Unsplit superconducting and time reversal symmetry breaking transitions in Sr${}_2$RuO${}_4$ under hydrostatic pressure and disorder

There is considerable evidence that the superconducting state of Sr${}_2$RuO${}_4$ breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking its onset temperature, $T_{\text{TRSB}}$, is generally found to match the critical temperature, $T_{\text{c}}$, within resolution. In combination with evidence for even parity, this result has led to consideration of a $d_{xz}\pm i{d}_{yz}$ order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding $T_$\text{TRSB}$ = T_$\text{c}$$,butithasahard-to-explainhorizontallinenodeat$k_z=0$. Therefore, $s\pm id$ and $d\pm ig$ order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain $T_{\text{TRSB}}\approx T_{\text{c}}$. To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr${}_2$RuO${}_4$ under hydrostatic pressure, and Sr${}_{1.98}$La${}_{0.02}$RuO${}_4$ at zero pressure. Both hydrostatic pressure and La substitution alter $T_{\text{c}}$ without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected $T_{\text{TRSB}}$ should track changes in $T_{\text{c}}$, while if it is accidental, these transition temperatures should generally separate. We observe $T_{\text{TRSB}}$ to track $T_{\text{c}}$, supporting the hypothesis of $d_{xz}\pm i{d}_{yz}$ order.