Inverse Nephelauxetic Effect in the Pressure Dependence of R-Line Energy of Ruby

Recently Mn⁴⁺-doped materials are drawing attention as candidates for novel red phosphors for white LED. Therefore, understanding the factors which determine the multiplet energies of d³ ions such as Mn⁴⁺ and Cr³⁺ in crystals is quite important. Experimentally the R-line (²E) energy of ruby (Cr³⁺:α-Al₂O₃) shows a redshift under pressure. However, this seems to be inconsistent with the interpretation based on the ordinary “Nephelauxetic effect.”  When the applied pressure increases, the molecular orbitals mainly consisting of Cr 3d should contract. Therefore, the Coulomb repulsion among d electrons increases and the energy of ²E, which belongs to (t_2g)³configuration, should increase.

In order to clarify the origin of this discrepancy, we have performed first-principles calculations of multiplet energies of ruby under various pressures. The structural optimization around the impurity Cr³⁺ ion in α-Al₂O₃ under pressure was performed using the CASTEP code. The model clusters consisting of 63 atoms were constructed based on the optimized structure and multiplet calculations were performed using the DVME code. The underestimation of electron correlation effects were corrected by the configuration dependent correction (CDC) and the correlation correction (CC). In order to clarify the factors which determine the behavior of ²E energy, the effect of covalency and the effect of correlation correction were investigated quantitatively based on the Coulomb integrals.

The results show that the pressure dependence of ²E energy was well reproduced by the first-principles calculations. The detailed analysis indicated that the Coulomb integral of t_2g orbital increases for higher pressure as expected from the contraction of the molecular orbitals. However, due to the strong electron correlation effect, the effective Coulomb integral of t_2g orbital significantly decreases, resulting in the decrease of ²E energy. This behavior is opposite to the prediction from the ordinary Nephelauxetic effect and can be called an “Inverse Nephelauxetic effect.”