PHYSICAL REVIEW B 102, 045120 (2020) Crystal fields of lithium rare-earth tetrafluorides and multiplet splitting of the +3 rare-earth ions Leila Mollabashi and S. Jalali-Asadabadi * Department of Physics, University of Isfahan (UI), Isfahan 81746-73441, Iran (Received 15 March 2020; revised 19 June 2020; accepted 30 June 2020; published 14 July 2020) 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 R 3+ in lithium rare-earth tetrafluorides LiRF 4 (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 Tm 3+ and Dy 3+ 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 LiDyF 3+ :Dy 3+ 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 D 2d symmetry for some systems having S 4 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 S 4 symmetry may provide more reliable results than its successor D 2d symmetry for the systems under study having S 4 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. DOI: 10.1103/PhysRevB.102.045120 I. INTRODUCTION Electronic structures and magnetic properties of the lanthanide-based compounds may be highly sensitive to their crystalline environments [1]. These features can considerably vary by their crystal electric fields (CEF) [1]. The ability to measure fine and localized magnetic fields plays a key role in developing sensitive magnetometer devices which are important in a variety of areas such as physics, chemistry, material science, and biology [2]. Furthermore, splittings of energy levels of the +3 rare-earth ions due to their crystalline electric fields are of significant importance for the determina- tion of various physical properties such as magnetic, electric, optical, and thermal properties [3]. These properties can be effectively studied by simulating the crystal fields utilizing an appropriate model Hamiltonian for a given system. To this end, the crystal fields exerted on the 4 f electrons of the rare earth elements immersed in a crystalline environment can be simulated above the Kondo temperature by an effective atomiclike Hamiltonian, including free ion interaction and single-particle crystal field Hamiltonians [4]. Therefore, the applications of the atomiclike Hamiltonian may be convenient for the study of the physical properties of the rare-earth-based * Corresponding author: sjalali@sci.ui.ac.ir; saeid.jalali.asadabadi @gmail.com materials [5]. So far, different theoretical and semiempirical Hamiltonians have been proposed to model the crystal field Hamiltonian, such as point charge, superposition, and over- lapping models [6–8]. A review of these models can be found in Ref. [9]. The performance and reliability of these models depend on their constituent terms which, in turn, themselves depend on the crystal field parameters (CFPs) [5]. Therefore, the CFPs play vital roles in the predictions of reliable physical properties and would be determined accurately. The CFPs can be determined by fitting to the experimen- tal data or empirically by employing a model Hamiltonian or theoretically by performing ab initio calculations. The semiempirical models require initial values to estimate the CFPs [10]. Furthermore, the semiempirical models suffer from some difficulties such as selecting a suitable reference system, fitting algorithms, and trapping into the local minima during the fitting process [10]. Moreover, the experimental data used in the semiempirical models may be insufficient to determine all the CFPs (without employing machine learn- ing algorithms) especially when the local symmetry is low. In other words, this is a well-known overparameterization drawback of experimental approaches. Michael Slota et al. have presented a multitechnique approach to overcome the latter experimental problem by a combination of various experimental spectroscopic and magnetometric techniques [11]. In addition, since the 1960s it has become clear that not only is CEF a simple electrostatic effect, but CEF also 2469-9950/2020/102(4)/045120(24) 045120-1 ©2020 American Physical Society