  Machine learning potentials have emerged as a powerful tool to extend the
time and length scales of first principles-quality simulations. Still, most
machine learning potentials cannot distinguish different electronic spin
orientations and thus are not applicable to materials in different magnetic
states. Here, we propose spin-dependent atom-centered symmetry functions as a
new type of descriptor taking the atomic spin degrees of freedom into account.
When used as input for a high-dimensional neural network potential (HDNNP),
accurate potential energy surfaces of multicomponent systems describing
multiple magnetic states can be constructed. We demonstrate the performance of
these magnetic HDNNPs for the case of manganese oxide, MnO. We show that the
method predicts the magnetically distorted rhombohedral structure in excellent
agreement with density functional theory and experiment. Its efficiency allows
to determine the N\'{e}el temperature considering structural fluctuations,
entropic effects, and defects. The method is general and is expected to be
useful also for other types of systems like oligonuclear transition metal
complexes.
