We experimentally demonstrate that arrays of interacting nanoscale ferromagnetic islands, known as artificial spin ice, develop reproducible microstates upon cycling an applied magnetic field. The onset of this memory effect is determined by the strength of the applied field relative to the array coercivity. Specifically, when the applied field strength is almost exactly equal to the array coercivity, several training cycles are required before the array achieves a nearly completely repeatable microstate, whereas when the applied field strength is stronger or weaker than the array coercivity, a repeatable microstate is achieved after the first minor loop. We show through experiment and simulation that this memory exhibited by artificial spin ice is due to a ratchet effect on interacting, magnetically-charged defects in the island moment configuration and to the complexity of the network of strings of reversed moments that forms during magnetization reversal.

19 pages, 8 figures