Nodal Behavior of the Superconducting State in Sr${_2}$RuO${_4}$

Multiple experimental and theoretical studies provide compelling support for triplet pairing of electrons and an odd, $p$-wave order parameter symmetry in superconducting Sr$_2$RuO$_4$. However, seemingly contradictory experimental results have left important questions concerning the detailed structure and coupling of the orbital and spin parts of the order parameter in this compound unresolved. The nodal behavior constrains the possibilities for the order parameter. We have used small-angle neutron scattering (SANS) to study the scattering intensity of the vortex lattice (VL) in Sr$_2$RuO$_4$, with $H$ along the [110] crystalline direction. Because the VL anisotropy in Sr$_2$RuO$_4$ is large [C. Rastovski $et$ $al.$, Phys. Rev. Lett. {\bf 111}, 087003 (2013)], this measurement effectively determines the current along the field direction, and hence the penetration depth along [1$\bar{1}$0]. The intensity vs. temperature curve is linear for $T/T{_c}$ of 0.25-0.75, but flattens out as $T$ approaches 0. This is consistent with a gap mode in the [110] direction, coupled with non-local effects.