Crystal fields of lithium rare-earth tetrafluorides and multiplet splitting of the +3 rare-earth ions

Abstract

Construction of an effective Hamiltonian including crystal field parameters (CFPs) by an accurate ab initio technique can provide a powerful approach for the measurements of tiny magnetic fields. Here, we first calculate the crystal field parameters (CFPs) of trivalent rare-earth magnetic ions R3+ in lithium rare-earth tetrafluorides LiRF4 (R = Tb, Dy, Ho, Er, Tm, and Yb) by the density functional theory plus the novel CFP scheme employing open-core treatment and Wannier functions. The behaviors of the real and imaginary parts of the CFPs are studied through the series of compounds. Then, by the calculated CFPs, we find the splittings of the energy levels of the +3 rare-earth ions by constructing an effective Hamiltonian for each case. The multiplet splittings of the +3 rare-earth ions are found to be consistent with those predicted by group theory and Hund's rules apart from some multiplet splitting of the Tm3+ and Dy3+ ions. For the former case, we have compared our theoretical results with the available empirical splittings of the multiplets. However, for the latter case due to the lack of experimental splittings, we have first empirically obtained the splittings of the multiplets employing the available experimental CFPs of the LiDyF3+:Dy3+ single crystal and then compared our empirical data with our ab initio theoretical predictions. The deviations of these two ions from the predictions of group theory and Hund's rules are found to be consistent with the experimental data. This validates the results reported and the reliability of the procedures performed to produce them. To simplify the effective Hamiltonian by reducing the number of CFPs, it is sometimes possible to use the D2d symmetry for some systems having S4 symmetry. However, by evaluating the matrix elements of the Stevens Hamiltonian term by term appeared in the Stevens CF Hamiltonian, it is shown that the actual S4 symmetry may provide more reliable results than its successor D2d symmetry for the systems under study having S4 symmetry. It can be predicted that this approach can be used for developing and improving sensitive magnetometer devices which, in turn, can play a key role in diverse areas. © 2020 American Physical Society.