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Impurity-induced antiferromagnetic order in Pauli-limited nodal superconductors: application to heavy fermion CeCoIn5

We investigate the properties of the coexistence phase of itinerant antiferromagnetism and nodal $d$-wave superconductivity (Q-phase) discovered in heavy fermion CeCoIn5 under applied magnetic field. We solve the minimal model that includes $d$-wave superconductivity and underlying magnetic correlations in real space to elucidate the structure of the $Q$-phase in the presence of an externally applied magnetic field. We further focus on the role of magnetic impurities, and show that they nucleate the Q-phase at lower magnetic fields. Our most crucial finding is that, even at zero applied field, dilute magnetic impurities cooperate via RKKY-like exchange interactions to generate a long-range ordered coexistence state identical to the Q-phase. This result is in agreement with recent neutron scattering measurements [S. Raymond et al., J. Phys. Soc. Jpn. {\bf 83}, 013707 (2014)].