Antiferromagnetic order in CeCoIn5 oriented by spin-orbital coupling

An incommensurate spin density wave ($Q$ phase) confined inside the superconducting state at high basal plane magnetic field is an unique property of the heavy fermion metal CeCoIn$_5$. The neutron scattering experiments and the theoretical studies point out that this state come out from the soft mode condensation of magnetic resonance excitations. We show that the fixation of direction of antiferromagnetic modulations by a magnetic field reported by Gerber et al., Nat. Phys. {\bf 10}, 126 (2014) is explained by spin-orbit coupling. This result, obtained on the basis of quite general phenomenological arguments, is supported by the microscopic derivation of the $\chi_{zz}$ susceptibility dependence on the mutual orientation of the basal plane magnetic field and the direction of modulation of spin polarization in a multi-band metal.