Stability Conditions for Cylindrical Domains in Ferromagnetic Elements: A Mathematical Approach to Microscopic Magnetometry

Thin magnetic films displaying perpendicular magnetic anisotropy, with an out-of-plane easy axis, often show the presence of stripe domains that can break into cylindrical domains, producing in the end the formation of bubbles or skyrmions. Perpendicular magnetic anisotropy is considered to provide spin texture stabilization in topological materials. This paper reports a theoretical study of the stability of cylindrical domains and the interaction of cylindrical domains with each other and with the magnetic host material. In particular, the case of cylindrical domains of circular cross section has been deepened and a method for experimental determination of the saturation magnetization in a thin ferromagnetic film has been proposed.