Fig. 1 | Nature Communications

Fig. 1

From: Coulomb spin liquid in anion-disordered pyrochlore Tb2Hf2O7

Fig. 1

Crystal chemistry of defective fluorites, pyrochlores and Tb2Hf2O7. In a, b each unit cell contains one A2B2O7 formula unit, but the actual unit cell in b is eight times larger than what is displayed. The A (black) and B (light gray) cations are fully ordered on distinct crystallographic sites in pyrochlore b and Tb2Hf2O7 c structures, while they are disordered on one site (shown in dark gray) in the defective fluorite a. Ordered cations imply three distinct Wyckoff positions for anions in the pyrochlore structure Fd-3m b: 48 f (red balls), 8b (green balls), and 8a that is vacant (center of the B-site tetrahedron, ‘occupied’ by a red dashed circle representing a vacancy). Oxygen anions (red and green balls) and vacancies (red dashed circles) can be disordered (a), ordered (b), or partially disordered (c). On average Tb2Hf2O7 c has ~8% of the 48 f positions that are vacant, exactly compensated for stoichiometry by ~50 % of 8a positions that are occupied (blue balls). This average structure corresponds to a random distribution of oxygen Frenkel pair defects. Such a local defect is shown at the top of c, where an empty 48 f position is compensated by a non-vacant neighbor 8a position, while the situation normally occurring in a perfect pyrochlore is shown at the bottom. Tb2Hf2O7 is characterized by a distribution of the two configurations shown respectively on the top and bottom of c. A Frenkel defect has two consequences for the magnetic pyrochlore sublattice of Tb3+ ions shown in the left part of c (dark gray). First, the first-neighbor symmetry around ~50 % of the Tb3+ cations is broken, because they have seven instead of eight anion ligands. Second, ~8% of the bonds defining the magnetic pyrochlore lattice have one instead of two Tb–O–Tb superexchange pathways, their strength being therefore modified

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