  Using a density functional method with explicit account for strong Coulomb
repulsion within the 4f shell, we calculate effective exchange parameters and
the corresponding ordering temperatures of the (ferro)magnetic insulating Eu
monochalcogenides (EuX; X=O,S,Se,Te) at ambient and elevated pressure
conditions. Our results provide quantitative account of the many-fold increase
of the Curie temperatures with applied pressure and reproduce well the
enhancement of the tendency toward ferromagnetic ordering across the series
from telluride to oxide, including the crossover from antiferromagnetic to
ferromagnetic ordering under pressure in EuTe and EuSe. The first and second
neighbor effective exchange are shown to follow different functional
dependencies. Finally, model calculations indicate a significant contribution
of virtual processes involving the unoccupied f states to the effective
exchange.
