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The antiferromagnetic (AFM) order in the Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) superconducting state is analyzed on the basis of a Ginzburg-Landautheory. To examine the possible AFM-FFLO state in CeCoIn_5, we focus on theincommensurate AFM order characterized by the wave vector Q = Q_{0} \pm q_incwith Q_0 =(\pi,\pi,\pi) and q_inc \parallel [110] or [1-10] in the tetragonalcrystal structure. We formulate the two component Ginzburg-Landau theory andinvestigate the two degenerate incommensurate AFM order. We show that thepinning of AFM moment due to the FFLO nodal planes leads to multiple phases inmagnetic fields along [100] or [010]. The phase diagrams for various couplingconstants between the two order parameters are shown for the comparison withCeCoIn_5. Experimental results of the NMR and neutron scattering measurementsare discussed.

Antiferromagnetic Phases in the Fulde-Ferrell-Larkin-Ovchinnikov State of CeCoIn_5