On the origin of the peak effect in the classical superconductor Nb$_{3}$Sn: the role of critical fluctuations

We found a sharp pronounced peak effect in the magnetization and the isothermal magnetocaloric effect of a single crystal of the classical superconductor Nb$_{3}$Sn. The construction of a new type of isothermal calorimeter allowed us to study the underlying thermodynamics with an extremely high resolution. A small lambda-type anomaly could be resolved superimposed on the specific heat jump at $T_{c}$. It follows scaling laws as expected for the presence of critical fluctuations. We interpret this feature as the first clear observation of the regime of critical fluctuations in a classical superconductor. Simultaneous measurements of the specific heat and the isothermal magnetocaloric effect reveal that the peak effect occurs at the onset of fluctuations below the $H_{c2}$ line. No indications of a thermodynamic transition as the origin of the peak effect could be found. Our investigation favours thus rather a scenario in which a vortex lattice looses its topological order more continously due to the increasing strength of thermal fluctuations upon approaching the $H_{c2}$ line.