  The Atomic Cluster Expansion (ACE) provides a formally complete basis for the
local atomic environment. ACE is not limited to representing energies as a
function of atomic positions and chemical species, but can be generalized to
vectorial or tensorial properties and to incorporate further degrees of freedom
(DOF). This is crucial for magnetic materials with potential energy surfaces
that depend on atomic positions and atomic magnetic moments simultaneously. In
this work, we employ the ACE formalism to develop a non-collinear magnetic ACE
parametrization for the prototypical magnetic element Fe. The model is trained
on a broad range of collinear and non-collinear magnetic structures calculated
using spin density functional theory. We demonstrate that the non-collinear
magnetic ACE is able to reproduce not only ground state properties of various
magnetic phases of Fe but also the magnetic and lattice excitations that are
essential for a correct description of the finite temperature behavior and
properties of crystal defects.
