  Elastic neutron diffraction measurements were performed on the quasi-two
dimensional heavy fermion system CeRh1-xCoxIn5, ranging from an incommensurate
antiferromagnet for low x to an unconventional superconductor on the Co-rich
end of the phase diagram. We found that the superconductivity competes with the
incommensurate antiferromagnetic (AFM) order characterized by qI=(1/2, 1/2,
delta) with delta=0.298, while it coexists with the commensurate AFM order with
qc=(1/2, 1/2, 1/2). This is in sharp contrast to the CeRh1-xIrxIn5 system,
where both the commensurate and incommensurate magnetic orders coexist with the
superconductivity. These results reveal that particular areas on the Fermi
surface nested by qI play an active role in forming the superconducting state
in CeCoIn5.
