  Resolving the high-field superconducting phase (HFSP), often called as the
Q-phase, and the antiferromagnetic or spin-density-wave (SDW) order appearing
in the phase remains a crucial issue on the superconductor CeCoIn$_5$. It is
shown that a switching of the SDW domain due to a tiny change of the magnetic
field direction in HFSP, reported and interpreted as an evidence of the
presence of a $\pi$-triplet pairing inducing the SDW order [S. Gerber et al.,
Nature Physics 10, 126 (2014)], can be explained with no triplet pairing
component if the $d$-wave superconducting order in HFSP includes the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulation parallel to the field. This
result corroborates the picture that HFSP of CeCoIn$_5$ and the SDW order found
only in the phase are consequences of the strong paramagnetic pair-breaking in
this $d$-wave superconductor.
