  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 N\'eel 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 N\'eel temperature.
