  It is theoretically shown that, in the four-fold symmetric d-wave
superconducting phase, a paramagnetic pair-breaking (PPB) enhanced sufficiently
by increasing the applied magnetic field induces not only the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state but also an
incommensurate antiferromagnetic (AFM) order with Q-vector parallel to a gap
node. This AFM ordering tends to occur only below H_{c2} at low temperatures,
i.e., in the presence of a nonvanishing superconducting energy gap $\Delta$
rather than in the normal phase. Through a detailed study on the resulting AFM
order and its interplay with the FFLO spatial modulation of $\Delta$, it is
argued that the strange high field and low temperature (HFLT) superconducting
phase of CeCoIn_5 is a coexisting phase of the FFLO and incommensurate AFM
orders, and that this PPB mechanism of an AFM ordering is also the origin of
the AFM quantum critical fluctuation which has occurred close to H_{c2}(0) in
several unconventional superconductors including CeCoIn_5.
