  The radiation pressure of next generation ultra-high intensity ($>10^{23}$
W/cm$^{2}$) lasers could efficiently accelerate ions to GeV energies. However,
nonlinear quantum-electrodynamic effects play an important role in the
interaction of these laser pulses with matter. Here we show that these effects
may lead to the production of an extremely dense ($\sim10^{24}$ cm$^{-3}$)
pair-plasma which absorbs the laser pulse consequently reducing the accelerated
ion energy and energy conversion efficiency by up to 30-50\% \& 50-65\%,
respectively. Thus we identify the regimes of laser-matter interaction where
either ions are efficiently accelerated or dense pair-plasmas are produced as a
guide for future experiments.
