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The classical Heisenberg model is applied in a Monte Carlo study toinvestigate 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 orderingtemperature, i.e., Curie, respectively, N\'eel temperature for ferromagneticand antiferromagnetic ordering on the exchange constants was determined. Thiswas then employed for the analysis of experimental data of hydrostatic pressureexperiments. It is shown that all experimental findings, i.e., the strongincrease of the critical temperatures, as well as the transition fromantiferromagnetic to ferromagnetic ordering for EuTe and EuSe with decreasinglattice parameter is well described by the magnetic Gr\"uneisen law, in whichthe exchange constants depend on the interatomic distances of the Eu ions inthe form of a power law. According to these calculations, the indirect NNexchange is characterized by a Gr\"uneisen exponent of approximately 20 and theNNN superexchange by an exponent of about 10 for all four europiummonochalcogenides. The latter agrees with Bloch's empirical 10/3 law for thevolume dependence of superexchange interactions in insulating magneticmaterials. The Monte Carlo calculations also yield significantly revisedexchange constants for unstrained bulk material because spin fluctuations atnon-zero temperatures are taken into account. The strong increase of theexchange constants with decreasing lattice parameter provides room forincreasing the Curie temperatures in strained epitaxial structures, which isimportant for device applications.

Exchange interactions in europium monochalcogenide magnetic semiconductors and their dependence on hydrostatic strain