Experimental determination of the magnetic interactions of frustrated Cairo pentagon lattice materials

We present inelastic neutron scattering measurements of the Cairo pentagon lattice magnets ${\mathrm{Bi}}₂{\mathrm{Fe}}₄{\mathrm{O}}₉$ and ${\mathrm{Bi}}₄{\mathrm{Fe}}₅{\mathrm{O}}₁₃\mathrm{F}$, supported by high field magnetization measurements of ${\mathrm{Bi}}₂{\mathrm{Fe}}₄{\mathrm{O}}₉$. Using linear spin wave theory and mean-field analyses we determine the spin exchange interactions and single-ion anisotropy in these materials. The Cairo lattice is geometrically frustrated and consists of two inequivalent magnetic sites, both occupied by ${\mathrm{Fe}}³⁺$ ions and connected by two competing nearest neighbor interactions. We found that one of these interactions, coupling nearest neighbor spins on the threefold symmetric sites, is extremely strong and antiferromagnetic. These strongly coupled dimers are then weakly coupled to a framework formed from spins occupying the other inequivalent site. In addition, we found that the ${\mathrm{Fe}}³⁺\phantom{\rule{4pt}{0ex}}S=5/2$ spins have a non-negligible single-ion anisotropy, which manifests as a spin anisotropy gap in the neutron spectrum and a spin-flop transition in high field magnetization measurements.