  The modern quantum theory of magnetism in solids is getting commonly derived
using Green's functions formalism. The popularity draws itself from remarkable
opportunities to capture the microscopic landscape of exchange interactions,
starting from a tight-binding representation of the electronic structure.
Indeed, the conventional method of infinitesimal spin rotations, considered in
terms of local force theorem, opens vast prospects of investigations regarding
the magnetic environment, as well as pairwise atomic couplings. However, this
theoretical concept practically does not devoid of intrinsic inconsistencies.
In particular, naturally expected correspondence between single and pairwise
infinitesimal spin rotations is being numerically revealed to diverge. In this
work, we elaborate this question on the model example and canonical case of bcc
iron. Our analytical derivations discovered the principal preference of on-site
magnetic precursors if the compositions of individual atomic interactions are
in focus. The problem of extremely slow or even absent spatial convergence
while considering metallic compounds was solved by suggesting the original
technique, based on reciprocal space framework. Using fundamental Fourier
transform-inspired interconnection between suggested technique and traditional
spatial representation, we shed light on symmetry breaking in bcc Fe on the
level of orbitally decomposed total exchange surrounding.
