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