High temperature superconductivity in cuprates arises upon adding or removing electrons into parent Mott insulators, but many other competing states such as spin/charge density waves, stripes, and loop current orders are encountered on the way, obscuring a precise determination of the mechanism of superconductivity. Recent advances in understanding of strongly spin-orbit coupled iridium oxides now reveal a strikingly similar phenomenology in Sr2IrO4. Examples include observation of Fermi arcs in angle-resolved photoemission spectra that shrink or elongate as a function of doping and temperature. Furthermore a recent optical second harmonic generation experiment indicates presence of a loop current order, which has been suggested to underlie the pseudogap phase in cuprates but has so far been elusive. We propose to perform a muSR to investigate signatures of loop current order in iridates