  The crystal and magnetic structures and underlying magnetic interactions of
Bi4Fe5O13F, a model system for studying the physics of the Cairo pentagonal
spin lattice, are investigated by transmission electron microscopy,
low-temperature synchrotron x-ray and neutron powder diffraction, thermodynamic
measurements, and density functional band-structure calculations. The crystal
structure of Bi4Fe5O13F contains infinite rutile-like chains of edge-sharing
FeO6 octahedra interconnected by the Fe2O7 groups of two corner-sharing FeO4
tetrahedra. The cavities between the chains are filled with the
fluorine-centered Bi4F tetrahedra. The Fe3+ cations form pentagonal units that
give rise to an unusual topology of frustrated exchange couplings and underlie
a sequence of the magnetic transitions at T1= 62 K, T2 = 71 K, and TN = 178 K.
Below T1, Bi4Fe5O13F forms a fully ordered non-collinear antiferromagnetic
structure, whereas the magnetic state between T1 and TN may be partially
disordered according to the sizable increase in the magnetic entropy at T1 and
T2. Therefore, Bi4Fe5O13F shows the evidence of intricate magnetic transitions
that were never anticipated for the pentagonal Cairo spin lattice.
Additionally, it manifests a sillimanite (Al2SiO5)-based homologous series of
compounds that feature the pentagonal magnetic lattice spaced by a variable
number of octahedral units along the rutile-type chains.
