Micromagnetics of domain walls at surfaces

High-spatial-resolution magnetization maps of ferromagnetic surfaces are generated with use of scanning electron microscopy with polarization analysis (SEMPA). The structure of surface Néel walls is measured by SEMPA and compared directly to the results of micromagnetics simulations. We find that the surface magnetic properties observed with SEMPA can be modeled using standard micromagnetic theory using only bulk parameters. Surface-domain-wall magnetization profiles were measured, using two different probe diameters in each case, for an Fe(100) single crystal and for Permalloy films with thicknesses of 0.12, 0.16, 0.20, and 0.24 μm. In making the quantitative comparison to the surface-domain-wall profiles calculated from (bulk) micromagnetic theory, the rms deviations, the ${\mathrm{\chi }}^2$ statistic, a correlation statistic, and rms deviations at 5% and 95% confidence levels were determined for each case. The calculated and measured domain wall profiles agree on the average to within ±7.8% for 180° walls in semi-infinite crystals of Fe(100), and ±4.5% for 180° walls in thin films of Permalloy. The micromagnetic simulations show the 180° wall of the bulk turning over into a Néel wall at the surface with the magnetization in the plane of the surface. The Néel wall extends from the surface into the bulk over a depth approximately equal to a Bloch-wall width.