Coexistence of local magnetism and superconductivity in the heavy-fermion CeRh${}_2$As${}_2$ revealed by $\mu$SR studies

The superconducting (SC) state ($T_{\mathrm{c}}$ = 0.3 K) of the heavy-fermion compound CeRh${}_2$As${}_2$, which undergoes an unusual field-induced transition to another high-field SC state, emerges from an unknown ordered state below $T_{\mathrm{o}}$ = 0.55 K. While an electronic multipolar order of itinerant Ce-4$f$ states was proposed to account for the $T_{\mathrm{o}}$ phase, the exact order parameter has not been known to date. Here, we report on muon spin relaxation ($\mu$SR) studies of the magnetic and SC properties in CeRh${}_2$As${}_2$ single crystals at low temperatures. We reveal a magnetic origin of the $T_{\mathrm{o}}$ order by identifying a spontaneous internal field below $T_{\mathrm{o}}$ = 0.55 K. Furthermore, we find evidence of a microscopic coexistence of local magnetism with bulk superconductivity. Our findings open the possibility that the $T_{\mathrm{o}}$ phase involves both dipole and higher order Ce-4$f$ moment degrees of freedom and accounts for the unusual non-Fermi liquid behavior.