Neutron powder diffraction has been performed on the MTbF6 fluorides (M=Cd, Ca, Sr, (α/β)-Ba). Four of these fluorides (Cd, Ca, Sr, β-Ba) are built of a (pseudo-) tetragonal packing of [TbF6]2− chains and only differs by the chains relative orientations. Thus this series represents a valuable opportunity to evaluate the Tb4+-Tb4+ magnetic interactions. All the compounds displayed antiferromagnetic order (TN=2.70 K (Cd), 2.15 K (Ca), 2.60 K (Sr), 2.10 K (β-Ba)), except for the α form of BaTbF6. The crystal structure of this latter fluoroterbate has also been investigated by means of high-resolution neutron powder diffraction. From Neutron Powder Diffraction data, CdTbF6 and β-BaTbF6 magnetic structures were determined, together with the metamagnetic behaviour of β-BaTbF6 as a function of an external magnetic field. A tentative phase diagram is then given for β-BaTbF6. Advantage was taken of the polymorphism of the BaTbF6 fluoroterbate to analyse, on the basis of topological parameters such as bond distances and angles, the magnetic behaviour of its α and β forms. It was shown that superexchange interactions are present in β-BaTbF6, and that these interactions may also rule the magnetic behaviour of the other MTbF6 (M=Ca, Sr, Cd) tetravalent terbium fluorides.< Leer menos