Verwey transition in mixed-valenceTbBaFe2O5: Two attempts to order charges

Electronic, magnetic, and structural phase transitions in nearly stoichiometric ${\mathrm{TbBaFe}}_2{\mathrm{O}}_{5+w}\hspace{0.5em}\mathrm{}(0.00<w<\mathrm{}0.05\mathrm{})\mathrm{}$ have been investigated. At high temperatures this compound is a paramagnetic, mixed-valence $\left({\mathrm{Fe}}^{2.5+}\right)$ conductor with identical square-pyramidal coordinations at all iron atoms. Upon cooling below $T_{\mathrm{N}}=450\mathrm{}\hspace{0.5em}\mathrm{K},$ an antiferromagnetic (AFM) spin order appears, accompanied by a magnetostrictive orthorhombic distortion. At lower temperatures the increasing distortion sets the frame for a first attempt to order charges. Mössbauer spectroscopy shows that one squeezed and one expanded square pyramid appear with different orientations of their magnetic and electric field tensors, each centered by its own mixed-valence iron state, one ${\mathrm{Fe}}^{2.5+\epsilon },$ the other ${\mathrm{Fe}}^{2.5-\epsilon }.$ The lattice retains its distortion, but a small, structurally homogeneous, and continuous increase in volume is experienced. At somewhat lower temperature ${(T}_{\mathrm{V}})$ a discontinuous increase of the orthorhombic distortion occurs, marking the second attempt to order charges, now with the classical symptoms of the Verwey transition: a large change in volume, entropy, and electrical conductivity. Below $T_{\mathrm{V}},$ a normal ${\mathrm{Fe}}^{3+}$ high-spin state in a symmetrical square-pyramidal coordination appears, whereas ${\mathrm{Fe}}^{2+}$ is distorted. The long-range order of this arrangement is solved from high-resolution powder neutron diffraction data. Rietveld refinements show that the charge-ordered spins have AFM interactions in all three directions $(G$ type) whereas in the mixed-valence state a ferromagnetic (FM) interaction appears between the iron atoms facing each other across the Tb layer. This FM interaction is suggested to be essential for the appearance of the mixed-valence state via the double-exchange sharing of the ${\mathrm{Fe}}^{2+}$-originated electron. This also allows for the total ordered spin moment being unchanged at the Verwey transition, following one single Brillouin curve. Analogous cases are pointed out where the Verwey transition proceeds in a similar manner, also at the molecular level.