This paper describes a scheme for the numerical calculation of crystal field (CF) energy levels and at the same time wave functions of the trivalent erbium ion in cubic symmetry. The 16-fold degenerate term 4I15=2 of the trivalent erbium ion splits into three Stark quartets Γ8 and two different doublets Γ6 and Γ7 (irreducible representations). The CF energy matrix of the Er3+ ion has been constructed and calculated from the complete diagonalization method, and the corresponding wave functions were used to calculate the ground state g-values. This method is outlined and illustrated by the examples of the Si:Er for comparison. The calculated g-factors are g = 6:8 and g = 6:0 for Γ6 and Γ7, respectively
This paper describes a scheme for the numerical calculation of crystal field (CF) energy levels and at the same time wave functions of the trivalent erbium ion in cubic symmetry. The 16-fold degenerate term 4I15=2 of the trivalent erbium ion splits into three Stark quartets Γ8 and two different doublets Γ6 and Γ7 (irreducible representations). The CF energy matrix of the Er3+ ion has been constructed and calculated from the complete diagonalization method, and the corresponding wave functions were used to calculate the ground state g-values. This method is outlined and illustrated by the examples of the Si:Er for comparison. The calculated g-factors are g = 6:8 and g = 6:0 for Γ6 and Γ7, respectively
Rare earth element of erbium implanted into silicon was studied by photoluminescence,and nine spectral lines were observed.The analysis of the symmetry of crystal field shows that the nine spectral lines come from the crystal-field splitting of the transition 4I13/2→4I15/2.We concludethat the symmetry of the two low-energy excited (initial) state levels,in order of increasing energy,are Γ8 and Γ6, from which to the splitting state levels of 4I15/2 nine radiative transitions are allowed.Oxygen codopants can increase greatly the PL intensity of Er3+, but the spectral features are similar,indicating oxygen codopants can enhance the intensity of Td crystal field rather than change the Td symmetry of the crystal field on the Er3+ sites.
We present an effective ab initio method to calculate the crystal field coefficients of an erbium (Er3+) ion experiencing different local site symmetries in several wide-band-gap oxides, and then evaluate crystal field splittings of these Er3+ ions for their ground and excited states. The optical transitions between the ground state (Z) and excited state (Y) manifolds of the environmentally shielded 4f states of these Er3+ ions have wavelengths ~1.5 microns and thus have potential applications to quantum communications and quantum memories. These results are in excellent agreement with recent low-temperature measurements, provided the inadequate calculation of the 4f shell screening is adjusted by reducing the radial extent of the 4f wavefunctions by approximately a factor of 2.
The energy levels of the I4 ground term of Er3+ in single crystals of CaWO4 were established by absorption and fluorescence spectra measurements. The measurements were made using crystals at temperatures of 2, 20, and 85°K. The energy level scheme allows an interpretation of the 1.612-μ four-level CaWO4:Er3+ laser transition and shows the terminal energy level of this transition to be 318 cm−1 above the ground state rather than 375 cm−1 as reported by Kiss and Duncan. An effective Hamiltonian of the form suggested by Karayianis was diagonalized in a basis of Russell–Saunders wavefunctions to obtain the calculated energy levels and wavefunctions for the entire ground term of Er3+. The calculation takes into account the complete J mixing of the states within the ground term and is equivalent to determining the effects of the spin–orbit interaction to better than second order. An rms deviation of 18 cm−1 was found as the best agreement between the calculated and experimental energy levels using the Hamiltonian: H = λ1(L·S) + λ2(L·S)2 + λ3(L·S)3 + ΣlmBlm†Clm. The empirically determined parameters are (in cm−1) λ1 = − 613, λ2 = − 19.3, λ3 = − 0.499, B20 = 404, B40 = − 685, B60 = 12.4, B44 = 728, ReB64 = 452, and ImB64 = 164. Using wavefunctions determined with these parameters, the g factors were calculated for the states of the ground term. The calculated and measured g factors for the two lower energy states are in good agreement where the calculated values are g‖ (ground state) = 1.265, g⊥ (ground state) = 8.487, g‖* (first excited state) = 3.22, and g⊥* (first excited state) = 7.06, and the measured values in the same order are g‖ = 1.247, g⊥ = 8.400, g‖* = 3.42, and g⊥* = 6.98. A Γ5,6 ground state wavefunction is compatible with the results obtained here, whereas a Γ7,8 ground state wavefunction is not. Previous studies had not established the ground state wavefunction uniquely.
Abstract Rare earth element of erbium implanted into silicon was studied by photoluminescence,and nine spectral lines were observed.The analysis of the symmetry of crystal field shows that the nine spectral lines come from the crystal field splitting of the transition 4 I 13/2 → 4 I 15/2 .We conclude that the symmetry of the two low energy excited (initial) state levels,in order of increasing energy,are Γ 8 and Γ 6 , from which to the splitting state levels of 4 I 15/2 nine radiative transitions are allowed.Oxygen codopants can increase greatly the PL intensity of Er 3+ , but the spectral features are similar,indicating oxygen codopants can enhance the intensity of T d crystal field rather than change the T d symmetry of the crystal field on the Er 3+ sites.
The absorption spectra of the Er3+ ions embedded in the AlN matrix have been investigated. The admixture of erbium was introduced in bulk AlN crystals by diffusion. The absorption lines, which are associated with the intraconfigurational electronic f–f-transitions from the ground 4 I 15/2-state to the levels of ion Er3+ excited states have been observed in the spectral range of 370–700 nm. The transitions to the state levels 4 F 9/2, 2 H 11/2, 4 F 7/2, 4 F 5/2, 2 H 9/2, and 4 G 11/2 have been investigated in detail at the temperature T = 2 K. The number of the observed lines for these transitions coincides with the theoretically possible one for the electronic f–f-transitions in the ions Er3+, which are in the crystal field with the symmetry below cubic. The narrowness of the observed lines and their number convincingly testify the replacement of preferably one regular crystalline position by erbium ions. The implementation of Er3+ in the Al3+ position with the local symmetry C 3v appears the most probable. The energy positions of the levels of excited states for the investigated transitions have been determined. The diagram of the Er3+ ion energy levels in the AlN crystals has been built.
Erbium ions in crystals show considerable promise for the technologies that will form the backbone of future networked quantum information technology. Despite advances in leveraging erbium’s fibre-compatible infrared transition for classical and quantum applications, the transitions are, in general, not well understood. We present detailed absorption and laser site-selective spectroscopy of the C 3v (O 2 − ) centre in CaF 2 :Er 3 + as an interesting erbium site case study. The 4 I 15 / 2 Z 1 → 4 I 13 / 2 Y 1 transition has a low-temperature inhomogeneous linewidth of 1 GHz with hyperfine structure observable from the 167 Er isotope. A parametrized crystal-field Hamiltonian is fitted to 34 energy levels and the two ground state magnetic splitting factors. The wavefunctions are used to perform a transition intensity analysis and electric-dipole parameters are fitted to absorption oscillator strengths. Simulated spectra for the 4 I 11 / 2 → 4 I 15 / 2 and 4 I 13 / 2 → 4 I 15 / 2 inter-multiplet transitions are in excellent agreement with the experimentally measured spectra. The 4 I 13 / 2 excited state lifetime is 25.0 ms and the intensity calculation is in excellent agreement with this value. • Detailed spectroscopic study of the C 3v (O 2 − ) Centre in CaF 2 :Er 3 + . • Crystal-field fit to 34 energy levels and ground-state magnetic splitting. • Transition intensity analysis for the technologically relevant infrared transitions.