We present a study combining neutron diffraction and ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy on a powder sample of ${\mathrm{CaBaMn}}_2{\mathrm{Fe}}_2{\mathrm{O}}_7$ belonging to the large family of swedenborgite compounds. The undistorted hexagonal crystal structure (space group $P{6}_{3}mc$) is preserved down to low temperatures, and all employed techniques reveal a transition into a magnetically long-range ordered phase at $T_{\mathrm{N}}$ = 205 K. The magnetic Bragg peak intensities from the powder diffraction patterns together with a symmetry analysis of the employed models unambiguously reveal the classical $\sqrt{3}\times \sqrt{3}$ magnetic structure on a hexagonal lattice with propagation vector $\mathbf{q}=\left(\frac{1}{3}\frac{1}{3}0\right)$. The nuclear Bragg peak intensities allowed the statistical distribution of Fe and Mn ions on both trigonal and kagome sites of the complex swedenborgite structure to be analyzed which was considered to explain the complex shape of the Mössbauer spectra.

• Received 28 July 2022
• Revised 6 October 2022
• Accepted 7 October 2022

DOI:https://doi.org/10.1103/PhysRevB.106.144428