Atypical vortex lattice and the magnetic penetration depth in superconducting Sr$_2$RuO$_4$ deduced by $μ$SR
The muon spin rotation ($μ$SR) technique has been applied to determine the behavior of the in-plane magnetic penetration depth ($λ_{ab}$) 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 $μ$SR study of Sr$_2$RuO$_4$ reported a $T$-linear temperature dependence for $λ_{ab}$ at low temperatures that was not identified in an earlier $μ$SR study. Here we show that there is no significant difference between the data in the early and recent $μ$SR studies and both are compatible with the limiting low-temperature $λ_{ab} \sim T^2$ dependence expected from measurements of the change in $λ_{ab}(T)$ 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 $λ_{ab}$ in Sr$_2$RuO$_4$ from $μ$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$_4$.