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

摘要: Construction of an effective Hamiltonian including crystal field parameters (CFPs) by accurate ab initio technique can provide a powerful approach for the measurements tiny magnetic fields. Here, we first calculate trivalent rare-earth ions ${\mathrm{R}}^{3+}$ in lithium tetrafluorides ${\mathrm{LiRF}}_{4}$ (R $=$ Tb, Dy, Ho, Er, Tm, and Yb) density functional theory plus novel CFP scheme employing open-core treatment Wannier functions. The behaviors real imaginary parts CFPs are studied through series compounds. Then, calculated CFPs, find splittings energy levels $+3$ constructing each case. multiplet found to be consistent with those predicted group Hund's rules apart from some splitting ${\mathrm{Tm}}^{3+}$ ${\mathrm{Dy}}^{3+}$ ions. For former case, have compared our theoretical results available empirical multiplets. However, latter case due lack experimental splittings, empirically obtained multiplets ${\mathrm{LiDyF}}^{3+}$:${\mathrm{Dy}}^{3+}$ single then data predictions. deviations these two predictions data. This validates reported reliability procedures performed produce them. To simplify reducing number it is sometimes possible use ${\mathrm{D}}_{\text{2d}}$ symmetry systems having ${\mathrm{S}}_{4}$ symmetry. evaluating matrix elements Stevens term appeared CF Hamiltonian, shown that actual may more reliable than its successor under study It this used developing improving sensitive magnetometer devices which, turn, play key role diverse areas.