Temperature dependence of the upper critical field of FeSe single crystals

We present a careful study of the resistive superconducting transition in FeSe single crystals down to $T=40$ mK in continuous magnetic fields up to 30 T applied perpendicular and parallel to the $ab$ plane. In the $\mathbf{H}\ensuremath{\parallel}\mathbf{c}$ geometry the temperature dependence of the resistive upper critical field ${H}_{c2}^{*}$, determined as the field at which the in-plane resistivity in the transition region is 90$%$ of the normal state resistivity is down to temperatures $T/{T}_{c}<0.006$, is in close agreement with the Werthamer-Helfand-Hohenberg (WHH) theoretical curve which describes the behavior of the upper critical field in conventional type-II superconductors. In contrast, for the $\mathbf{H}\ensuremath{\parallel}\mathbf{ab}$ geometry, the data depart from the WHH model with increasing applied magnetic field according to the paramagnetic limitation of superconductivity. An anisotropy parameter $\ensuremath{\gamma}$ in our FeSe crystals decreases with decreasing temperature and FeSe becomes nearly isotropic when the temperature $T\ensuremath{\rightarrow}0$.