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We theoretically investigate k-space structures of $d_{x^2-y^2}$-wavesuperconducting (SC) and spin-density-wave (SDW) orders in their coexistentphase induced by a paramagnetic pair-breaking (PPB) effect in relation to thehigh field and low temperature (HFLT) SC phase in CeCoIn$_5$. It is shown that,in k-space, the SDW order develops near the gap nodes where the SC order issuppressed by PPB, and the nesting condition for the SDW ordering is satisfied.By comparing the results in the $d_{x^2-y^2}$-wave SC model and those in anartificial model with no sign change of the gap function in k-space with eachother, it is shown that the $d_{x^2-y^2}$-wave SC and SDW orders are enhancedaltogether in k-space due to the sign change of the $d_{x^2-y^2}$-wave gapfunction there, and that this mutual enhancement largely stabilizes thecoexistence of these orders in real space. It is also discussed that the fielddependence of a SDW moment can be affected by the k-space structure of theseorders, which is dependent on the curvature of the Fermi surface.

Coupled k-space structure of $d$-wave superconducting and magnetic orders induced by paramagnetic pair-breaking effect