Abstract
The first-order structural phase transition at ${T}_{S}\ensuremath{\sim}240\text{ }\text{K}$ in the extended kagome antiferromagnet ${\text{TmBaCo}}_{4}{\text{O}}_{7}$ has been studied by neutron powder diffraction. In order to comprehend the microscopic origin of the transition, a detailed symmetry analysis is performed, based on crystallographic parameters obtained by Rietveld analysis of the neutron data. The results are consistent with the $P31c\ensuremath{\rightarrow}Pna{2}_{1}$ symmetry lowering and support a displacive nature of the phase transition. The complex tilting pattern of ${\text{CoO}}_{4}$ tetrahedra in both triangular and kagome sublattices is described based on symmetry-adapted pseudovector distortion modes of the parent $P{6}_{3}mc$ hexagonal structure. Our analysis reveals that the unusual topology of the crystal structure does not allow ${\text{CoO}}_{4}$ tetrahedra to rotate as rigid units, resulting in their inevitable distortions, whatever the combination of rotational modes considered. A possible analogy between polyhedral distortions and spin frustration in this system is discussed.
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