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, Néel 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 Grüneisen 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 Grüneisen 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.

The temperature dependences of the magnetizations of individual atomic layers across an epitaxial antiferromagnetic EuTe film were derived from virtually background-free magnetic Bragg peaks with pronounced Laue oscillations recorded with soft x rays at the Eu-M5 resonance. The magnetizations of the outermost layers decrease significantly differently from those of bulk layers, in agreement with Heisenberg-Monte Carlo calculations. The results demonstrate the applicability of the method to complex ordering phenomena at surfaces and interfaces of thin films.