The bistability of ordered spin states in ferromagnets (FMs) provides the magnetic memory functionality. Traditionally, the macroscopic moment of ordered spins in FMs is utilized to write information on magnetic media by a weak external magnetic field, and the FM stray field is used for reading. However, the latest generation of magnetic random access memories demonstrates a new efficient approach in which magnetic fields are replaced by electrical means for reading and writing. This concept may eventually leave the sensitivity of FMs to magnetic fields as a mere weakness for retention and the FM stray fields as a mere obstacle for high-density memory integration. In this paper we report a room-temperature bistable antiferromagnetic (AFM) memory which produces negligible stray fields and is inert in strong magnetic fields. We use a resistor made of an FeRh AFM whose transition to a FM order 100 degrees above room-temperature, allows us to magnetically set different collective directions of Fe moments. Upon cooling to room-temperature, the AFM order sets in with the direction the AFM moments pre-determined by the field and moment direction in the high temperature FM state. For electrical reading, we use an antiferromagnetic analogue of the anisotropic magnetoresistance (AMR). We report microscopic theory modeling which confirms that this archetypical spintronic effect discovered more than 150 years ago in FMs, can be equally present in AFMs. Our work demonstrates the feasibility to realize room-temperature spintronic memories with AFMs which greatly expands the magnetic materials base for these devices and offers properties which are unparalleled in FMs

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