The antiferromagnetic state of TbB6 has been investigated by means of magnetic susceptibility, magnetostriction, and x-ray diffraction measurements on a single crystal. The anisotropy of the magnetic susceptibility and the magnetostriction data point to a tetragonal symmetry in the antiferromagnetic state. Below T-N, the x-ray diffraction investigation shows the emergence of charge reflections related to wave vectors of the < 1/2 00 > and < 1/2 1/2 0 > types, similar to those observed in GdB6. The < 1/200 >-type reflections clearly result from the formation of static atomic displacement waves. The stabilization of atomic displacement waves is described as a compromise between the exchange coupling and a single-ion elastic energy. This mechanism is shown to be responsible for the recurrence of the < 1/4 1/4 1/2 > magnetic wave vectors in rare-earth hexaborides. A combined analysis of experimental and theoretical data points to only two stable tetragonal models for TbB6 antiferromagnetic structure. This study confirms the influence of exchange displacements in rare-earth hexaborides and highlights the need for a systematic investigation of the magnetic anisotropy of antiferromagnets.
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