Paramagnetic resonance and local position ofCr3+in ferroelectricBaTiO3

EPR spectra of ${\mathrm{Cr}}^{3+}$, S=(3/2), substituting for ${\mathrm{Ti}}^{4+}$ are reported as a function of temperature T in all four phases of ${\mathrm{BaTiO}}_3$. In the three ferroelectric phases (FEP’s), the principal axis of the Hamiltonian is always along the polar axis. There are two crystal-field terms, one proportional to the square of the polarization and a large one linear in T. The latter is the same in all FEP’s. The existence of the first term shows that the ${\mathrm{Cr}}^{3+}$ remains centered in the octahedral cell. The existence of the latter, not observed for ${\mathrm{Fe}}^{3+}$, points to large thermal fluctuations of the ${\mathrm{Cr}}^{3+}$. These are ascribed to the absence of antibonding, repelling $e_g$ electrons directed towards the oxygen atoms which are present for ${\mathrm{Fe}}^{3+}$. Saturation of the $b_2^0$(T) term for low T is accounted for by a Debye model for ${\mathrm{Cr}}^{3+}$ with an energy of only 236.6 K, proving independently a flat ionic potential for ${\mathrm{Cr}}^{3+}$. The picture of considerable ${\mathrm{Cr}}^{3+}$ amplitude fluctuations agrees with an effectively reduced ${\mathrm{Cr}}^{3+}$-${\mathrm{O}}^{2\mathrm{-}}$ distance of 0.02 Å compared to the ${\mathrm{Fe}}^{3+}$-${\mathrm{O}}^{2\mathrm{-}}$ distance obtained from the superposition-model analysis. The latter yields the correct sign and magnitude of the crystal-field $b_2^0$ terms in all FEP’s. It confirms that a maximum of the intrinsic superposition-model parameter $b_2$¯(R) for ${\mathrm{Cr}}^{3+}$, derived earlier by Müller and Berlinger, occurs for R between 1.95 and 1.96 Å.