Fluctuations and order of antiferromagnetism induced by paramagnetic pair breaking in superconducting vortex lattices

Abstract

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 CeCoIn${}_{5}$, the anomalous field dependence of the vortex lattice form factor and the AFM order appearing inside the high-field and low-temperature superconducting phase.