Covalency-driven Structural Evolution in the Polar Pyrochlore Series Cd₂Nb₂O_7–xS_x

Abstract

The arrangement of cations on the triangular pyrochlore lattice leads to a wealth of interesting physical phenomena influenced by geometric frustration. Although uncommon, several pyrochlore materials overcome this frustration and exhibit polar structures. Unraveling the origin of such behavior is key to understanding how broken inversion symmetry arises in complex crystal structures. Here we investigate the effect of varying degrees of covalency in the pyrochlore lattice through a detailed structural and lattice dynamical analysis of the pyrochlore oxysulfide series Cd 2 Nb 2 O 7−x S x above and below the ferroelectric transition temperatures (T C) using synchrotron x-ray diffraction (SXRD) and first principles calculations. All compositions exhibit the cubic F d3m pyrochlore aristotype above T C , whereas the amplitude and character of various structural distortions are found to be composition dependent below T C. For x = 0, large Cd and Nb cation displacements occur to produce the polar Ima2 structure accompanied by a change in translational symmetry. Our symmetry and lattice dynamical calculations indicate Cd 2 Nb 2 O 7 undergoes a proper ferroelectric transition through T C. Analysis of the sulfur-substituted niobates indicates that although the polar space group F dd2 is adopted by the nominal x = 0.25 sample, the transition into the polar phase is improper. For the nominally x = 0.7 composition, the lattice remains nearly cubic, but exhibits a high degree of structural disorder in the pyrochlore channel, with a deviation from the linear Cd-X'-Cd bond by nearly 15 • to accommodate the large size of S while preventing extreme stretching of the Nb-O bond. This highly distorted Cd-X' network is accompanied by a highly distorted NbO 6 network, which is accommodated by the polarizable NbO 6 coordination environment. This sheds light on the limited existence of oxysulfide pyrochlores, for example, the lack of reported S substitution in the case of the similar yet less-polarizable Cd 2 Ta 2 O 7. Our work both provides new understanding of how inversion-symmetry lifting displacements arise and how anion substitution, which tunes covalent cation-anion interactions, is a useful strategy for manipulating polar behavior in the pyrochlore lattice.

Leggett Modes Accompanying Crystallographic Phase Transitions

“…Condensing each mode along the cubic axis of its respective sphere gives rise to F dd2. Interestingly, F dd2 has been identified as the local structure of Cd 2 Nb 2 O 7 from diffuse scattering studies [30] and is also the global space group upon sulfur doping [31]. But what is evident from both the DFT and structural studies is that there are a number of space groups which are close in energy and provide comparable descriptions of the data.…”

“…That is, the free energy landscape of these two coupled spheres is relatively flat (i.e., the warping of the spheres is small). DFT calculations indicate that structures where Γ − 4 is dominant have a slightly lower free energy than ones where Γ − 5 is dominant [31], whereas order parameter-like behavior of the mode amplitudes as a function of temperature has only been claimed for Γ − 5 based on global structural refinements [32]. Regardless, the net result is that one has two coupled flat energy surfaces, one for Γ − 4 , the other for Γ − 5 , which only differ from each other by a few meV per formula unit [31].…”

“…Although the F dd2 space group is realized upon sulfur doping [31], stoichiometric Cd 2 Re 2 O 7 is thought to be Ima2 below the ferroelectric transition. The Ima2 case is similar to the F dd2 one.…”

Chloride Reduction of Mn3+ in Mild Hydrothermal Synthesis of a Charge Ordered Defect Pyrochlore, CsMn2+Mn3+F6, a Canted Antiferromagnet with a Hard Ferromagnetic Component

“…The pyrochlore structure-type has long been used for the design of new materials with a number of potential applications encompassing magnetism, − oxygen evolution reactions and storage, − energy storage materials, , optical materials, and others . The pyrochlore structure, A 2 B 2 O 7 , consists of two interpenetrating vertex-sharing tetrahedral frameworks with A and B metal cations, which offers a unique atomic arrangement that promotes frustrated magnetism. ,− This arrangement has resulted in the development of a number of rare-earth titanate and zirconate compounds exhibiting spin ice and spin liquid behavior. − A spin ice does not have a single ground state with a minimum energy; on the contrary, magnetic frustration results in multiple ground states with a nonzero residual entropy, making a spin ice material closely related to water ice and offering a unique magnetic system to study quantum effects and abnormal thermodynamics in extended solids.…”

An unusual O2−/F− distribution in the new pyrochlore oxyfluorides: Na2B2O5F2 (B = Nb, Ta)

“…6 For instance, the sulfur concentration in pyrochlore oxysulfides cannot exceed x = 1 in A 2 B 2 O 7Àx S x (i.e. Cd 2 Nb 2 O 6 S or Sn 2 Nb 2 O 6 S) 7,8 due to the O/S size mismatch that drives the O/ S ordering. In such cases, the large 8b anionic site, located in the center of the pyrochlore channel, is ideal for a large anion such as S 2À in contrast to the 48f site.…”