We report a high precision search for orbital-like magnetic order in the pseudogap region of La2-xSrxCuO4 single crystals using zero-field muon spin relaxation (ZF-muSR). In contrast to previous studies of this kind, the effects of the dipolar and quadrupolar interactions of the muon with nearby nuclei are calculated. ZF-muSR spectra with a high number of counts were also recorded to determine whether a magnetically ordered phase exists in dilute regions of the sample. Despite these efforts, we find no evidence for static magnetic order of any kind in the pseudogap region above the hole-doping concentration p = 0.13.
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