Magnetic charges suppress effects of anisotropy in polycrystalline soft ferromagnetic materials

Abstract

Micromagnetic simulations of polycrystalline iron washers show that grain boundary charges, ρ = -div M, suppress bad effects of magnetocrystalline anisotropy. A single domain wall divides the washer into two domains with opposite magnetization; M is almost = ± Ms ϕ, where ϕ circulates about the hole in the washer. There is a ripple structure. M tilts back and forth toward the inner and outer surfaces. Magnetic charge densities, σm = n·M, on the surfaces keep M at the surfaces very close to lying in the surfaces. The exchange εx and magnetostatic εd energy densities try to keep M parallel to the surfaces throughout the washer, except at the domain wall. An anisotropy energy in each grain is reduced linearly in the angle of rotation away from the circulating pattern towards the nearest anisotropy axis. Both εx and εd near grain boundaries increase as the square of these angles. Anisotropy wins for small rotations. However, the coefficients of the positive quadratic terms are so much larger than the coefficients of the negative linear terms that the rotations are quite small. If the height of the washer is sufficiently greater than 300 nm, M in the washer no longer acts as it would in a thin film. If 300 nm washers are stacked with a spacing of 4 nm, the ripple structure is not lost. The stacked washers can then be used as the core of a transformer. The most remarkable effect is that starting with M = Ms ϕ everywhere, the reversal of M by the field from a current along the z-axis produces a single domain wall. It is stable even in zero field because the wall has Néel caps that act as springs against the surfaces. The suppression of crystalline anisotropy in polycrystalline iron also occurs for geometries other than the toroid; some might be better for creating transformers.