  MoEDAL is designed to identify new physics in the form of stable or
pseudostable highly ionizing particles produced in high-energy Large Hadron
Collider (LHC) collisions. Here we update our previous search for magnetic
monopoles in Run 2 using the full trapping detector with almost four times more
material and almost twice more integrated luminosity. For the first time at the
LHC, the data were interpreted in terms of photon-fusion monopole direct
production in addition to the Drell-Yan-like mechanism. The MoEDAL trapping
detector, consisting of 794 kg of aluminum samples installed in the forward and
lateral regions, was exposed to 4.0 fb$^{-1}$ of 13 TeV proton-proton
collisions at the LHCb interaction point and analyzed by searching for induced
persistent currents after passage through a superconducting magnetometer.
Magnetic charges equal to or above the Dirac charge are excluded in all
samples. Monopole spins 0, 1/2 and 1 are considered and both
velocity-independent and -dependent couplings are assumed. This search provides
the best current laboratory constraints for monopoles with magnetic charges
ranging from two to five times the Dirac charge.
