phase transition between two different antiferromagnetic orderings of the $z$–components of the spins. This new transition line was supposed to result from the decomposition of the tricritical point into a bicritical point and a critical end point, a possible scenario emerging from the mean field treatment of Ising metamagnets.[@kin75] Remarkably, however, such a decomposition of the tricritical point has not been observed in Monte Carlo simulations of three-dimensional Ising antiferromagnets.[@her93; @sel96; @ren96] Furthermore, there are no indications of an antiferromagnetic–antiferromagnetic phase transition in the magnetometric measurements in an axial magnetic field.[@dea95; @pet97]

Recent investigations in an external field with an axial and a planar component have shown evidence for jumps in the magnetization parallel and perpendicular to the field.[@pet98] The authors suggest that this transition–like phenomenon may involve a nondiagonal exchange between the axial and planar components of the spins.

Hitherto, theoretical progress in understanding the properties of FeBr$_2$ has mainly been achieved by analyzing simplified spin $\frac{1}{2}$ Ising antiferromagnets.[@her93a; @sel95; @sel96; @aru96; @ple97] However, the lowest state of an iron ion in FeBr$_2$ is a triplet consisting of a lowest doublet and a singlet.[@bal85] Therefore, in Ref.9, anomalies of the magnetization and the specific heat have also been studied 