Helical patterns of magnetization and magnetic charge density in iron whiskers

Studies with the (1 1 1) axis along the long axis of an iron whisker, 40 years ago, showed two phenomena that have remained unexplained: 1) In low fields, there are six peaks in the ac susceptibility, separated by 0.2 mT; 2) Bitter patterns showed striped domain patterns. Multipole columns of magnetic charge density distort to form helical patterns of the magnetization, accounting for the peaks in the susceptibility from the propagation of edge solitons along the intersections of the six sides of a (1 1 1) whisker. The stripes follow the helices. We report micromagnetic simulations in cylinders with various geometries for the cross-sections from rectangular, to hexagonal, to circular, with wide ranges of sizes and lengths, and different anisotropies, including (0 0 1) whiskers and the hypothetical case of no anisotropy. The helical patterns have been there in previous studies, but overlooked. The surface swirls and body helices are connected, but have their own individual behaviors. The magnetization patterns are more easily understood when viewed observing the scalar divergences of the magnetization as isosurfaces of magnetic charge density. The plus and minus charge densities form columns that interact with unlike charges attracting, but not annihilating as they are paid for by a decrease in exchange energy. Just as they start to form the helix, the columns are multipoles. If one could stretch the columns, the self-energy of the charges in a column would be diminished while making the attractive interactions of the unlike charges larger. The columns elongate by becoming helical. The visualization of 3-D magnetic charge distributions aids in the understanding of magnetization in soft magnetic materials.