Visualization and Interpretation of Magnetic Configurations Using Magnetic Charge

The calculation and graphic imaging of magnetic charge density provides fresh insights into old problems in micromagnetics. (1) The full saturation magnetization M
_s
of polycrystalline iron can be used in a transformer when magnetic charge at the grain boundaries suppresses the adverse effects of anisotropy. A single domain wall separates two regions of opposite magnetization |M| = M
_s
in toroidal geometry. This is a three-dimensional expression of the ripple effect, long known in polycrystalline thin films of Permalloy. (2) Helical patterns of M result from interaction of regions of opposite magnetic charge developed by the introduction of some ∇ · M when the exchange energy primarily invokes ∇ × M to accommodate to the boundary conditions set by geometry and surface charge density n · M. The helical structures resolve 40-year-old mysteries in the appearance of periodic stripe domains associated with the propagation of edge solitons in a hexagonal [1 1 1] oriented iron whisker.