Mapping the magnetic exchange interactions from first principles: Anisotropy anomaly and application to Fe, Ni, and Co

Mapping the magnetic exchange interactions from model Hamiltonian to density functional theory is a crucial step in multi-scale modeling calculations. Considering the usual magnetic force theorem but with arbitrary rotational angles of the spin moments, a spurious anisotropy in the standard mapping procedure is shown to occur provided by bilinear-like contributions of high order spin interactions. The evaluation of this anisotropy gives a hint on the strength of non-bilinear terms characterizing the system under investigation.