Muon spin rotation study of type-I superconductivity: elemental $\beta -$Sn

Abstract

The application of the muon-spin rotation/relaxation ($\mu$SR) technique for studying type-I superconductivity is discussed. In the intermediate state, i.e. when a type-I superconducting sample with non-zero demagnetization factor $N$ is separated into normal state and Meissner state (superconducting) domains, the $\mu$SR technique allows to determine with very high precision the value of the thermodynamic critical field $B_{\mathrm{c}}$, as well as the volume of the sample in the normal and the superconducting state. Due to the microscopic nature of $\mu$SR technique, the $B_{\mathrm{c}}$ values are determined directly via measurements of the internal field inside the normal state domains. No assumptions or introduction of any type of measurement criteria are needed. Experiments performed on a 'classical' type-I superconductor, a cylindrically shaped $\beta -$Sn sample, allowed to reconstruct the full $B-T$ phase diagram. The zero-temperature value of the thermodynamic critical field $B_{\mathrm{c}}(0)=30.578(6)$ mT and the transition temperature $T_{\mathrm{c}}=3.717(3)$ K were determined and found to be in a good agreement with the literature data. An experimentally obtained demagnetization factor is in very good agreement with theoretical calculations of the demagnetization factor of a finite cylinder. The analysis of $B_{\mathrm{c}}(T)$ dependence within the framework of the phenomenological $\alpha -$model allow to obtain the value of the superconducting energy gap $\Delta =0.59(1)$ meV, of the electronic specific heat ${\gamma }_e=1.781(3)$ $\mathrm{mJ}/\mathrm{mol}{\mathrm{K}}^2$ and of the jump in the heat capacity $\Delta C(T_c)/\gamma T_{\mathrm{c}}=1.55(2)$.

arXiv comment14 pages, 15 pictures

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