Pressure study of nematicity and quantum criticality in Sr$_3$Ru$_2$O$_7$ for an in-plane field

We study the relationship between the nematic phases of Sr$_3$Ru$_2$O$_7$ and quantum criticality. At ambient pressure, one nematic phase is associated with a metamagnetic quantum critical end point (QCEP) when the applied magnetic field is near the \textit{c}-axis. We show, however, that this metamagnetic transition does not produce the same nematic signatures when the QCEP is reached by hydrostatic pressure with the field applied in the \textit{ab}-plane. Moreover, a second nematic phase, that is seen for field applied in the \textit{ab}-plane close to, but not right at, a second metamagnetic anomaly, persists with minimal change to the highest applied pressure, 16.55 kbar. Taken together our results suggest that metamagnetic quantum criticality may not be necessary for the formation of a nematic phase in Sr$_3$Ru$_2$O$_7$.