Calculating the exchange interaction parameters between spins in MnF2 compound by Green’s function method

We investigate the magnetic properties of the compound MnF ${}_2$ by means of the double-time Green${}^{\prime }$s function method. Using the Tyablikov decoupling approximation, we derive analytical expressions for the system${}^{\prime }$s phase transition temperature $T_N$, the magnetic susceptibility at the phase transition point $\chi \left(T_N\right)$ under zero field, and the Curie–Weiss temperature $\theta$. In principle, any two of them can be used to determine the nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ in terms of the experimentally measured $T_N$, $\chi \left(T_N\right)$ and $\theta$. All three possible combinations are tested: using $T_N$ and $\chi \left(T_N\right)$ are named as scenario I, $\chi \left(T_N\right)$ and $\theta$ named as scenario II, and $T_N$ and $\theta$ named as scenario III. Fitting experimental data shows that the results of scenario I are in good agreement with the experiment, indicating that it is reasonable to use $T_N$ and $\chi \left(T_N\right)$ to determine the values of $J_1$ and $J_2$. At the same time, the rationality of these three physical quantities in determining the values of $J_1$ and $J_2$ is demonstrated, and the conclusion is that: when selecting the physical quantity to determine the value of the exchange interaction parameter, the effect of $\chi \left(T_N\right)$ is better than other physical quantities.