S-wave superconductivity probed by measuring magnetic penetration depth and lower critical field of MgCNi${}_3$ single crystals

The magnetic penetration depth $\lambda$ has been measured in MgCNi${}_3$ single crystals using both a high precision Tunnel Diode Oscillator technique (TDO) and Hall probe magnetization (HPM). In striking contrast to previous measurements in powders, $\delta \lambda$(T) deduced from TDO measurements increases exponentially at low temperature, clearly showing that the superconducting gap is fully open over the whole Fermi surface. An absolute value at zero temperature $\lambda (0)=230$nm is found from the lower critical field measured by HPM. We also discuss the observed difference of the superfluid density deduced from both techniques. A possible explanation could be due to a systematic decrease of the critical temperature at the sample surface.