Free-ion Hamiltonian Research Articles

Compositional dependence of the luminescence properties of Nd3+ ions in lead phosphate glasses: The efficient laser active materials

Spectroscopic investigations on 1 mol% Nd3+ embedded xPbO + (100-x) P2O5 (where x = 40, 50, and 60 mol %) glasses have been reported. Adopting a free-ion Hamiltonian, the energy values and the free-ion parameters are determined. Judd-Ofelt intensity parameters (Ω2, Ω4, Ω6) of Nd3+ ions in lead phosphate glasses are evaluated. Symmetry and covalency of Nd3+ ions are studied with increasing PbO contents in the host glasses. Strong emission due to 4F3/2 → 4I11/2 transition at 1055 nm in the near infrared (NIR) region is observed in the glasses upon excitation at 585 nm. Using the Judd-Ofelt intensity parameters, the radiative transition probability (AR), branching ratio (βR), radiative decay lifetime (τR), stimulated emission cross-section (σP), optical gain parameter and gain bandwidth are calculated for the 4F3/2 metastable state of Nd3+ ion. The luminescence lifetimes are estimated from the decay profiles. Various luminescence parameters for 4F3/2 → 4IJ (J = 9/2, 11/2 and 13/2) transitions are compared with some commercially available Neodymium doped phosphate-based laser glasses. Our investigation indicates that the present glasses could be utilized as the more efficient laser active materials for emission in the NIR region at 1055 nm.

Theoretical calculations of energies, and radiative rates for parity-forbidden transitions within the 4f3 configuration in La-like ions Pr2+ and Nd3+

The observed 4f3 energy levels of La isoelectronic sequence ions Pr2+ and Nd3+ were analyzed using a standard f-shell free-ion Hamiltonian. The root mean square (rms) deviation of 13.54cm−1, 6.17cm−1 between calculated and observed energies was obtained from the fit of 16 free-ion parameters to 38 levels for Pr2+, and to the complete set of 41 levels for Nd3+, respectively. Then, the fitted values of free-ion parameters were used to compute wavelengths, oscillator strengths, and transition rates for the forbidden magnetic dipole and electric quadrupole transitions between the 4f3 levels in Pr2+ and Nd3+ La-like ions. Detailed comparisons with other available theoretical data are also reported and discussed in this work.

Properties of the Energy Bands, Judd-Ofelt Parameters and the Fluorescence of Neodymium Chloride (NdCl3) in Methanol, Iso-propanol and Butanol Solvents.

Absorption bands of neodymium chloride (NdCl3) dissolved in methanol, iso-propanol and butanol organic solvents at room temperature have been recorded in the ultraviolet-visible and near infrared regions between 190 and 1100nm. Adopting a free-ion Hamiltonian we have calculated and assigned the energy multiplets of the 4f (3) electronic configuration of the Nd(3+) ion, and thereby the best-fit parameters are estimated. We have measured the oscillator strengths of the observed absorptions and using the experimentally measured oscillator strengths the three Judd-Ofelt intensity parameters Ω2, Ω4 and Ω6 have been derived. Hence we have calculated the line strengths and the oscillator strengths for electric-dipole transitions. An intense fluorescence emission is found for (4)F3/2 → (4)I9/2 transition at 873nm, upon excitation with 581nm. The fluorescence characteristics are also investigated by evaluating the spontaneous transition probability (A), luminescence branching ratio (β), radiative lifetime (τ) and the stimulated emission cross section (σ).

Semi-empirical calculations of radiative rates for parity-forbidden transitions within the 4f2 configuration of Ba-like ions La+, Ce2+, Pr3+ and Nd4+ and 4f12 configuration of Dy-like Yb4+

The experimental free ion 4f12 energy levels for Yb4+ have been fitted to the standard f-shell free ion Hamiltonian, which includes the major electrostatic and spin–orbit terms as well as various minor contributions like two-body, spin–spin, spin–other-orbit and electrostatically correlated spin–orbit interactions. Then, the fitted values of free ion parameters and the corresponding eigenstates are used to calculate the oscillator strengths for all absorption transitions and the spontaneous emission rates for all magnetic dipole and electric quadrupole transitions, originating from levels of the 4f2 configuration in Ba-like ions La+, Ce2+, Pr3+ and Nd4+, and the conjugate electron configuration 4f12 in Dy-like Yb4+ ions. Our calculated results are also compared with some findings available in the literature.

Systematic analysis of spectroscopic characteristics of the lanthanide and actinide ions with the 4fN−15d and 5fN−16d electronic configurations in a free state

Systematic consideration of the spectroscopic properties of the fN−1d excited electronic configurations of the di-, tri- and tetravalent lanthanide and actinide ions in a free state is presented. Variations of the Hartree–Fock calculated Slater parameters for the fN−1d electron configurations, spin–orbit (SO) interaction constant ζ for the f and d electrons, and averaged values of the second, fourth and sixth powers of the 4f, 5f, 5d, 6d electrons’ radial coordinate across both series were considered; functional dependencies between the mentioned quantities were obtained. It has been shown that the Coulomb interaction parameters F2(ff), F4(ff), and F6(ff) for the fN−1 core increase linearly with the atomic number Z, whereas the direct and exchange Coulomb parameters F2(fd), F4(fd), G1(fd), G3(fd), G5(fd) for the fN−1d configuration decrease linearly with Z. Since the SO interaction constant ζ1/4 is also proportional to Z, it was possible to find linear relationships between the Coulomb interaction parameters and SO constants for the f and d electrons, which effectively reduce the number of independent parameters in the free ion Hamiltonian. The constraining relations between the free ion Hamiltonian’s parameters obtained in the present paper can be used for simulations of the f–d transition spectra of these ions in various crystals.

Systematic analysis of spectroscopic characteristics of the lanthanide and actinide ions with the 4fN and 5fN (N = 1…14) electronic configurations in a free state

Systematic consideration of the spectroscopic properties of the di-, tri- and tetravalent lanthanide and actinide ions in a free state is presented. Variations of the Hartree–Fock calculated Slater parameters F2, F4, F6, spin–orbit interaction constant ζ and averaged values of the 4f, 5f electrons’ radial coordinate across both series were considered; functional dependencies between the mentioned quantities were obtained. It has been shown that the F2, F4, F6 parameters grow up linearly with the atomic number Z. The spin–orbit interaction constant ζ1/4 is also proportional to Z, and, therefore, to the Slater integrals as well. Moreover, the ratios F4/F2 and F6/F2 are practically constant for the isovalent ions in the considered series. The energy barycenters of all electronic configurations and the third, fourth and fifth ionization energies were all calculated. The energy barycenter moves up with increasing number of f-electrons until the f-shell becomes half-filled (7 f electrons) and then moves down. The ionization energies increase linearly with atomic number across the considered series. The established relations between F2, F4, F6 and ζ reduce the number of independent parameters in the free ion Hamiltonian and can be further applied to the case of crystal-field fitting calculations as the empirical constraints.

Systematic analysis of spectroscopic characteristics of heavy transition metal ions with 4dN and 5dN (N=1…10) electronic configurations in a free state

Systematic consideration of the spectroscopic properties of the di-, tri- and tetravalent 4d and 5d ions in a free state is presented. Variations of the Racah parameters A, B, C, spin-orbit interaction constant ζ and averaged values of the 4d and 5d electrons' radial coordinate across the considered series were considered; functional dependencies between the mentioned quantities were obtained. As a result, knowledge of one out of four parameters (A, B, C, and ζ) allows to estimate the remaining three. The established relations between A, B, C, and ζ reduce the number of independent parameters in the free ion Hamiltonian and can be further applied to the case of crystal-field fitting calculations as the empirical constraints. The third, fourth and fifth ionization energies and barycenters of the electronic 4dN/5dN configurations were calculated; systematic trends across the considered groups of ions were revealed and discussed.

Optical and luminescence properties of Dy3+ ions in phosphate based glasses

Phosphate glasses with compositions of 44P2O5 + 17K2O + 9Al2O3 + (30 − x)CaF2 + xDy2O3 (x = 0.05, 0.1, 0.5, 1.0, 2.0, 3.0 and 4.0 mol %) were prepared and characterized by X-ray diffraction (XRD), differential thermal analysis (DTA), Fourier transform infrared (FTIR), optical absorption, emission and decay measurements. The observed absorption bands were analyzed by using the free-ion Hamiltonian (HFI) model. The Judd–Ofelt (JO) analysis has been performed and the intensity parameters (Ωλ, λ = 2, 4, 6) were evaluated in order to predict the radiative properties of the excited states. From the emission spectra, the effective band widths (Δλeff), stimulated emission cross-sections (σ(λp)), yellow to blue (Y/B) intensity ratios and chromaticity color coordinates (x, y) have been determined. The fluorescence decays from the 4F9/2 level of Dy3+ ions were measured by monitoring the intense 4F9/2 → 6H15/2 transition (486 nm). The experimental lifetimes (τexp) are found to decrease with the increase of Dy3+ ions concentration due to the quenching process. The decay curves are perfectly single exponential at lower concentrations and gradually changes to non-exponential for higher concentrations. The non-exponential decay curves are well fitted to the Inokuti–Hirayama (IH) model for S = 6, which indicates that the energy transfer between the donor and acceptor is of dipole–dipole type. The systematic analysis of revealed that the energy transfer mechanism strongly depends on Dy3+ ions concentration and the host glass composition.

Magnetic dipole and electric quadrupole transitions in the trivalent lanthanide series: Calculated emission rates and oscillator strengths

Given growing interest in optical-frequency magnetic dipole transitions, we use intermediate coupling calculations to identify strong magnetic dipole emission lines that are well suited for experimental study. The energy levels for all trivalent lanthanide ions in the 4fn configuration are calculated using a detailed free ion Hamiltonian, including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit, and electrostatically correlated spin-orbit interactions. These free ion energy levels and eigenstates are then used to calculate the oscillator strengths for all ground-state magnetic dipole absorption lines and the spontaneous emission rates for all magnetic dipole emission lines including transitions between excited states. A large number of strong magnetic dipole transitions are predicted throughout the visible and near-infrared spectrum, including many at longer wavelengths that would be ideal for experimental investigation of magnetic light-matter interactions with optical metamaterials and plasmonic antennas.

The parameters of the free ions Mn5+ and Fe6+

The analysis of the behavior of iron-group ions in crystals, using a free-ion Hamiltonian that involves terms with only three parameters (B, C and ξ), seems to be erroneous since it is incapable of correctly predicting the levels of even a free ion. Such calculations may lead to erroneous conclusions concerning the crystal-field effects and the electron–phonon interaction. In this paper, we present the results of the most exact calculation of the parameters for free ions and the energy levels of Mn5+ and Fe6+ with 3d2 configuration. In the single-configuration approximation, the effective Hamiltonian of the free ions takes into account not only the electrostatic and the spin–orbit interactions, but also the relativistic ones (spin–spin, orbit–orbit and spin–other–orbit) and the linear correlation effect. For both free ions we have calculated the semi-empirical parameters included in the interaction Hamiltonian and the energy level scheme. The values of these parameters are obtained by fitting experimental data with the minimum value of rms errors. The final results are discussed.

Absorption and fluorescence properties of Sm 3+ ions in fluoride containing phosphate glasses

Optical absorption, fluorescence and lifetime characteristics of Sm 3+-doped fluoride containing phosphate glasses (PKFBASm) with molar composition of (56− x/2) P 2O 5 + 14 K 2O + 6KF + (15− x/2) BaO + 9Al 2O 3 + x Sm 2O 3, ( x = 0.01, 0.05, 0.1, 1.0, 2.0, 4.0 and 6.0 mol%) were studied. From the measured energies of absorption bands, different free-ion energy level parameters along with calculated energies were determined using the free-ion Hamiltonian (H FI) model. Judd–Ofelt (J–O) theory was applied to the experimental oscillator strengths to evaluate three phenomenological J–O intensity parameters Ω λ ( λ = 2, 4 and 6). Using these J–O parameters as well as from the emission and decay measurements, various radiative parameters such as transition probabilities ( A R), radiative lifetimes ( τ R), measured lifetimes ( τ mes), calculated branching ratios ( β R), measured branching ratios ( β mes), effective bandwidths (Δ λ eff) and stimulated emission cross-sections ( σ λ p) have been calculated for the excited 4G 5/2 luminescent level. The nature of decay curves of 4G 5/2 level for different Sm 3+ ion concentrations in all PKFBASm glasses has been analyzed using Inokuti–Hirayama (I–H) model and the lifetimes are noticed to decrease with increase of concentration. The cross-relaxation mechanism responsible for the quenching of measured lifetimes with concentration is also discussed.

Luminescence and laser transition studies of Dy3+:K–Mg–Al fluorophosphate glasses

Abstract Dysprosium ion doped fluorophosphate glasses with compositions of PKMAFDy: (56−x/2) P2O5+17K2O+8Al2O3+(15−x/2)MgO+4AlF3+xDy2O3 (x=0.01, 0.05, 0.1, 1.0 and 2.0 mol%) have been prepared by melt quenching technique and are characterized by optical absorption, emission spectra and fluorescence lifetime measurements. The observed bands in the absorption spectrum are analysed by using free-ion Hamiltonian (HFI) model. The Judd–Ofelt (JO) analysis has been performed and the intensity parameters (Ωλ, λ=2, 4, 6) have been evaluated that are used to predict radiative properties. From emission spectra, the effective bandwidth (Δλeff) and the stimulated emission cross-section (σ(λp)) were evaluated. The fluorescence decay from the 4F9/2 level of Dy3+ ions have been measured by monitoring the intense 4F9/2→6H13/2 transition (573 nm). The lifetimes (τ) are found to decrease with increasing concentration due to concentration quenching. The decay curves are single exponential for lower concentrations and gradually changes to non-exponential for higher concentrations. The non-exponential decay curves are well fitted to the Inokuti–Hirayama (IH) model for S=6 which indicates that the energy transfer between the donor and acceptor is of dipole–dipole type. The systematic analysis on decay measurements reveals that the energy transfer mechanism strongly depends on concentration as well as glass composition.

Visible luminescence characteristics of Dy 3+-doped LBTAF glasses

The visible luminescence of Dy 3+-doped lead borate titanate aluminium fluoride (LBTAF) glasses has been investigated. The observed energy levels of 1.0 mol% Dy 2O 3-doped LBTAF glass have been fitted to the well-known free-ion Hamiltonian ( H FI) model. The experimentally determined oscillator strengths have been determined by measuring the areas under the absorption peaks and the Judd–Ofelt (J–O) intensity parameters Ω t ( t = 2, 4 and 6) were evaluated using least square fit. From the evaluated J–O parameters the radiative transition probability rates, radiative lifetime and branching ratios were calculated for 4F 9/2 excited level. Room temperature fluorescence spectra for different concentrations of Dy 3+-doped LBTAF glasses were obtained by exciting the glass samples at 386 nm. The intensity of Dy 3+ emission spectra increases with increasing concentration of 0.1, 0.5 and 1.0 mol% and beyond 1.0 mol% the concentration quenching is observed. The measured branching ratios are reasonably high for transitions 4F 9/2 → 6H 15/2 and 6H 13/2 suggesting that the emissions at 484 and 576 nm, respectively, can give rise to lasing action in the visible region.

Spectroscopic study of Pr 3+ ions in CdCl 2 solution

Absorption spectra of the Pr 3+ ions in saturated CdCl 2 solution are studied at room temperature in the UV–Visible region. From the observed spectra four energy levels are identified and assigned. It is very interesting that in 3H 4 → 1D 2 transition we observe clear splitting which occurs due to the effect of the surrounding ligand ions. The free ion energies are calculated using a fitting procedure. Thereby, the best values of all the parameters in the free ion Hamiltonian, i.e., the Slater-Condon electrostatic, spin-orbit, configuration interaction, Marvin parameters, and the two-body electrostatically correlated magnetic parameters are evaluated.

Optical spectroscopy of Sm3+ ions in phosphate and fluorophosphate glasses

Spectral characterization of Sm3+-doped phosphate (PKBAS: P2O5+K2O+BaO+Al2O3+Sm2O3) and fluorophosphate (PKBFAS: P2O5+K2O+BaO+BaF2+Al2O3+Sm2O3) glasses through absorption, emission and decay curves are presented. The observed bands in absorption spectra, responsible for transitions from ground state to various excited states, are assigned and analyzed using free-ion Hamiltonian (HFI) model. Radiative properties are predicted using Judd–Ofelt theory. Experimental branching ratios and lifetimes of the 4G5/2 level are compared with theoretical values. The decay curves of Sm3+-doped phosphate and fluorophosphate glasses are perfectly single exponential for lower concentration (0.01mol%) and gradually change to non-exponential for higher concentrations. The analysis of non-exponential behavior of decay curves through Inokuti–Hirayama model indicates that the energy transfer between Sm3+ ions is of dipole–dipole type. Our systematic analysis on decay measurements reveals that energy transfer mechanism strongly depends on concentration as well as glass composition.

Characterization of spectroscopic of Pr(DBM) 3(TPPO) 2 containing poly(methyl methacrylate)

The absorption and fluorescence spectra of Pr(DBM) 3(TPPO) 2 (DBM: dibenzoylmethane, TPPO: triphenylphosphine oxide) containing poly(methyl methacrylate) (PMMA) were measured. The energy levels are assigned and analyzed in terms of the free-ion Hamiltonian model. From the data available in the absorption spectrum, various spectroscopic parameters such as the spherically symmetric part of the free-ion Hamiltonian ( E AVG), Slater–Condon ( F 2, F 4, F 6), spin-orbit interaction ( ζ), Judd–Ofelt ( Ω 2, Ω 4, Ω 6) parameters and the reduced matrix elements are derived. The radiative properties of Pr(DBM) 3(TPPO) 2 containing PMMA were also predicted according to the Judd–Ofelt theory. The values of the fluorescence branching ratio and the emission cross section of 3P 0 → 3F 2 fluorescence transition revealed that Pr(DBM) 3(TPPO) 2 containing PMMA is an efficient luminescent material.

Crystal-field excitations in the visible spectrum of Nd 2CuO 4

A phenomenological simulation was carried out for 41 experimental crystal-field (CF) levels within the 4 I 9/2–15/2 , 4 F 3/2–9/2 , 4 S 3/2 and 2 H 9/2 J manifolds, including the available infrared (IR) data up to ∼15 000 cm −1 for the Nd 3+ ions in the Nd 2CuO 4 single crystals. The CF Hamiltonian for the tetragonal C 4v symmetry was diagonalized together with the free-ion Hamiltonian in a basis that spans the entire 4f 3 configuration. A rms error of 9 cm −1 between the calculated and experimental energy level schemes was obtained. A comparison of the spectra in the visible region between the insulating Nd 2CuO 4 and the metallic Nd 2− x Ce x CuO 4, allowed identifying the absorption bands associated with the development of the charge-doping induced local structural distortions in the superconducting regime.

Luminescence of non-hygroscopic polymer electrolytes modified by europium picrate complexes

The luminescence features of new europium-based PEO electrolytes where the lanthanide ion is encapsulated into a ligand structure cage ( eg Eu 3+-picrate complexes with trans-1,4-dithiane-1,4-dioxide, TDTD) were reported. The complexes are non-hygroscopic and strongly luminescent in the temperature range of 10 to 300 K. The emission spectra were recorded in this temperature range and the corresponding lines assigned to the 5D 0.1→ 7F 0-4 transitions. The measured line widths, which are of the same order of magnitude of the one observed in crystals (1–2 Å), are approximately two orders of magnitude sharper than the ones observed in glasses and other Eu 3+-based polymeric materials. The Stark components of the 7F 0-4, 5D 0 levels and the corresponding barycenters were calculated and modeled by the superposition of the free ion Hamiltonian with a local-field perturbation. The average cation–nearest ligand distance was determined for the PEO-Eu(pic) 3TDTD 1.5 complexes and the results obtained, R̄ =2.45 Å, agree very well with the X-ray average ion–nearest ligands distances measured for the picrate salt, R̄ =2.448 Å.

Crystal-field determination for trivalent erbium in yttrium orthoaluminate

A free-ion-model crystal-field calculation has been performed for YAl${\mathrm{O}}_{3}$:${\mathrm{Er}}^{3+}$. A free-ion calculation was done by fitting a free-ion Hamiltonian, which included Coulomb, spin-orbit, configuration, spin-spin, and spin-other-orbit interactions. The coefficients which gave the best least-squares deviation of the calculated centers of gravity from the observed centers of gravity were ${E}^{1}=6174.1$, ${E}^{2}=32.836$, ${E}^{3}=651.69$, $\ensuremath{\xi}=2350.5$, $\ensuremath{\alpha}=27.825$, $\ensuremath{\beta}=\ensuremath{-}722.32$, $\ensuremath{\gamma}=3729.4$, ${M}^{0}=3.525$, ${M}^{2}=[1.974]$, ${M}^{4}=[1.339]$, ${P}^{2}=2.4779$, ${P}^{4}=\ensuremath{-}0.0406$, ${P}^{6}=0.1247$, ${T}^{2}=157.04$, ${T}^{3}=42.522$, ${T}^{4}=62.23$, ${T}^{6}=\ensuremath{-}259.93$, ${T}^{7}=402.94$, ${T}^{8}=66.377$ with an rms deviation of 29.1; where all quantities have units of ${\mathrm{cm}}^{\ensuremath{-}1}$. The intermediate-coupled free-ion vectors were then used to fit a ${C}_{s}$ (${C}_{1h}$) Hamiltonian to the observed Stark splittings. The crystal-field parameters obtained from a previous calculation on YAl${\mathrm{O}}_{3}$:${\mathrm{Tm}}^{3+}$ were used as starting parameters. The parameters which gave the best fit to the observed YAl${\mathrm{O}}_{3}$:${\mathrm{Er}}^{3+}$ Stark spectra were ${B}_{0}^{2}=\ensuremath{-}183.2$, $\mathrm{Re}{B}_{2}^{2}=385.6$, $\mathrm{Im}{B}_{2}^{2}=185.2$, ${B}_{0}^{4}=\ensuremath{-}816.2$, $\mathrm{Re}{B}_{2}^{4}=444.0$, $\mathrm{Im}{B}_{2}^{4}=39.7$, $\mathrm{Re}{B}_{4}^{4}=637.0$, $\mathrm{Im}{B}_{4}^{4}=\ensuremath{-}222.8$, ${B}_{0}^{6}=\ensuremath{-}603.8$, $\mathrm{Re}{B}_{2}^{6}=\ensuremath{-}42.2$, $\mathrm{Im}{B}_{2}^{6}=305.4$, $\mathrm{Re}{B}_{4}^{6}=229.7$, $\mathrm{Im}{B}_{4}^{6}=523.8$, $\mathrm{Re}{B}_{6}^{6}=317.0$, $\mathrm{Im}{B}_{6}^{6}=87.0$ with an rms deviation of 6.9; where all units are in ${\mathrm{cm}}^{\ensuremath{-}1}$.

Energy Levels of Pr3+ in Various Crystal Hosts

The results of a least squares fit of the energy levels of Pr3+ in various crystal hosts are reported. By using an expanded eight-variable semiempirical free-ion Hamiltonian, the average deviation between the calculated and observed levels was reduced by an order of magnitude from the average deviation found using the usual four-variable free-ion Hamiltonian. The best fit parameters F2′, F4′, ζ4f′, α′, β′, γ′, and M0′ determined for various crystal hosts are reported. In addition the magnitudes of the configuration interaction screening factors of the 4f interelectric Coulombic F2, F4, and F6 integrals are presented. The effects of the crystalline hosts on the empirical parameters are examined. It is suggested that changes in the various screening factors involved in the expanded free-ion Hamiltonian may be responsible for sizable contributions to the over-all host effects on the empirical parameters.