In-Plane Magnetic Penetration Depth in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>RuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math>: Muon-Spin Rotation and Relaxation Study

Abstract

We report on measurements of the in-plane magnetic penetration depth (${\ensuremath{\lambda}}_{\mathrm{ab}}$) in single crystals of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ down to $\ensuremath{\simeq}0.015\text{ }\text{ }\mathrm{K}$ by means of muon-spin rotation-relaxation. The linear temperature dependence of ${\ensuremath{\lambda}}_{\mathrm{ab}}^{\ensuremath{-}2}$ for $T\ensuremath{\lesssim}0.7\text{ }\text{ }\mathrm{K}$ 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 ${\ensuremath{\lambda}}_{ab}^{\ensuremath{-}2}$ as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of ${\ensuremath{\lambda}}_{\mathrm{ab}}=124(3)\text{ }\text{ }\mathrm{nm}$ agrees with ${\ensuremath{\lambda}}_{\mathrm{ab}}\ensuremath{\simeq}130\text{ }\text{ }\mathrm{nm}$, 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 ${\ensuremath{\lambda}}_{\mathrm{ab}}^{\ensuremath{-}2}$ on $T$, so the higher angular harmonics of the energy gap function need to be introduced.

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