Evidence for low octahedral-shell potential in ${\mathrm{BaTiO}}_3$ and ${\mathrm{KNbO}}_3$ from ground-state splitting of ${\mathrm{Fe}}^{3+}$ in cubic oxides

Measured octahedral ${}_{}{}^6{}_{}{}^{}S_{\frac{5}{2}}^{}{}_{}{}^{}$-state splittings $a\left(d\right)\mathrm{}$ of ${\mathrm{Fe}}^{3+}$ paramagnetic ions in near-cubic oxides are compared, and vary in a systematic way as a function of lattice parameter $2d$. In ${\mathrm{BaTiO}}_3$ and ${\mathrm{KNbO}}_3$ $a\left(d\right)\mathrm{}$ is a factor 2.5 too small. This gives microscopic electronic evidence for a 30% low octahedral-shell potential $V_4$ in these two ferroelectrics. In contrast to other $\mathrm{AB}{\mathrm{O}}_3$ crystals these two undergo the cubic-to-rhombohedral phase-change sequence and have anisotropic overdamped soft modes.