Magnetic Specific Heat of (Cd$\text{}_{1-x-y}$Zn$\text{}_{y}$Mn$\text{}_{x}$)$\text{}_{3}$As$\text{}_{2}$

The specific heat of (Cd$\text{}_{1-x-y}$Zn$\text{}_{y}$Mn$\text{}_{x}$)$\text{}_{3}$As$\text{}_{2}$ with low Mn concentration (x ≤ 0.067) and for two Zn contents (y = 0.14 and y = 0.34) has been measured in the temperature range of 1.5-30 K. The magnetic contribution to the total specific heat has been analysed within our generalized pair approximation model which takes into account the complicated tetragonal crystal structure of Cd$\text{}_{1-x-y}$Zn$\text{}_{y}$Mn$\text{}_{x}$)$\text{}_{3}$As$\text{}_{2}$. Assuming that the total Mn-Mn interaction strength is a sum of superexchange and the Bloembergen-Rowland exchange, we have obtained a very good agreement between our approach and experiment by using the analytical formulae with only two adjustable parameters, i.e. the first nearest-neighbour exchange constants for both mechanisms which appear to be strongly dependent on Zn content.