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It has been proposed that the pseudogap state of underdoped cupratesuperconductors may be due to a transition to a phase which has circulatingcurrents within each unit cell. Here, we use polarized neutron diffraction tosearch for the corresponding orbital moments in two samples of underdopedYBa$_2$Cu$_3$O$_{6+x}$ with doping levels $p=0.104$ and 0.123. In contrast tosome other reports using polarized neutrons, but in agreement with nuclearmagnetic resonance and muon spin rotation measurements, we find no evidence forthe appearance of magnetic order below 300 K. Thus, our experiment suggeststhat such order is not an intrinsic property of high-quality cupratesuperconductor single crystals. Our results provide an upper bound for apossible orbital loop moment which depends on the pattern of currents withinthe unit cell. For example, for the CC-$\theta_{II}$ pattern proposed by Varma,we find that the ordered moment per current loop is less than 0.013 $\mu_B$ for$p=0.104$.

No Evidence for Orbital Loop Currents in Charge Ordered YBa$_2$Cu$_3$O$_{6+x}$ from Polarized Neutron Diffraction