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

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 $\tau$, which generated the formation of metal clusters in non-centrosymmetrical F$\bar43m$-phases from high symmetry phases with Fd$\bar3m$ space group, is a one dimensional irreducible representation $\kappa_{11}$ ($\tau_4$(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 Fd$\bar3m$ 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.