Conventional 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 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, $j_{c}\left(H\right)$, reveals an unusual result. While in the ZFC protocol, $j_{c}\left(H\right)$ 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 the formation of the peak effect, which involves both static and dynamic aspects.