Ground State of the Easy-Axis Rare-Earth Kagom\'e Langasite Pr${}_3$Ga${}_5$SiO${}_{14}$

We report muon spin relaxation ($\mu$SR) and ${}^{69,71}$Ga nuclear quadrupolar resonance (NQR) local-probe investigations of the kagom'e compound Pr${}_3$Ga${}_5$SiO${}_{14}$. Small quasi-static random internal fields develop below 40 K and persist down to our base temperature of 21 mK. They originate from hyperfine-enhanced ${}^{141}$Pr nuclear magnetism which requires a non-magnetic Pr${}^{3+}$ crystal-field (CF) ground state. Besides, we observe a broad maximum of the relaxation rate at $\simeq 10$ K which we attribute to the population of the first excited magnetic CF level. Our results yield a Van-Vleck paramagnet picture, at variance with the formerly proposed spin-liquid ground state.