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

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 in the critical temperatures as well as the transition from antiferromagnetic to ferromagnetic ordering for EuTe and EuSe with decreasing lattice parameter are 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 nonzero temperatures are taken into account. The strong increase in the exchange constants with decreasing lattice parameter provides room for increasing the Curie temperatures in strained epitaxial structures, which is important for device applications.