Absence of superfluid density anomaly at 0.6 K in superconducting PrOs$_4$Sb$_{12}$

The lower critical field $H_{c1}(T)$ in PrOs$_{4}$Sb$_{12}$ exhibits an enhancement below $T\mbox{*} = 0.6$ K [1], suggesting a transition between two superconducting phases. Small anomalies are observed at $T\mbox{*}$ in some other properties but not in the specific heat. We have carried out muon spin rotation experiments in the vortex state for fields just above $H_{c1}$. The muon spin relaxation rate, which is proportional to the rms width~$\delta B_{\rm rms}$ of the vortex-state field distribution, also shows no anomaly at $T\mbox{*}$. In a simple picture both $H_{c1}$ and $\delta B_{\rm rms}$ are proportional to the superfluid density~$\rho_s$, i.e., $\delta B_{\rm rms} \propto H_{c1}$ contrary to observation. Our results suggest that the $H_{c1}$ anomaly is due to flux pinning effects rather than a thermodynamic phase transition.\\ \frenchspacing [1] T. Cichorek et al., Phys. Rev. Lett. {\bf94}, 107002 (2005).