  We show for a simple non-collinear configuration of the atomistic spins (in
particular, where one spin is rotated by a finite angle in a ferromagnetic
background) that the pairwise energy variation computed in terms of multiple
scattering formalism cannot be fully mapped onto a bilinear Heisen- berg spin
model even in the lack of spin-orbit coupling. The non-Heisenberg terms induced
by the spin-polarized host appear in leading orders in the expansion of the
infinitesimal angle variations. However, an Eg-T2g symmetry analysis based on
the orbital decomposition of the exchange param- eters in bcc Fe leads to the
conclusion that the nearest neighbor exchange parameters related to the T2g
orbitals are essentially Heisenberg-like: they do not depend on the spin
configuration, and can in this case be mapped onto a Heisenberg spin model even
in extreme non-collinear cases.
