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.
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