Pronounced enhancement of the lower critical field and critical current deep in the superconducting state of PrOs$_{4}$Sb$_{12}$

We have observed an unexpected enhancement of the lower critical field \textit{H}$_{c1}$(\textit{T}) and the critical current \textit{I}$_{c}$(\textit{T}) deep in the superconducting state below \textit{T}$\approx$0.6~K (\textit{T}/\textit{T}$_{c}$$\approx$0.3) in the filled skutterudite heavy fermion superconductor PrOs$_{4}$Sb$_{12}$. From a comparison of the behavior of \textit{H}$_{c1}$(\textit{T}) with that of the heavy fermion superconductors U$_{1-x}$Th$_{x}$Be$_{13}$ (\textit{x}=0.027) and UPt$_{3}$, we speculate that the enhancements in PrOs$_{4}$Sb$_{12}$ reflect a transition into another superconducting phase that occurs below \textit{T}/\textit{T}$_{c}$$\approx$0.3. An examination of the literature reveals unexplained anomalies in other physical properties of PrOs$_{4}$Sb$_{12}$ near \textit{T}/\textit{T}$_{c}$$\approx$0.3 that correlate with the features we have observed in \textit{H}$_{c1}$(\textit{T}) and \textit{I}$_{c}$(\textit{T}). On the other hand, the lack of obvious features in the heat capacity at \textit{T}/\textit{T}$_{c}$$\approx$0.3 is somewhat reminiscent of the transition between the A and B phases of superfluid $^{3}$He. Vortices in PrOs$_{4}$Sb$_{12}$ are very strongly pinned. They relax from a metastable state following a logarithmic law with decay rates smaller than 0.5\%.