The critical point separating superconducting and incommensurate magnetic phases in CeCo_0.5Rh_0.5In₅

We apply neutron diffraction as a function of magnetic field to access a critical point separating superconducting and incommensurate magnetic orders in CeCo_0.5Rh_0.5In₅. At zero applied field, CeCo_0.5Rh_0.5In₅ displays both superconductivity (Tc=1.3 K) and spatially long-ranged commensurate antiferromagnetism (TN=3.5 K) with a propagation vector of Q=(1/2, 1/2, 1/2). On applying a magnetic field that suppresses the superconducting order parameter, the magnetic intensity scales as ~H/Hc2 ln (c/H) in the vortex phase, predicted for the response in close vicinity of quantum criticality owing to changes in the superconducting order parameter outside the vortex cores. This critical point separates a superconducting phase from one that consists of coexisting superconducting and spin density wave phases. In the low temperature field induced normal phase, an incommensurate magnetic order with propagation vector of Q=(1/2, 1/2, 1/2+0.0055 r.l.u.) replaces the commensurate response present in the superconducting and vortex phases. Metallic incommensurate order competes with intertwined unconventional superconductivity and commensurate magnetism in the ``115" superconductor series.