Muon spin rotation study of type-I superconductivity: Elemental β -Sn

Abstract

The application of the muon spin rotation/relaxation (μSR) technique for studying type-I superconductivity is discussed. In the intermediate state, i.e., when a type-I superconducting sample with nonzero demagnetization factor N is separated into normal state and Meissner state (superconducting) domains, the μSR technique allows one to determine with very high precision the value of the thermodynamic critical field Bc, as well as the volume of the sample in the normal and the superconducting states. Due to the microscopic nature of the μSR technique, the Bc 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 β-Sn sample, allowed to reconstruct the full B-T phase diagram. The zero-temperature value of the thermodynamic critical field Bc(0)=30.578(6) mT and the transition temperature Tc=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 Bc(T) dependence within the framework of the phenomenological αmodel allow one to obtain the value of the superconducting energy gap Δ=0.59(1) meV, of the electronic specific heat γe=1.781(3)mJ/molK2, and of the jump in the heat capacity ΔC(Tc)/γTc=1.55(2).