Effects of the strong Pauli-paramagnetic pair-breaking (PPB) on the vortex
lattice in d-wave superconductors are theoretically studied by putting emphasis
on consequences of the PPB-induced antiferromagnetic (AFM) ordering in the
spatial modulation in the vortex lattice. It is shown that the PPB-induced AFM
fluctuation in the superconducting state leads to an enhancement of the vortex
lattice form factor which is a measure of spatial variations of the internal
magnetic field and that the enhancement becomes more remarkable as an AFM
instability is approached. It is also demonstrated that the PPB-induced AFM
ordering is assisted by the vortex-lattice modulation, and thus, that the
resulting AFM order is spatially modulated, while it is not localized in the
vortex cores but coexistent with the nonvanishing superconducting order
parameter. These results are discussed in connection with two phenomena
observed in CeCoIn5, the anomalous field dependence of the vortex lattice form
factor and the AFM order appearing inside the high-field and low-temperature
superconducting phase.Comment: 26 pages, 13 figure