  We present the magnetic Moment Tensor Potentials (mMTPs), a new generation of
machine-learning interatomic potentials, accurately reproducing both
vibrational and magnetic degrees of freedom as provided, e.g., from
first-principles calculations. The accuracy is achieved by a two-step
minimization scheme that coarse-grains the atomic and the spin space. The
performance of the mMTPs is demonstrated for the prototype magnetic system bcc
iron, with applications to phonon calculations for different magnetic states,
and molecular dynamics simulations with fluctuating magnetic moments.
