Role of the spin-orbit coupling in the spin-resonance formation in Fe-based superconductors*

Determination of the gap symmetry is an important step towards uncovering mechanism of superconductivity in Fe-based materials. One of the key experiments in support of the $s_\pm$ spin-fluctuation-mediated gap was observation of the spin-resonance peak in many pnictides and chalcogenides, see P.J. Hirschfeld et al., Rep.Prog.Phys. 74, 124508 (2011). Recently, in inelastic polarized neutron scattering measurements by Lipscombe et al., Phys.Rev. B 82, 064515 (2010), it was found that the peaks in the transverse and longitudinal components of the spin susceptibility of BaFe$_{1.9}$Ni$_{0.1}$As$_2$ exhibit rather different behavior, and argued that the true spin resonance exists in the transverse channel only. Here, on the basis of the 5-orbital model, we argue that this disparity arises from spin-orbit coupling. It also leads to the relative shift of the two component's resonance frequency with lower frequency one exhibiting larger enhancement.