Nodeless Superconducting State in the Presence of Zero-Field Staggered Magnetization in CeRh$_{2}$As$_{2}$

The tetragonal heavy-fermion superconductor CeRh$_{2}$As$_{2}$ with a critical temperature $T_c$ $\approx$ 0.34 K exhibits an intriguing magnetic field-induced transition between likely distinct superconducting states. In zero field, an even-parity state emerges within another ordered phase of unknown origin with $T_0$ $\approx$ 0.54 K. Here, we investigated the spin-singlet state of CeRh$_{2}$As$_{2}$ at temperatures down to $\approx$ 0.02$T_c$ by means of local magnetization measurements performed using micro-Hall probe magnetometry. We determined the temperature dependencies of the lower critical field for both in-plane and out-of-plane field directions, and demonstrated their consistency with predominantly fully gapped superconductivity. In the magnetization measured along the $a$ axis, we found a clear increase below $T_0$, while no similar anomaly was observed along the $c$ axis. Our results place important constraints on the spin-singlet order parameter in CeRh$_{2}$As$_{2}$ and highlight an important role of static magnetic moments in the nature of $T_0$ phase.