Atypical vortex lattice and the magnetic penetration depth in superconducting Sr$_2$RuO$_4$ deduced by $\mu$SR

TL;DR

This study uses muon spin rotation to analyze the vortex lattice and magnetic penetration depth in Sr$_2$RuO$_4$, revealing an unusual square vortex lattice and questioning the reliability of current models for absolute penetration depth measurement.

Contribution

It demonstrates the formation of an atypical square vortex lattice in Sr$_2$RuO$_4$ and discusses limitations in current methods for determining the absolute magnetic penetration depth via $bc$SR.

Findings

No significant difference between early and recent $bc$SR data.

Both datasets are compatible with a $T^2$ dependence of $bc$ at low temperatures.

Identification of an unusual square vortex lattice in Sr$_2$RuO$_4$.

Abstract

The muon spin rotation ($\mu$SR) technique has been applied to determine the behavior of the in-plane magnetic penetration depth ($\lambda_{ab}$) in the vortex state of the unconventional superconductor Sr$_2$RuO$_4$ as a means of gaining insight into its still unknown superconducting order parameter. A recent $\mu$SR study of Sr$_2$RuO$_4$ reported a $T$-linear temperature dependence for $\lambda_{ab}$ at low temperatures that was not identified in an earlier $\mu$SR study. Here we show that there is no significant difference between the data in the early and recent $\mu$SR studies and both are compatible with the limiting low-temperature $\lambda_{ab} \sim T^2$ dependence expected from measurements of the change in $\lambda_{ab}(T)$ in the Meissner state by other techniques. However, we argue that at this time there is no valid theoretical model for reliably determining the absolute value of $\lambda_{ab}$ in Sr$_2$RuO$_4$ from $\mu$SR measurements. Instead, we identify the formation of an unusual square vortex lattice that introduces a new constraint on candidate superconducting order parameters for Sr$_2$RuO$_4$.