We report low temperature muon spin relaxation ($\mu \mathrm{SR}$) measurements of the high-transition-temperature ($T_c$) cuprate superconductors ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2-x}{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.57}$, aimed at detecting the mysterious intra-unit cell (IUC) magnetic order that has been observed by spin-polarized neutron scattering in the pseudogap phase of four different cuprate families. A lack of confirmation by local magnetic probe methods has raised the possibility that the magnetic order fluctuates slowly enough to appear static on the time scale of neutron scattering, but too fast to affect $\mu \mathrm{SR}$ or nuclear magnetic resonance signals. The IUC magnetic order has been linked to a theoretical model for the cuprates, which predicts a long-range ordered phase of electron-current loop order that terminates at a quantum crictical point (QCP). Our study suggests that lowering the temperature to $T\sim 25$ mK and moving far below the purported QCP does not cause enough of a slowing down of fluctuations for the IUC magnetic order to become detectable on the time scale of $\mu \mathrm{SR}$. Our measurements place narrow limits on the fluctuation rate of this unidentified magnetic order.

• Received 6 June 2016
• Revised 27 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.134514