Evidence for vertical line nodes in Sr${}_2$RuO${}_4$ from nonlocal electrodynamics

By determining the superconducting lower and upper critical fields $H_{\mathrm{c}1}(T)$ and $H_{\mathrm{c}2}(T)$, respectively, in a high-purity spherical Sr${}_2$RuO${}_4$ sample via ac-susceptibility measurements, we obtain the temperature dependence of the coherence length $\xi$ and the penetration depth $\lambda$ down to 0.04$T_c$. Given the high sample quality, the observed $T^2$ dependence of $\lambda$ at low temperatures cannot be explained in terms of impurity effects. Instead, we argue that the weak type-II superconductor Sr${}_2$RuO${}_4$ has to be treated in the non-local limit. In that limit, the penetration depth data agree with a gap structure having vertical line nodes, while horizontal line nodes cannot account for the observation.