report.[@ple98] A short summary concludes the paper.

The models
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The low-temperature properties of FeBr$_2$ (space group D$_{3d}^3$) may be described by the effective S = 1 Heisenberg Hamiltonian[@yel75; @pou93; @muk81; @ple97] $$\begin{aligned}
{\cal H} &=& - \sum\limits_{\alpha > \beta }  J_{\alpha \beta } \left\{  \frac{1}{\eta} S_{\alpha}^z 
S_{\beta}^z
+  S_{\alpha}^x S_{\beta}^x + S_{\alpha}^y S_{\beta}^y \right\} \nonumber \\
&& - \sum\limits_{\alpha} D \left( S_{\alpha}^z \right)^2 
- \sum\limits_{\alpha} \left[ 
H_x S_{\alpha}^x + H_z S_{\alpha}^z
\right] + {\cal H}_{nd}(J_{xz})\end{aligned}$$ defined on a three-dimensional hexagonal lattice consisting of a layered system of triangular lattice planes stacked along the $c$–axis. Two different sets of interactions $J_{\alpha \beta}$ have been derived from inelastic neutron scattering studies:[@yel75; @pou93] the ferromagnetic nearest neighbor interaction in the triangular layers perpendicular to the $c$–axis (corresponding to the $z$–direction), $J_1$, is weakened by antiferromagnetic in–layer couplings, extending either up to next-nearest neighbors,[@yel75] $J_2$, or up to third neighbors,[@pou93] $J_3$. Every spin is coupled antiferromagnetically with the strength $J'$ to ten spins in the neighboring layer.[@her93a] The constant $\eta$ describes the anisotropy in the exchange interactions. The second term in Equation (1) describes a single–ion anisotropy with the easy axis of the spin along the $z$–axis, i.e. $D > 0$, whereas $H_x$ 