a single-domain (SD) state does not exist; d2Dmin, below which no two-domain state exists; and d0, at which the SD and two-domain states have equal energies, all as a function of temperature up to the Curie point TC. We also compute the structures, widths, and net moments of domain walls in two-domain particles from room temperature up to TC. In two-domain grains just above d2Dmin, the domain wall expands to fill an increasing fraction of the particle volume. In cubic SD grains just below dSDmax, magnetic moments are twisted symmetrically away from the easy axis at opposite ends of the crystal. The limits dSDmax and d2Dmin are determined with a precision of Domain walls in two-domain magnetites expand with rising temperature; however, the expansion is slow and the domain wall fills no more than 50% of the particle except within a few degrees of TC. The √(A/K) expansion predicted by Landau and Lifschitz and subsequent theories, in which there is no upper limit to the size of the walls, is a result of ignoring the demagnetizing energy of the domain wall. Domain walls have considerable structure, including ‘skirts’ of magnetic moments rotated beyond 0° and 180°. The skirts partly compensate the wall moment and expand as the temperature rises. As a result of the competing effects of expanding walls and expanding skirts flanking the walls, the net two-domain particle moment, normalized to the saturation magnetization MS, changes slowly as the temperature rises and may actually decrease. Remanence peaks observed at