Universal mechanism of tetrahedral metal cluster formation in structures with breathing pyrochlore sublattices

Abstract

A universal mechanism of tetrahedral metal cluster formation in crystal with geometrically frustrated pyrochlore sublattices is proposed. It has been shown that the critical irreducible representation τ , which generated the formation of metal clusters in non-centrosymmetrical F43m-phases from high symmetry phases with Fd3m space group, is a one dimensional irreducible representation κ 11 (τ 4 (A 2u )) (in Kovalev notation). The structural theory of metal cluster formation based on group theoretical calculations was published earlier for the case of A-ordered spinel. In this work, the theory is generalized in the case of any high symmetry Fd3m structures that include pyrochlore sublattices. We presented a brief review of such structures and mechanisms of the tetrahedral metal cluster formation. The existence of so called "breathing" pyrochlore sublattices in ordered phases is predicted theoretically. The groups of atoms, between which bond clusters, are found. These groups of atoms define electron correlation effects. Examples of tetrahedral metal cluster formation in ordered spinels, ordered lacunar spinels, ordered Laves phases (MgCu 4 Sn structural type) and ordered pyrochlore are considered. The theoretical results are confirmed by the known experimental facts.

Vanadium clusters formation in geometrically frustrated spinel oxide AlV2O4

“…In many cases, molecular metallic clusters appear in dielectric matrices, formed by the anions and atoms of non-transition elements. Well known examples of such multimers are: linear chains in NaTiO 2 (Takeda et al, 1992;Clarke et al, 1998), LiCoO 2 (Talanov et al, 2007); trimerons in Fe 3 O 4 (Senn et al, 2012a(Senn et al, ,b, 2015Attfield, 2015); dimers in MgTi 2 O 4 (Schmidt et al, 2004;Talanov et al, 2015a;Ivanov et al, 2011), CuTe 2 O 5 (Hanke et al, 1973;Ushakov & Streltsov, 2009), VO 2 (Imada et al, 1998), CuGeO 3 (Hase et al, 1993); bunch of dimers in CuTi 2 S 4 (Talanov et al, 2016); trimers in LiVO 2 (Pen, Tjeng et al, 1997), LiVS 2 (Katayama et al, 2009), NaV 6 O 10 (Kato et al, 2001), BaV 10 O 15 (Liu & Greedan, 1996;Bridges et al, 2004;Kajita et al, 2010), SrV 8 Ga 4 O 19 (Miyazaki et al, 2009), AV 13 O 18 (A = Ba, Sr) (Ikeda et al, 2011), A 2 V 13 O 22 (A = Ba, Sr) (Miyazak et al, 2010), Ba 4 Ru 3 O 10 (Streltsov & Khomskii, 2012); tetramers in A-site-ordered spinel (Talanov, 1986b;, CaV 4 O 9 (Starykh et al, 1996), LiGaCr 4 O 8 and LiInCr 4 O 8 (Okamoto et al, 2013); tetramers in ordered structures with breathing pyrochlore sublattices (Talanov & Talanov, 2017); hexamers in ZnCr 2 O 4 (Lee et al, 2002); heptamers in AlV 2 O 4 (Horibe et al, 2006); octamers in CuIr 2 S 4 (Radaelli et al, 2002); dodecamers in a doubleexchange spin-ice model on a Kagomé lattice (Shimomura et al, 2004).…”

Two Different Mechanisms of Metal Cluster Formation in the Rhombohedral Spinel Structures: AlV2O4 and CuZr1.86(1)S4

“…One of the characteristic structural phenomena, particularly observed in geometrically frustrated spinel systems, is the spontaneous formation of high-order atom structuresunusual molecular metal clusters or orbital molecules . Well known examples of such atom clusters in ordered spinel structures are Ti 2 dimers in Mg­Ti 2 O 4 , , decagons in Na 4 ­Ir 3 O 8 , (such decagons are also in Na 3 ­Ir 3 O 8 and in other ordered inorganic structures), trimers in LiVO 2 , “trimerons” in Fe 3 O 4 , − heptamers or trimers + tetramers in AlV 2 O 4 , octamers in CuIr 2 S 4 , tetrahedra in Li­XY 4 O 8 (X = Ga, Fe, In; Y = Cr, Rh), Cr 4 Ga­LiO 8 , Cr 4 In­LiO 8 , Rh 4 In­LiO 8 , Ag 0.5 ­In 0.5 ­Cr 2 S 4 , and Cu 0.5 ­In 0.5 ­Cr 2 S 4 , − and in others. The formation of metal clusters is accompanied by the charge and/or spin and orbital orderings.…”