Calculations of the ferromagnet-to-spin-glass transition in diluted magnetic systems with an RKKY interaction

The transition temperatures and phase diagram of a diluted magnetic system with a Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction are studied by extension of the model by Sherrington and Southern. The model provides a way to calculate the distribution of interactions in the material. Some of these distributions are presented. Using the mean and the width of the distributions, the magnetic transition temperatures can be calculated. Furthermore, the phase boundary separating the ferromagnetic state from the spin-glass state can be determined. The results are compared with experimental data obtained for Sn_1-x{Mn}ₓ$Te and ${Pb}_{0.28{{-}}x}Sn0.72{Mn}ₓ$Te. In these compounds the magnetic phase depends on both the manganese concentration and the concentration of free carriers. Therefore, these compounds are very suitable to study the RKKY interaction. The calculated transition temperatures can describe the experimental results only qualitatively, whereas the calculated phase boundaries are quantitatively in accordance with the experimental data.