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Mapping the magnetic exchange interactions from model Hamiltonian to densityfunctional theory is a crucial step in multi-scale modeling calculations.Considering the usual magnetic force theorem but with arbitrary rotationalangles of the spin moments, a spurious anisotropy in the standard mappingprocedure is shown to occur provided by bilinear-like contributions of highorder spin interactions. The evaluation of this anisotropy gives a hint on thestrength of non-bilinear terms characterizing the system under investigation.

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