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The Journal of Chemical Physics

Optical Spectrum of Triply Ionized Erbium in Calcium Tungstate

D. E. Wortman

Published Jan 1, 1971• 20 citations

Abstract

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.

DOI: 10.1063/1.1674609

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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.

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.

Near-UV excited-state absorption spectra obtained with a pulsed pump–probe technique were recorded in LiYF4:Pr3+ at 77 and at 8 K and revealed a detailed structure of the 4f2 1D2→4f5d and 4f2 (3P0+1I6)→4f5d optical transitions. These experimental results, together with those previously obtained at room temperature, are compared with the numerical predictions of a full calculation of the 4f5d sublevels and of the electric dipole transitions toward these sublevels from different states of the 4f2 configuration. The agreement is good, provided that the four adjustable parameters of the theory are taken as B20(5d)=7290 cm-1,B40(5d)=-14 900 cm-1,F0=60 557 cm-1, and 〈r〉fd=0.245 Å. The level structure of the 4f5d configuration of LiYF4:Pr3+ is shown to be dominated, as expected, by the crystal field coupling of the 5d electron but also, to a noticeable extent, by the spin–orbit coupling of the 4f electron and the Coulomb repulsion of both electrons. The former of these two interactions is somewhat more efficient than the latter in the low-energy part of the 4f5d configuration, i.e., in the spectral region where the largest amount of experimental data is currently available.

Spectroscopy, Crystal-Field, and Transition Intensity Analyses of the C

_{\rm 3v}

(O

^{2-}

) Centre in Er

^{3+}

Doped CaF

_{2}

Crystals

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

_{\rm 3v}

(O

^{2-}

) centre in CaF

_2

:Er

^{3+}

as an interesting erbium site case study. The

^{4}

I

_{15/2}

Z

_1 \rightarrow {^{4}}

I

_{15/2}

Y

_1 \rightarrow {^{4}}

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}\rightarrow {^{4}}

I

_{15/2}

and

^{4}

I

_{13/2} \rightarrow {^{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.

The analysis of the absorption spectrum of Er3+ in LaF3 is extended into the ultraviolet region to 2000 Å. A number of fluorescence lines recently observed in the region from 3000 to 25 000 Å is also reported. Based on the best over-all agreement between the predicted ``free-ion'' 4f11 SLJ states and 21 experimentally observed levels for Er3+ in LaF3, one finds a set of atomic wavefunctions for the ion based on F2 = 435.7 cm—1, F4 = 67.21 cm—1, F6 = 7.388 cm—1, and ζ = 2350.8 cm—1. Laser experiments are described and the details of coherent emission found at 1.61 μ are presented.

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.

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