Probing unconventional superconductivity using the field dependent magnetic penetration depth

The temperature dependence of the magnetic penetration depth $\lambda$ has been widely used to investigate the momentum space structure of the superconducting energy gap, in-particular whether it has nodes or not. Here we show that the magnetic field dependence of $\lambda$ is strongly enhanced in low-$T_c$ unconventional superconductors and that $\lambda(T,H)$ can be used to distinguish nodal pairing states from those where there is a small residual gap, which in the presence of small amounts of disorder are difficult to differentiate using $\lambda(T)$ alone. We show data for CeCoIn$_5$ and LaFePO which are consistent with a nodal gap and for KFe$_2$As$_2$ where the non-linear response is dominated by a small but finite gap.