Normal state field induced modulated magnetism in superconducting 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 (T_c=1.3 K) and spatially long-ranged commensurate antiferromagnetism (T_N=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 linearly in the vortex state.   In the low temperature field induced normal phase, an incommensurate magnetic order with propagation vector of  Q=(1/2, 1/2, 1/2+δ) (δ=0.0055 $\pm$ 0.0007 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.