Supression of superconductivity in CeRh$_{1-x}$Co$_{x}$In$_5$ by incommensurate antiferromagnetic order

CeCoIn$_5$ shows superconductivity (SC) below 2.3~K, while the SC is highly suppressed in a related system CeRhIn$_5$, which exhibits the antiferromagnetic (AF) order below 3.8~K\@. Then the mixed compound CeRh$_{1-x}$Co$_{x}$In$_5$ is expected to have a complex $x$-$T$ phase diagram where the SC and magnetism coexist. In order to understand the relationship between the SC and the antiferromagnetism in CeRh$_{1-x}$Co$_{x}$In$_5$, we have performed neutron diffraction measurements on this system for various $x$\@. A commensurate (C) AF order with a propagating vector {\boldmath $q$}$_c=(1/2, 1/2, 1/2)$ is observed for $0.3 \le x \le 0.6$, coexisting with the SC\@. However, they are strongly suppressed at $x \sim 0.3$, and an incommensurate (IC) AF order with {\boldmath $q$}$_I=(1/2, 1/2, 0.298)$ simultaneously appears. We interpret that there is no intrinsic coexistence between the IC- and C-AF orders and that the SC competes with the IC-AF order but coexists with the C-AF one. These results imply that particular areas on the Fermi surface nested by {\boldmath $q$}$_I$ play an active role in forming the superconducting state in CeCoIn$_5$.