Unusual Structural Relaxation for Rare-Earth Impurities in Sapphire:Ab InitioStudy of Lanthanum

A first-principles density-functional local density approximation study of substitutional La, using 120-atom supercells of α-Al₂O₃, shows that La assumes a highly displaced position, moving over 0.5 from the original Al site. The La-O nearest neighbor distance is much smaller than the sum of standard La⁺³ and O^-2 ionic radii. This is due to La being more ionic than in its own oxide, and to the role of the 5dshell, as the electron density within the displaced La is quite anisotropic. We discuss the implications for a systematic description of rare-earth ions implanted in sapphire.