We report on measurements of the in-plane magnetic penetration depth (${\lambda }_{\mathrm{ab}}$) in single crystals of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ down to $\simeq 0.015\mathrm{K}$ by means of muon-spin rotation-relaxation. The linear temperature dependence of ${\lambda }_{\mathrm{ab}}^{-2}$ for $T\lesssim 0.7\mathrm{K}$ suggests the presence of nodes in the superconducting gap. This statement is further substantiated by observation of the Volovik effect, i.e., the reduction of ${\lambda }_{ab}^{-2}$ as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of ${\lambda }_{\mathrm{ab}}=124(3)\mathrm{nm}$ agrees with ${\lambda }_{\mathrm{ab}}\simeq 130\mathrm{nm}$, calculated based on results of electronic structure measurements reported in A. Tamai et al. [High-resolution photoemission on ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies, Phys. Rev. X 9, 021048 (2019)]. Our analysis reveals that a simple nodal superconducting energy gap, described by the lowest possible harmonic of a gap function, does not capture the dependence of ${\lambda }_{\mathrm{ab}}^{-2}$ on $T$, so the higher angular harmonics of the energy gap function need to be introduced.

• Received 24 April 2023
• Revised 2 October 2023
• Accepted 3 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.236001