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Non-collinear spin DFT for lanthanide ions in doped hexagonal NaYF4

Trivalent lanthanide ions (Ln3+) doped in hexagonal (β)-NaYF4 nanocrystals (Na24Y23Ln1F96, 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 Na24Y23Ln1F96 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.