This Letter presents a search for highly ionizing magnetic monopoles in 262$~\mu$b$^{-1}$ of ultraperipheral Pb+Pb collision data at $\sqrt{s_{_\textrm{NN}}}=5.36$ TeV collected by the ATLAS detector at the LHC. A new methodology that exploits the properties of clusters of hits reconstructed in the innermost silicon detector layers is introduced to study highly ionizing particles in heavy-ion data. No significant excess above the background, which is estimated using a data-driven technique, is observed. Using a nonperturbative semiclassical model, upper limits at 95% confidence level are set on the cross-section for pair production of monopoles with a single Dirac magnetic charge in the mass range of 20-150 GeV. The search significantly improves on the previous cross-section limits for production of low-mass monopoles in ultraperipheral Pb+Pb collisions.
Expected and observed cross-section upper limits computed using the CL$_{s}$ method for $|q_{m}| = 1 g_{\textrm{D}}$ and assuming FPA model
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