Abstract
We report on muon-spin rotation and relaxation ($\ensuremath{\mu}$SR) and ${}^{119}$Sn nuclear magnetic resonance (NMR) measurements to study the microscopic superconducting and magnetic properties of the Heusler compound with the highest superconducting transition temperature, YPd${}_{2}$Sn (${T}_{c}=5.4$ K). Measurements in the vortex state provide the temperature dependence of the effective magnetic penetration depth $\ensuremath{\lambda}(T)$ and the field dependence of the superconducting gap $\ensuremath{\Delta}(0)$. The results are consistent with a very dirty $s$-wave BCS superconductor with a gap $\ensuremath{\Delta}(0)=0.85(3)$ meV, $\ensuremath{\lambda}(0)=212(1)$ nm, and a Ginzburg-Landau coherence length ${\ensuremath{\xi}}_{\mathrm{GL}}(0)\ensuremath{\cong}23$ nm. In spite of its very dirty character, the effective density of condensed charge carriers is high compared to that in the normal state. The $\ensuremath{\mu}$SR data in a broad range of applied fields are well reproduced by taking into account a field-related reduction of the effective superconducting gap. Zero-field $\ensuremath{\mu}$SR measurements, sensitive to the possible presence of very small magnetic moments, do not show any indications of magnetism in this compound.
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