Conventional single-gap $s-$wave superconductivity and hidden peak effect in single crystals of Mo$_8$Ga$_{41}$ superconductor

Abstract

London and Campbell penetration depths were measured in single crystals of the endohedral gallide cluster superconductor, Mo$_8$Ga$_41$. The full temperature range superfluid density, $\rho_s(T)$, is consistent with the clean isotropic $s-$wave weak-coupling BCS theory without any signs of the second gap or strong coupling. The temperature dependence of the Campbell length is hysteretic between zero-field cooling (ZFC) and field-cooling (FC) protocols, indicating an anharmonic vortex pinning potential. The field dependence of the effective critical current density, $j_{c}(H)$, reveals an unusual result. While in the ZFC protocol, $j_{c}(H)$ is monotonically suppressed by the magnetic field, it exhibits a profound "hidden" peak effect in the FC protocol, that is, without a vortex density gradient. We suggest a possible novel mechanism for such a peak effect, which involves both static and dynamic aspects of vortex pinning.