  The classical Heisenberg model is applied in a Monte Carlo study to
investigate the distance dependence of the indirect nearest neighbor (NN)
exchange and next-nearest neighbor (NNN) superexchange interaction in EuO, EuS,
EuSe and EuTe. For this purpose, first, the dependence of the magnetic ordering
temperature, i.e., Curie, respectively, N\'eel temperature for ferromagnetic
and antiferromagnetic ordering on the exchange constants was determined. This
was then employed for the analysis of experimental data of hydrostatic pressure
experiments. It is shown that all experimental findings, i.e., the strong
increase of the critical temperatures, as well as the transition from
antiferromagnetic to ferromagnetic ordering for EuTe and EuSe with decreasing
lattice parameter is well described by the magnetic Gr\"uneisen law, in which
the exchange constants depend on the interatomic distances of the Eu ions in
the form of a power law. According to these calculations, the indirect NN
exchange is characterized by a Gr\"uneisen exponent of approximately 20 and the
NNN superexchange by an exponent of about 10 for all four europium
monochalcogenides. The latter agrees with Bloch's empirical 10/3 law for the
volume dependence of superexchange interactions in insulating magnetic
materials. The Monte Carlo calculations also yield significantly revised
exchange constants for unstrained bulk material because spin fluctuations at
non-zero temperatures are taken into account. The strong increase of the
exchange constants with decreasing lattice parameter provides room for
increasing the Curie temperatures in strained epitaxial structures, which is
important for device applications.
