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It is shown theoretically that, in the superconducting state with$d_{x^2-y^2}$-pairing, a strong Pauli paramagnetic depairing (PD) induces notonly the modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductingstate but also an incommensurate antiferromagnetic (AFM) (or spin-density wave)ordering with ${\bf Q}$-vector nearly paralle to a gap node. This intrinsicmechanism of field-induced coexistence of the $d$-wave superconducting and AFMorders does not need to assume a pair-density wave but is enhanced by the FFLOordering. It is argued that this is the common origin of {\it both} thecoexistent FFLO and AFM phases of CeCoIn$_5$ {\it and} the AFM quantum criticalbehavior around the superconducting $H_{c2}(0)$ seen in several heavy fermionsuperconductors and overdoped cuprates.

Coexistence of d-wave superconductivity and antiferromagnetism induced by paramagnetic depairing