We present a study of the in-plane and out-of-plane magnetoresistance (MR) in heavily-underdoped, antiferromagnetic YBa_{2}Cu_{3}O_{6+x}, which reveals a variety of striking features. The in-plane MR demonstrates a d-wave-like anisotropy upon rotating the magnetic field H within the ab plane. With decreasing temperature below 20-25 K, the system acquires memory: exposing a crystal to the magnetic field results in a persistent in-plane resistivity anisotropy. The overall features can be explained by assuming that the CuO_2 planes contain a developed array of stripes accommodating the doped holes, and that the MR is associated with the field-induced topological ordering of the stripes.
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