Antiferromagnetic State in the Chrome Alums

The molecular field method is applied to the magnetic interactions in the chrome alums to describe the ordered state that occurs at low temperatures. An antiferromagnetic Curie point is predicted even in the absence of any exchange between the chromium ions. The predicted critical temperature is $T_c=1.7\mathrm{}\tau (\sigma +v)$, where $\tau$ is the characteristic temperature, $\frac{15N{\beta }^2}{k}$, $v$ represents the exchange interaction between nearest neighbors in units of the magnetic interaction, and $\sigma =0.78\mathrm{}$ is a sum of $\frac{(1-3\mathrm{}{cos}^2\theta )}{r^3}$ over lattice points. The entropy and susceptibility are calculated as functions of the temperature and applied field. The variation of the zero-field susceptibility with entropy below the critical temperature fits the observed results if $v$ is put equal to -0.13, and this value of $v$ gives a critical temperature within the range of observed values.