Coupled SDW and Superconducting Order in FFLO State of CeCoIn$_5$

The mechanism of incommensurate (IC) spin-density-wave (SDW) order observed in the Flude-Ferrell-Larkin-Ovchinnikov (FFLO) phase of CeCoIn$_5$ is discussed on the basis of new mode-coupling scheme among IC-SDW order, two superconducting orders of FFLO with B$_{1{\rm g}}$ ($d_{x^{2}-y^{2}}$) symmetry and $\pi$-pairing of odd-parity. Unlike the mode-coupling schemes proposed by Kenzelmann et al, Sciencexpress, 21 August (2008), that proposed in the present Letter can offer a simple explanation for why the IC-SDW order is observed only in FFLO phase and the IC wave vector is rather robust against the magnetic field.