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We demonstrate magnetic switching between two $360^\circ$ domain wall vortexstates in cobalt nanorings, which are candidate magnetic states for robust andlow power MRAM devices. These $360^\circ$ domain wall (DW) or "twisted onion"states can have clockwise or counterclockwise circulation, the two states fordata storage. Reliable switching between the states is necessary for anyrealistic device. We accomplish this switching by applying a circular Oerstedfield created by passing current through a metal atomic force microscope tipplaced at the center of the ring. After initializing in an onion state, werotate the DWs to one side of the ring by passing a current through the center,and can switch between the two twisted states by reversing the current, causingthe DWs to split and meet again on the opposite side of the ring. A largercurrent will annihilate the DWs and create a perfect vortex state in the rings.

Switching of +/-360deg domain wall states in a nanoring by an azimuthal Oersted field