The isostructural piezoelectrics BaMF₄ crystallize in the orthorhombic space group Cmc2₁ at ambient conditions. The M-cation (M = Zn, Cu, Ni, Co, Fe, Mn, or Mg) is surrounded by six fluorines in an irregular octahedron. Each octahedron shares four fluorines with neighbouring octahedra forming layers perpendicular to the b axis. The barium atoms are accomodated in the interlayer space with coordination number nine. Individual representatives (M=Mn, Fe, Co, and Ni) of the BaMF₄ family show a multiferroic behaviour [1].
Based on inelastic-neutron scattering experiments [2], it was concluded that the BaMF₄ compounds have a structural instability at low temperatures. Up to now, this has been confirmed only for BaMnF₄ - a transition to an incommensurately modulated phase at temperatures below 250K being reported in [3]. BaMnF₄ also presents antiferroelectric anomalies in the magnetic susceptibility curve at 45K related to an intermediate magnetic phase [4].
We studied the thermal behavior of three representative members of the family (M = Mg, Zn and Mn) by powder diffraction measurements from 290K to 10K at the beamline ID31 (Grenoble, ESRF). No phase transition in this temperature range was observed for BaMgF₄  and BaZnF₄. However, refinements reveal a negative thermal expansion of the a lattice parameter and a "bump" of the c parameter below 70K. For BaMnF₄, we can confirm the transition to the incommensurate phase. However, our high resolution data cannot be explained with the model given earlier [3]. Instead, we propose a new superspace group X2₁(½ ½ γ) with X=(½ ½ 0 ½). The γ-component of the q-vector increases continuously with decreasing temperature till at 45K (coinciding with the magnetic anomaly) a constant value of 0.3948Å^-1 is reached.

Normalized lattice parameters and γ-component of the q-vector of BaMnF₄.

[1]C. Ederer & N.A. Spaldin (2006) Phys. Rev. B74, 024102.

[2] R. Almairac, et al. (1997), Phys. Rev. B55, 8249.
[3] Ph. Sciau, et al. (1988), Acta Cryst. B44, 108.
[4] M. Yoshimura, et al. (2006), J. Magn. Magn. Mat. 299, 404.

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