Unique hyper-kagome atomic order in geometrically frustrated iridium spinel-like structures

The review briefly outlines the results of authors’ theoretical research into unique hyperkagome atomic and orbital order in geometrically frustrated iridium spinel-like structures. The structural mechanism of formation of the hyper-kagome atomic order is established. It is shown that closed loops of Ir—Ir bonds represent a fundamental feature of the iridium spinel-like structures. Each loop consists of ten atoms, thus being a decagon. We assume that decagons are responsible for abnormal chemical and physical properties of crystals. A prediction is made of structural types of crystals in which the hyper-kagome atomic order can exist.