Interplay of magnetism and superconductivity in Cecoin₅

CeCoIn₅ is a heavy fermion superconductor which appears to be straddling the boundary between the superconducting and magnetic ground states. At the superconducting critical field H_c2 this material displays NFL behavior in transport and thermodynamic properties, pointing at a Quantum Critical Point (QCP) at H_c2, and hinting at the presence of magnetic fluctuations, probably due to an AFM order superseded by the superconductivity. In the High-Field-Low-Temperature (HFLT) corner of the superconducting phase of CeCoIn₅, within 20% off H_c2, an additional phase appears within the superconducting phase, and the normal-to-superconducting transition itself becomes first order. This behavior is consistent with a strong Pauli limited superconductivity, and the low temperature high field phase being an inhomogeneous superconducting FFLO phase. Recent NMR experiments, however, point to a long range magnetic order within HFLT state. Experiments on CeRhIn5 under pressure show magnetic field induced AFM order within the superconducting phase, with some similarities to the phase diagram of CeCoIn₅. Could the HFLT phase transition be due to magnetic order? Importantly, the HFLT phase does not extend into the normal state above H_c2. We need a picture of a magnetism "attracted" to superconductivity to explain the data on the HFLT phase in CeCoIn₅.