Supercooling magnetic field and thermodynamic fluctuations in very thin superconducting aluminum films

We have used the fluctuation conductivity of very thin superconducting aluminum films in parallel magnetic fields $H>\mathrm{}{H}_c\mathrm{}\left(T\right)\mathrm{}$ to determine the supercooling field associated with Pauli paramagnetism at low temperature. Fields up to 9 T and temperatures down to 0.4 K were employed. The supercooling field was compared with theory and values of the spin-orbit scattering rate $b$ and orbital Maki parameter $c$ were obtained. The width of the superconducting transitions was compared with the Aslamazov-Larkin (AL) and Maki-Thompson (MT) contributions to the fluctuation conductivity as extended by Aoi to the Pauli paramagnetic limit. In general, the transitions were wider than expected from the AL contribution alone, but narrower than expected from the sum of the AL and MT contributions.