We present a theory describing the single-ion anisotropy of rare-earth (RE) magnets in the presence of
point defects. Taking the RE-lean 1∶12 magnet class as a prototype, we use first-principles calculations to
show how the introduction of Ti substitutions into SmFe12 perturbs the crystal field, generating new
coefficients due to the lower symmetry of the RE environment. We then demonstrate that these
perturbations can be described extremely efficiently using a screened point charge model. We provide
analytical expressions for the anisotropy energy that can be straightforwardly implemented in atomistic
spin dynamics simulations, meaning that such simulations can be carried out for an arbitrary arrangement
of point defects. The significant crystal field perturbations calculated here demonstrate that a sample that is
single phase from a structural point of view can nonetheless have a dramatically varying anisotropy profile
at the atomistic level if there is compositional disorder, which may influence localized magnetic objects like
domain walls or skyrmions.
