Theoretical characterization of charge transport in chromia $(α-Cr2O3)$

Transport of conduction electrons and holes through the lattice of $α-Cr2O3$ (chromia) is modeled as a valence alternation of chromium cations using ab initio electronic structure calculations and electron-transfer theory. In the context of the small polaron model, a cluster approach was used to compute quantities controlling the mobility of localized electrons and holes, i.e., the reorganization energy and the electronic coupling matrix element that enter Marcus’ theory. The calculation of the electronic coupling followed the generalized Mulliken-Hush approach using the complete active space self-consistent-field (CASSCF) method and the quasidiabatic method. Our findings indicate that hole mobility is more than three orders of magnitude larger than electron mobility in both (001) and [001] lattice directions. The difference arises mainly from the larger internal reorganization energy calculated for electron-transport relative to hole-transport processes while electronic couplings have similar magnitudes. The much larger hole mobility versus electron mobility in $α-Cr2O3$ is in contrast to similar hole and electron mobilities in hematite $α-Fe2O3$ previously calculated. Our calculations also indicate that the electronic coupling for all charge-transfer processes of interest is smaller than for the corresponding processes in hematite. This variation is attributed to the weaker interaction between the metal $3d$ states and the $O(2p)$ states in chromia than in hematite, leading to a smaller overlap between the charge-transfer donor and acceptor wave functions and smaller superexchange coupling in chromia. Nevertheless, the weaker coupling in chromia is still sufficiently large to suggest that charge-transport processes in chromia are adiabatic in nature. The electronic coupling is found to depend on both the superexchange interaction through the bridging oxygen atoms and the $d$-shell electron-spin coupling within the Cr-Cr donor-acceptor pair, while the reorganization energy is essentially independent of the electron-spin coupling.