A common perception assumes that magnetic memories require ferromagnetic materials with a non-zero net magnetic moment. However, it has been recently proposed that compensated antiferromagnets with a zero net moment may represent a viable alternative to ferromagnets. So far, experimental research has focused on bistable memories in antiferromagnetic metals. In the present work we demonstrate a multiple-stable memory device in epitaxial manganese telluride (MnTe) which is an antiferromagnetic counterpart of common II-VI semiconductors. Favorable micromagnetic characteristics of MnTe allow us to demonstrate a smoothly varying antiferromagnetic anisotropic magnetoresistance (AMR) with a harmonic angular dependence on the applied magnetic field, analogous to ferromagnets. The continuously varying AMR provides means for the electrical read-out of multiple-stable antiferromagnetic memory states which we set by heat-assisted magneto-recording and by changing the angle of the writing field. We explore the dependence of the magnitude of the zero-field read-out signal on the strength of the writing field and demonstrate the robustness of the antiferromagnetic memory states against strong magnetic field perturbations. We ascribe the multiple-stability in our antiferromagnetic memory to different distributions of domains with the Neel vector aligned along one of the three $c$-plane magnetic easy axes in the hexagonal MnTe film. The domain redistribution is controlled during the heat-assisted recording by the strength and angle of the writing field and freezes when sufficiently below the Neel temperature.
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