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A space-symmetry approach to the p-d hybridization and direct p-p hopping in yttrium-iron garnets

The first thorough symmetry analysis of the p-d hybridization and p-p hopping is performed for yttrium-iron garnets. Group-theoretical calculations of spin-independent p-d hybridization and p-p transfer-matrix elements allow us to determine symmetry-adapted `channels' in the crystal unit cell. The results clearly indicate what role is played by each of the interactions in a possible charge transportation. The p-d hybridization turns out to be restricted to the small-sized octahedral and tetrahedral clusters of iron-oxygen neighbours; which results from the specific complex geometry of garnets. A propagation between the hybridizing clusters of the same type is realized by the p-p hopping to the second neighbours. The p-p hopping itself is shown to be restricted to small-sized oxygen clusters. Moreover, the second-neighbour p-p hopping between octahedral hybridizing clusters shows a strong anisotropy along the ⟨111⟩ axis. The p-p hopping between the nearest neighbours appears less important. An inter-sublattice charge motion may be mediated solely by the p-d hybridization since the nearest-neighbour hybridizing clusters share a common oxygen.