Probing the vortex state ofPrRu4Sb12through muon spin rotation and relaxation

Abstract

We have investigated the magnetic penetration depth $\ensuremath{\lambda}$ and the superconducting coherence length $\ensuremath{\xi}$ in the vortex lattice of the filled skutterudite compound $\mathrm{Pr}{\mathrm{Ru}}_{4}{\mathrm{Sb}}_{12}$ $({T}_{c}\ensuremath{\sim}0.97\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ using transverse-field muon-spin rotation measurements. Zero-field and longitudinal-field studies were also carried out to investigate the time-reversal symmetry of the superconducting state. We found $\ensuremath{\lambda}=3650(20)\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ and $\ensuremath{\xi}=345(5)\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ at $0.05\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and using these values of $\ensuremath{\lambda}$ and $\ensuremath{\xi}$, together with the Sommerfeld constant we have calculated an effective mass of the quasiparticles ${m}^{*}\ensuremath{\approx}10{m}_{e}$ and superfluid carrier density ${n}_{s}\ensuremath{\approx}4\ifmmode\times\else\texttimes\fi{}{10}^{27}\phantom{\rule{0.3em}{0ex}}\text{carriers}∕{\mathrm{m}}^{3}$. The temperature dependence of the vortex state muon-spin relaxation rate ${\ensuremath{\sigma}}_{s}(T)$ is consistent with the phenomenological two-fluid model. Further, the zero-field and longitudinal field measurements do not reveal any signature of a spontaneous internal magnetic field below the superconducting transition temperature, indicating the preservation of time-reversal symmetry in the superconducting state of $\mathrm{Pr}{\mathrm{Ru}}_{4}{\mathrm{Sb}}_{12}$, unlike the broken time-reversal symmetry of the superconducting state of the heavy-fermion superconductor $\mathrm{Pr}{\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$.