“…In this context, the onset of quasi-uniform magnetic states as a function of the element size and geometry is of particular interest as is the determination of the boundary that separates the stability regions of such states, since this allows one to controllably select a given magnetic state by choosing adequate geometrical parameters. [21][22][23][24][25][26][27] However, such a boundary depends on a whole range of intrinsic and extrinsic factors, such as the physical dimensions, material, edge and surface roughness, defects, temperature, etc., and the extent to which a given magnetic state may depend on these factors is key. For example, the equilibrium states of rings and disks are now understood to depend strongly on the presence of defects which act as pinning sites for the magnetization, thereby stabilizing magnetic states which are not the lowest in energy; 28 this is case with the "onion" state in rings 14,15 and the diamond and triangle state in disks.…”