Quasi-Static Internal Magnetic Field Detected in the Pseudogap Phase of Bi$_{2+x}$Sr$_{2-x}$CaCu$_2$O$_{8+\delta}$ by $\mu$SR

Abstract

We report muon spin relaxation ($\mu$SR) measurements of optimally-doped and overdoped Bi$_{2+x}$Sr$_{2-x}$CaCu$_2$O$_{8+\delta}$ (Bi2212) single crystals that reveal the presence of a weak temperature-dependent quasi-static internal magnetic field of electronic origin in the superconducting (SC) and pseudogap (PG) phases. In both samples the internal magnetic field persists up to 160~K, but muon diffusion prevents following the evolution of the field to higher temperatures. We consider the evidence from our measurments in support of PG order parameter candidates, namely, electronic loop currents and magnetoelectric quadrupoles.