Reduced matrix elements of spin–spin interactions for the atomic -electron configurations

Unveiling the Local Structure and Luminescence Mechanism of Er3+-Doped LiYF4: A Promising Near-Infrared Laser Crystal

“…To obtain the accurate Stark levels of YLF:Er 3+ , our developed WEPMD method was introduced to calculate the energy levels, − and this method has been successfully applied to the systems of lanthanide ions doped into various crystals we studied previously. − For the Er 3+ -doped LiYF 4 system, Er 3+ ions replace Y 3+ ions in sites with the S 4 local symmetry, and the Hamiltonian is given in eqs – where Most of the parameters ( E AVE , F k , ζ nl , α, β, γ, T i , P j , and M n ) in the atomic Hamiltonian were described in our previous study. − The S 4 point symmetry of Er 3+ in YLF can indirectly infer the corresponding nonvanishing parameters of the crystal field (CF) Hamiltonian. In combination with free-ion (FI) parameters, it is worth mentioning that the total number of parameters is 22 for the energy level fitting of Er 3+ -doped LiYF 4 , and only six nonvanishing crystal field parameters (CFP) have to be considered in the S 4 symmetry.…”

“…Here, in this paper, a unique Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) − is proposed to predict a novel ground-state structure for YLF:Er 3+ , which was identified by us for the first time. In addition, we employ a method for regulating the f-shell energy levels of YLF:Er 3+ by our newly developed well-established parametrization matrix diagonalization (WEPMD) method, − and we present the first such in-depth investigation of the Stark levels in Er 3+ ions in the YLF crystal. Furthermore, according to the Judd–Ofelt (J–O) theory, , the electric dipole (ED) transitions were systematically investigated to acquire the most efficient luminescence of Er 3+ ions at 809 and 990 nm.…”

Parametrization of free ion levels of four isoelectronic 4f2 systems: Insights into configuration interaction parameters

“…The M j (j = 0, 2, 4) parameters describe the spin-spin and spinother orbit interactions between electrons, whereas the electrostatically correlated spin-orbit interaction, P k (k = 2, 4, 6), allows for the effect of additional configurations upon the spin-orbit interaction. With respect to the spin-spin interactions, tables have recently been provided for the relevant reduced matrix elements of the relevant four double-tensor operators of rank two in both the orbital and spin spaces [7].…”

New Theoretical Insights into the Crystal-Field Splitting and Transition Mechanism for Nd3+-Doped Y3Al5O12

“…For the [NdO 8 ] 13– ligand complex of the Nd:YAG crystal lattice, we have constructed the model Hamiltonians to parametrize the Coulomb, magnetic, and interconfiguration interactions for the 4f 3 electronic configuration for Nd 3+ ions as well as the crystal-field interactions at D 2 site symmetry between Nd 3+ and its nearby ligands. The atomic energy levels of Nd 3+ ions are analyzed by using our developed WEPMD method. − The details of the method have been described in our previous study; thus, we have just listed the equations in the Supporting Information with the literature. − The state vectors are calculated from the eigensolution in eq A1 (Supporting Information) that can be used to study the transition intensities based on eqs A3–A7 (Supporting Information).…”

“…The structure of the Nd:YAG crystal is extensively searched and successfully identified by the CALYPSO (crystal structure analysis by particle swarm optimization) − method combined with first-principles calculations. Based on the obtained structures, we have further investigated the crystal-field characteristics of Nd 3+ in YAG using our developed WEPMD (well-established parametrization matrix diagonalization) method. − The crystal-field correlations chosen for inclusion in the fitting process enable a significantly improved description of the crystal-field splitting. Finally, 22 Stark levels are predicted for further investigations, and the physical origin of the dipole transitions is analyzed in detail.…”