We have investigated the lateral and vertical magnetic interactions of submicron-sized Fe single-layer ring arrays and Fe/Au/ Fe trilayer ring structures by measuring the magneto-optical Kerr effect. The lateral magnetic interaction significantly increases when the edge-to-edge distance of the ring array decreases to below 200 nm. The onion (vortex) to vortex (onion) transition field is proportional to 1=l n x with n ¼ 2:37 (0.73). In the vertical magnetic interaction, the trilayer wide ring shows a drastic change of the magnetization reversal in comparison with the single-layer ring, whereas the trilayer narrow ring shows a clear onion (vortex) to vortex (onion) transition, which is similar to the magnetization reversal process of the single-layer ring.
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