If Permalloy rings are, both, asymmetric and subject to an in-plane magnetic field we have observed that additional spin-wave modes occur if compared to symmetric rings. Most importantly, we have found that offsetting the hole from the central position leads to a control of the global-vortex circulation direction. In a large array of 750 rings more than 97 % of the rings showed the same circulation direction of the vortex state. This number was estimated from the signal-to-noise level. The degree of ordering might be even better. The circulation direction was determined unambiguously from the spin-wave excitations that we monitored. Broadband ferromagnetic resonance measurements have thus turned out to be powerful to evaluate the switching statistics of large arrays of rings.

	(A): Spin excitations for asymmetric rings which are coherently ordered in the global-vortex state (colored open symbols).
(a), (b): Spin excitations in nanostructured symmetric Permalloy rings as a function of magnetic field H. (c), (d): Spin excitations of asymmetric rings under the same experimental conditions. Further modes occur in the onion and global-vortex states.	(B): Spin excitations after a magnetic history that generates a statistical distribution between left- and right-handed circulation directions of the global-vortex state (open black squares). The number of spin-wave resonances has increased accordingly in the vortex state. Spectra are measured on the same array of asymmetric rings.