Antiferromagnets are magnetically ordered materials without a macroscopic magnetization. As a result, they could be of use in the development of memory devices because data cannot be erased by external magnetic fields. However, this also makes it difficult to electrically control their magnetic order (Neel vector). Here, we show that pillars of antiferromagnetic PtMn, which are grown on a heavy-metal layer and have diameters down to 800 nm, can be reversibly switched between different magnetic states by electric currents. The devices are based on materials that are typically used in the magnetic memory industry, and we observe switching down to a current density of ~2 MA cm−2. Furthermore, by varying the amplitude of the writing current, multilevel memory characteristics can be achieved. Micromagnetic simulations suggest that the different magnetic states may consist of domains separated by domain walls with vortex and anti-vortex textures that move in response to current, modifying the average Neel vector. Pillars of antiferromagnetic PtMn, grown on a heavy-metal layer, can be reversibly switched between different magnetic states by electric currents, illustrating the potential of silicon-compatible antiferromagnetic materials in the development of memory and computing devices.