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Density-functional calculations of lattice dynamics and high-resolutionsynchrotron powder diffraction uncover antiferroelectric distortion in thekagome francisite Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl below 115K. Its Br-containinganalogue is stable in the room-temperature crystal structure down to at least10K, although the Br compound is on the verge of a similar antiferroelectricinstability and reveals local displacements of Cu and Br atoms. TheI-containing compound is stable in its room-temperature structure according todensity-functional calculations. We show that the distortion involvescooperative displacements of Cu and Cl atoms, and originates from theoptimization of interatomic distances for weakly bonded halogen atoms. Thedistortion introduces a tangible deformation of the kagome spin lattice and maybe responsible for the reduced net magnetization of the Cl compound compared tothe Br one. The polar structure of Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl is onlyslightly higher in energy than the non-polar antiferroelectric structure, butno convincing evidence of its formation could be obtained.

Antiferroelectric instability in kagome francisites Cu$_3$Bi(SeO$_3$)$_2$O$_2$X (X = Cl, Br)