  Schwinger showed that electrically-charged particles can be produced in a
strong electric field by quantum tunnelling through the Coulomb barrier. By
electromagnetic duality, if magnetic monopoles (MMs) exist, they would be
produced by the same mechanism in a sufficiently strong magnetic field. Unique
advantages of the Schwinger mechanism are that its rate can be calculated using
semiclassical techniques without relying on perturbation theory, and the finite
MM size and strong MM-photon coupling are expected to enhance their production.
Pb-Pb heavy-ion collisions at the LHC produce the strongest known magnetic
fields in the current Universe, and this article presents the first search for
MM production by the Schwinger mechanism. It was conducted by the MoEDAL
experiment during the 5.02 TeV/nucleon heavy-ion run at the LHC in November
2018, during which the MoEDAL trapping detectors (MMTs) were exposed to 0.235
nb$^{-1}$ of Pb-Pb collisions. The MMTs were scanned for the presence of
magnetic charge using a SQUID magnetometer. MMs with Dirac charges 1$g_D$
$\leq$ $g$ $\leq$ 3$g_D$ and masses up to 75 GeV/c$^2$ were excluded by the
analysis. This provides the first lower mass limit for finite-size MMs from a
collider search and significantly extends previous mass bounds.
