  The so-called neutron spin resonance consists of a prominent enhancement of
the magnetic response at a particular energy and momentum transfer upon
entering the superconducting state of unconventional superconductors. In the
case of iron-based superconductors, the neutron resonance has been extensively
studied experimentally, and a peculiar spin-space anisotropy has been
identified by polarized inelastic neutron scattering experiments. Here we
perform a theoretical study of the energy- and spin-resolved magnetic
susceptibility in the superconducting state with $ s_{+-} $-wave order
parameter, relevant to iron-pnictide and iron-chalcogenide superconductors. Our
model is based on a realistic bandstructure including spin-orbit coupling with
electronic Hubbard-Hund interactions included at the RPA level. Spin-orbit
coupling is taken into account both in the generation of spin-fluctuation
mediated pairing, as well as the numerical computation of the spin
susceptibility in the superconducting state. We find that spin-orbit coupling
and superconductivity in conjunction can reproduce the salient experimentally
observed features of the magnetic anisotropy of the neutron resonance. This
includes the possibility of a double resonance, the tendency for a $c$-axis
polarized resonance, and the existence of enhanced magnetic anisotropy upon
entering the superconducting phase.
