  Recently, a superconducting (SC) transition from low-field (LF) to high-field
(HF) SC states was reported in CeRh$_2$As$_2$, indicating the existence of
multiple SC states. It has been theoretically noted that the existence of two
Ce sites in the unit cell, the so-called sub-lattice degrees of freedom owing
to the local inversion symmetry breaking at the Ce sites, can lead to the
appearance of multiple SC phases even under an interaction inducing
spin-singlet superconductivity. CeRh$_2$As$_2$ is considered as the first
example of multiple SC phases owing to this sub-lattice degree of freedom.
However, microscopic information about the SC states has not yet been reported.
In this study, we measured the SC spin susceptibility at two
crystallographically inequivalent As sites using nuclear magnetic resonance for
various magnetic fields. Our experimental results strongly indicate a
spin-singlet state in both SC phases. In addition, the antiferromagnetic phase,
which appears within the SC phase, only coexists with the LF SC phase; there is
no sign of magnetic ordering in the HF SC phase. The present work reveals
unique SC properties originating from the locally noncentrosymmetric
characteristics.
