Coupling of magnetic orders inLa2CuO4+x

High transverse magnetic field and zero field muon spin rotation and relaxation measurements have been carried out in a lightly oxygen-doped high-${T}_c$ parent compound ${\mathrm{La}}₂{\mathrm{CuO}}₄$ in a temperature range from 2 K to 300 K. As in the stoichiometric compound, muon spin rotation spectra reveal, along with the antiferromagnetic local field, the presence of an additional source of magnetic field at the muon. The results indicate that this second magnetic order is driven by the antiferromagnetism at low temperature but the two magnetic orders decouple at higher temperature. The ability of ${\ensuremath{\mu}}⁺\mathrm{SR}$ to detect this additional magnetism deteriorates with doping, thus rendering the technique impotent to reveal time-reversal symmetry breaking in superconductors.