Broken time-reversal symmetry in superconducting Pr1−xLaxPt4Ge12

The superconducting state of the filled skutterudite alloy series ${\mathrm{Pr}}_{1\ensuremath{-}x}{\mathrm{La}}_x{\mathrm{Pt}}₄{\mathrm{Ge}}₁₂$ has been systematically studied by specific heat and zero-field muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$), while the critical fields have been determined by magnetization measurements. An additional inhomogeneous local magnetic field, indicative of broken time-reversal symmetry, is observed in the superconducting states of the alloys. For $x\ensuremath{\lesssim}0.5$, the broken-TRS phase sets in below a temperature ${T}_m$, distinctly lower than the superconducting transition temperature ${T}_c$. For $x\ensuremath{\gtrsim}0.5,{T}_m\ensuremath{\approx}{T}_c$. The local field strength decreases as $x\ensuremath{\rightarrow}1$, where ${\mathrm{LaPt}}₄{\mathrm{Ge}}₁₂$ is characterized by conventional pairing. The lower critical field ${H}_c1(T)$ of ${\mathrm{PrPt}}₄{\mathrm{Ge}}₁₂$ shows the onset of a second quadratic temperature region below ${T}_q\ensuremath{\sim}{T}_m$. Upper critical field ${H}_c2(T)$ measurements suggest multiband superconductivity, and point gap nodes are consistent with the specific heat data. In ${\mathrm{Pr}}_{1\ensuremath{-}x}{\mathrm{La}}_x{\mathrm{Pt}}₄{\mathrm{Ge}}₁₂$, only a single specific-heat discontinuity is observed at ${T}_c$, in contrast to the second jump seen in ${\mathrm{PrOs}}₄{\mathrm{Sb}}₁₂$ below ${T}_c$. These results suggest that superconductivity in ${\mathrm{PrPt}}₄{\mathrm{Ge}}₁₂$ is characterized by a complex order parameter.