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We propose a theoretical design for a magnetic memory cell, based on thin-film ferromagnetic nanorings, that can efficiently store, record, and read out information. An information bit is represented by the polarity of a stable 360deg domain wall introduced into the ring. Switching between the two magnetization states is done by a current applied to a wire passing through the ring, whereby the 360deg domain wall splits into two charged 180deg walls, which then move to the opposite extreme of the ring to recombine into a 360deg wall of the opposite polarity.

Bit Storage by 360 $^{\circ}$ Domain Walls in Ferromagnetic Nanorings