  We report on a search for magnetic monopoles (MMs) produced in
ultraperipheral Pb--Pb collisions during Run-1 of the LHC. The beam pipe
surrounding the interaction region of the CMS experiment was exposed to 184.07
\textmu b$^{-1}$ of Pb--Pb collisions at 2.76 TeV center-of-mass energy per
collision in December 2011, before being removed in 2013. It was scanned by the
MoEDAL experiment using a SQUID magnetometer to search for trapped MMs. No MM
signal was observed. The two distinctive features of this search are the use of
a trapping volume very close to the collision point and ultra-high magnetic
fields generated during the heavy-ion run that could produce MMs via the
Schwinger effect. These two advantages allowed setting the first reliable,
world-leading mass limits on MMs with high magnetic charge. In particular, the
established limits are the strongest available in the range between 2 and 45
Dirac units, excluding MMs with masses of up to 80 GeV at 95\% confidence
level.
