Non-collinear spin DFT for lanthanide ions in doped hexagonal NaYF ₄

Trivalent lanthanide ions (Ln³⁺) doped in hexagonal (β)-NaYF₄ nanocrystals (Na₂₄Y₂₃Ln ₁F₉₆, Ln = La, Ce, Pr, Nd, Pm, Sm, Eu, Gd) were systematically studied by density functional theory (DFT) with a perturbative account for spin-orbit coupling. The simulated results, including the optimised molecular structures, electronic and magnetic properties, are compared to previous spin-polarised DFT studies in the same system. The spin-orbit coupling effects become significant with the increase in the number of unpaired 4f electrons in the doped lanthanide ions, particularly for the Sm³⁺-, Eu³⁺- and Gd³⁺-doped nanocrystals. Abnormal behaviour of Eu³⁺-doped nanocrystals was observed due to the Wybourne-Downer mechanism. A sandwich-like 2p-4f-4d,5d electronic structure for Na ₂₄Y₂₃Ln₁F₉₆ and the energies of the highest occupied 4f electrons from Ce³⁺ to Gd³⁺ are consistent with Dorenbos's relationship. The energy difference between the first and second Russell-Saunders terms (^2S+1L) of the lanthanide dopant is consistent with Carnall's experimental results and with earlier spin-polarised DFT calculations.