Antiferromagnetic Order oriented by Fulde-Ferrell-Larkin-Ovchinnikov Superconducting Order

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.