  Various extensions of the Standard Model motivate the existence of stable
magnetic monopoles that could have been created during an early high-energy
epoch of the Universe. These primordial magnetic monopoles would be gradually
accelerated by cosmic magnetic fields and could reach high velocities that make
them visible in Cherenkov detectors such as IceCube.
  Equivalently to electrically charged particles, magnetic monopoles produce
direct and indirect Cherenkov light while traversing through matter at
relativistic velocities.
  This paper describes searches for relativistic (v>0.76c) and mildly
relativistic (v>0.51c) monopoles, each using one year of data taken in 2008/09
and 2011/12 respectively. No monopole candidate was detected. For a velocity
above 0.51c the monopole flux is constrained down to a level of 1.55x10^-18
cm-2 s-1 sr-1. This is an improvement of almost two orders of magnitude over
previous limits.
