Magnetic transitions in ultra-small nanoscopic magnetic rings: Theory and experiments

In this paper, we report on experimental and theoretical investigations of magnetic transitions in cobalt rings of size (diameter, width and thickness) comparable to the exchange length of cobalt. Magnetization measurements and calculations were performed for two sets of magnetic ring arrays: ultra-small magnetic rings (outer diameter 13 nm, inner diameter 5 nm and thickness 5 nm) and small magnetic rings (outer diameter 150 nm, width 5 nm, and thickness 5 nm). Our calculations suggest that if the linear dimensions of a magnetic ring are comparable to, or smaller than, the exchange length of the magnetic material, then only one magnetic state is important---the pure single-domain state. Vortex and onion-shape magnetic states do not arise. For a ring of larger diameter, magnetization reversal at zero field occurs via a vortex state. Theoretical calculations are based on an energetic analysis of pure and slightly distorted single-domain and vortex magnetic states. The calculations have been verified by micromagnetic simulations for ultra-small and small ring geometries. The hysteresis curves measured for small rings are consistent with the calculations, but there is a discrepancy for ultra-small rings. Micromagnetic simulations suggest that the discrepancies may be due to the variations in the shape and size of the ultra-small rings in the measured sample.