  The paramagnetic properties in non-centrosymmetric superconductors with and
without antiferromagnetic (AFM) order are investigated with focus on the heavy
Fermion superconductors, CePt_3Si, CeRhSi_3 and CeIrSi_3. First, we investigate
the spin susceptibility in the linear response regime and elucidate the role of
AFM order. The spin susceptibility at T=0 is independent of the pairing
symmetry and increases in the AFM state. Second, the non-linear response to the
magnetic field are investigated on the basis of an effective model for CePt_3Si
which may be also applicable to CeRhSi_3 and CeIrSi_3. The role of
antisymmetric spin-orbit coupling (ASOC), helical superconductivity,
anisotropic Fermi surfaces and AFM order are examined in the dominantly s-, p-
and d-wave states. We emphasize the qualitatively important role of the mixing
of superconducting (SC) order parameters in the p-wave state which enhances the
spin susceptibility and suppresses paramagnetic depairing effect in a
significant way. Therefore, the dominantly p-wave superconductivity admixed
with the s-wave order parameter is consistent with the paramagnetic properties
of CePt_3Si at ambient pressure. We propose some experiments which can
elucidate the novel pairing states in CePt_3Si as well as CeRhSi_3 and
CeIrSi_3.
