the $y$–components do not vanish at the phase transition at $T_{xy}$, but take a small value which is different for the two layer types. Only when the $z$–components of the sublattice magnetizations are equal, at $T_c$, do the $y$–components vanish and the $x$–components take the same value. This effect is also observed when applying a field with axial and planar components to the tetragonal antiferromagnetic model discussed in the previous Section.

Increasing the value of the planar field moves $T_{xy}$ to lower temperatures, as it is also the case for the tetragonal antiferromagnetic model. Furthermore, the specific heat seems to loose its peculiar shape for large values of $H_x$. At least for the temperature resolution used in the present study, only one, rather broad, peak is seen instead of the shoulder or maximum with a superposed sharp peak which is observed for $H_x = 0$.

The presented data clearly indicate that the quantum nature of the S = 1 spins has to be taken into account in a theoretical description of the low temperature behaviour of FeBr$_2$. The semi–classical approach adopted in the present work leads to different disordering temperatures for the planar and the axial spin components. Hence, the 