$\mu$SR Study of Non-Magnetic Non-Centrosymmetric Superconductor LaRhSi$_3$

We report on results of $\mu$SR experiments in a transverse field geometry of the non-centrosymmetric non-magnetic superconductor LaRhSi$_3$. LaRhSi$_3$ crystallizes in the BaNiSn$_3$-type tetragonal structure (space group I4mm) and it has a critical temperature T$_c$ of 2.2 K. LaRhSi$_3$ is a type II superconductor which in magnetic fields presents an unusually sharp specific heat transition suggesting first order transitions. Under a field 250 G, LaRhSi$_3$ has a relatively low H$_{c2}$ in respect to its H$_{c1}$ of 90 G and a Pauli limit of 3.3 T. Surprisingly, at a field of 150 G we find the onset of depolarization of the muons to occur at a temperature which is a factor of 4 higher than the T$_c$ obtained from transport measurements.