The upper critical field of NaFe$_{1-x}$Co$_x$As superconductors

Measurement of the upper critical field $H_{\rm c2}$ is a crucial part of the experimental effort to understand unconventional superconductivity. Studying the temperature dependence of $H_{\rm c2}$ and the interplay between the various pair-breaking mechanisms may hint towards the underlying pair-forming interaction. $H_{\rm c2}$ and its anisotropy are also sensitive to the cooper-pair symmetry, as well as the underlying dimensionality and electronic structure of the system. Here, we present the results of upper critical field measurements on the 111 system NaFe$_{1-x}$Co$_x$As in fields up to 45 T, across the phase diagram from the parent to the over-doped compound. We show that a multi-band model is required to describe $H_{\rm c2}$. We find the in-plane critical field to be strongly dominated by paramagnetic pair-breaking. In the parent compound the paramagnetic limit is shown to be equal to the BCS value; however addition of Co leads to a significant enhancement of the paramagnetic limit above the BCS value, most likely due to a combination of spin-orbit and strong-coupling effects.