On Concentration Dependence of Spin-Glass Freezing Temperature in Mn-Alloyed II-V Compounds

Basing on recent studies of the magnetic properties of (Zn$\text{}_{1-x}$Mn$\text{}_{x}$)$\text{}_{3}$As$\text{}_{2}$ (ZMA) and (Cd$\text{}_{1-x}$Mn$\text{}_{x}$)$\text{}_{3}$As$\text{}_{2}$ (CMA) as well as on theoretical works devoted to the Mn-Mn interaction in semimagnetic semiconductors, we have determined the distance dependence of this interaction taking into account the complicated crystal structure of both systems. The resulting radial dependence of the exchange interaction (being a sum of superexchange and the Bloembergen-Rowland mechanism) together with the scaling analysis have allowed us to describe the Mn-concentration dependence of spin-glass freezing temperature in ZMA, CMA and, for comparison, also in Cd$\text{}_{1-x}$Mn$\text{}_{x}$Te in very good agreement with experimental data.