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The 4f5d configuration and VUV absorption of Pr3+ in YPO4
ARTICLE IN PRESS
Journal of Luminescence 122–123 (2007) 25–27 www.elsevier.com/locate/jlumin
The 4f5d configuration and VUV absorption of Pr3+ in YPO4 Shihua Huanga,, Fangtian Youa, Chunxia Menga, Dawei Wanga, Ye Taob, Guobin Zhangc a
Key Laboratory of Luminescence and Optical Information, Institute of Optoelectronic Technology, Beijing Jiaotong University, Beijing 100044, China b Institute of High Energy Physics, CAS, Beijing 100039, China c NSRL, University of Science and Technology of China, Heifei 230026, China Available online 20 March 2006
Abstract Crystal field interaction of the 5d electron [HCF(5d )] and the Coulomb interaction between the 5d and the 4f electrons [HC(fd )] are the most important interactions in determining the structure of the 4f5d configuration of Pr3+ in solids. Energy levels of the 4f5d configuration in YPO4:Pr were calculated by diagonalizing the simplified Hamiltonian HCF(5d )+HC(fd ). Coulomb exchange interaction compresses the extension of the triplet states, while expands that of the singlet states. Thus, for the triplet states, HC(fd ) could be considered approximately as a perturbation to HCF(5d ). Since the ground state of the 4f 2 configuration is a triplet, the triplet state structure in the 4f 5d configuration determines the spectroscopic properties of the ground state absorption. Absorption spectrum calculated by using the obtained 4f5d wave functions is comparable with the experimental ones. r 2006 Elsevier B.V. All rights reserved. Keywords: Pr3+; 4f5d configuration; VUV spectrum
1. Introduction For rare-earth ions in solids, Hamiltonian of the 4f n15d configuration can be expressed as H ¼ ½H 0 þ H C ðff Þ þ H SO ðf Þ þ H CF ðd Þ þ H C ðfd Þ ¼ Hð4f n1 Þ þ H CF ðd Þ þ H SO ðd Þ þ H C ðfd Þ,
ð1Þ
where H0 is the kinetic energy of the electrons and the potential energy between electrons and the nucleus, HC, HSO and HCF are, respectively, Coulomb, spin–orbit, and crystal field interactions; H(4f n1) is the Hamiltonian of the 4f n1 core. In comparison with the 4f n configuration, less spectroscopic data of the 4f n15d configuration can be obtained experimentally. Hamiltonian (1) requires so many parameters that are difficult to obtain by fitting the experimental data, which is the usual procedure for the 4f n configuration. Even though the parameters can be obtained with the help of ab initio calculation, the characteristics of the wave functions obtained by diagonalizing the complete Hamiltonian or with HSO(d ) and Corresponding author. Tel.: +86 10 5168 3414; fax: +86 10 5168 3933.
E-mail address: [email protected] (S. Huang). 0022-2313/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2006.01.071
HCF(f ) neglected are generally unclear. To further simplify the Hamiltonian is necessary. There are basically three models in doing so. The simplest model includes only n1 H (d ). H ð5d Þ b Hð4f Þ , H C ðfd Þ (we denote CF CF 4f 5d jH j4f 5d by jH j) is required to ensure the approximation reasonable. For it does not hold in most cases, applicability of such simplified Hamiltonian is rather limited. Second model describes the 4f n15d states with j5dGa ij4f n1 SLJ coupling scheme, and simplifies the Hamiltonian by neglecting HC(fd) [1,2]. Certainly, its availability depends on if the inequality Hð4f n1 Þ; H CF ð5dÞbH C ðfdÞ (2) holds. An improvement was made in the third model by introducing a simplified HC(fd) [3] as a perturbation. This model is acceptable and workable, since it requires less parameters in the calculation and was successful in assigning transition bands and calculating transition intensities. H C ðfd Þ is An exception occurs in Pr3+ ion, where 1 10 000–20 000 cm , comparable to H CF ðd Þ , while H SO ðf Þ [for 4f5d with HCF( f ) neglected, it is right H(4f n1)] is no more than 3000 cm1. Instead of (2), the
ARTICLE IN PRESS S. Huang et al. / Journal of Luminescence 122–123 (2007) 25–27
26
inequality H CF ð5dÞ; H C ðfdÞbHð4f n1 Þ
(3) Triplets
holds. Thus, with neglecting HSO(f ), the basic properties of the 4f5d configuration might still be well described. In this paper, the features of the 4f5d configuration are discussed with the state densities obtained by diagonalizing the simplified Hamiltonian HCF(d )+HC(fd ), then the ground state absorption is calculated and compared with the experimental excitation spectrum.
T B1
ions in crystals
E
As mentioned above, the Hamiltonian for the 4f5d configuration of Pr3+ ions in solids can be simplified by H H CF ðdÞ þ H C ðfdÞ,
(4)
where H0 determines the center of gravity of the configuration, and can be absorbed into the parameter F0. 4fm; 5dGa i was chosen as the basis for expressing the 4f5d wave functions. Since all the wavefunctions must change their sign under permutation of both spin and orbital coordinates of the f and d electrons, and the spin wave function of the singlet is antisymmetric while that of the triplets is symmetric, orbitals of the singlets and triplets must be, respectively, symmetric and antisymmetric com binations of 4fm; 5dGa i and j5dGa ; 4fm . They are distinguished by total spin S, and split under Coulomb exchange interaction. Neglecting HSO makes S a good quantum number. The 4f5d energy levels and wave functions were calculated by diagonalization of the Hamiltonian in Eq. (4). In YPO4, Pr3+ ions replace Y3+ with D2d site symmetry. Crystal field parameters Bkq(d) and Coulomb interaction parameters F’s and G’s, except F0, were taken from Ref. [2]. F0 ¼ 56 800 cm1 was chosen to fit the excitation spectrum in III. In Fig. 1, curves T and S denote the calculated state densities of triplets and singlets. Huang–Rhys factor of the f–d transition is S E 2–4; the 1/e half-width of the phonon sideband is dE (2So1+ 2n4)1/2 _o, where hni is the average phonon population at given temperature, _o is the phonon energy. d ¼ 1000 cm1 and a Gaussian profile g(EEj, d) were assumed for each state j in the 4f5d configuration of YPO4:Pr at room temperature. The density of j5dGa i in a state j with energy Ej is calculated by DðGa ; EÞ ¼ ð2S þ 1Þ
3 X X 4fm5dGa j 2 gðE E j ; dÞ: j m¼3
(5) The densities of four crystal field components of the 5d electron are also shown in Fig. 1. Fig. 1 indicates that the j5dGa i feature is well preserved in the triplets, especially, j5dB1 i and j5dB2 i are concentrated at the low and high portion of the configuration, respectively. Mixing occurs mainly in the middle of the
State Density (a. u.)
2. The 4f5d configuration of Pr
3+
A1 B2 Singlets S B1 E A1 B2
40000
50000
60000
70000
Wavenumbers (cm-1) Fig. 1. Total (T, S) and compositional singlet and triplet state densities of the 4f5d configuration of Pr3+ in YPO4. 5dGa components are denoted by Ga.
configuration, where the separation between j5dE i and j5dA1 i is small. For singlets, however, spreads of j5dGa i densities are much wider. It should be noted that in the 4f5d configuration of Pr3+ the values even the signs of the separations between the singlets and the corresponding triplets are different; the approximation in ref. [3] for the f–d interaction is not valid for Pr3+. The difference between the structures of triplets and singlets comes from the difference in Coulomb exchange interaction. Fig. 2 is the energy levels calculated separately with HC(fd) and HCF(d ) for the 4f5d configuration. Coulomb exchange interaction compresses the extension of the triplets while expands that of the singlets. In comparison with the crystal field interaction of the 5d electron, HC(fd ) is smaller for the triplets and hence can be roughly considered as a perturbation. For the singlets, however, HC(fd ) is comparable to HCF(d), state mixing would both be serious, either by choosing the set of 4fm; 5dGa i or 4f ; 5d; LSi as the zero-order wave functions. Based on this consideration, we may expect that 4fm; 5dGa i would be better for describing the triplet 4f5d states of Pr3+ in solids with strong crystal field interaction (such as fluorides); while 4f ; 5d; LSi might be applicable
ARTICLE IN PRESS S. Huang et al. / Journal of Luminescence 122–123 (2007) 25–27
HCdir+HCexch
HCdir(fd )
HCdir+HCexch
27
HCF(fd )
1P 1H
P
65000
B2
60000
(b) H 1F
3D
E
D 55000
3G
A1
1D
F
3H
50000
3F
(a) G
1G
B1 Triplets
Intensity (a.u.)
Energy (cm-1)
3P
40000
for the singlets in solids with weak crystal field strength (such as SrAl12O19). 3. VUV absorption of Pr3+ in YPO4 To check if the 4f5d structure obtained from the simplified Hamiltonian makes sense, VUV excitation spectrum was measured and compared to the calculated one. The measurement was carried out at the Spectroscopy Station of Beijing Synchrotron Radiation Laboratory. The excitation spectrum (Fig. 3a) was measured by monitoring the 4f 5d-4f 23H6 emission at 263 nm and was calibrated with the fluorescence of sodium salicylate for spectral response of the instruments. Because of the lowest state of the 4f 2 configuration is a triplet, with only few percents of singlet components [4], the 4f 5d absorption is dominated by the structure of triplet 4f 5d states. All Stark levels of the ground 3H4 state were assumed to be equally occupied. Absorption from 3H4 to the triplets was calculated and shown in Fig. 3b. It seems to be comparable to the experimental one.
60000
70000
Wavenumbers (cm-1)
Singlets
Fig. 2. Split of the 4f5d configuration of Pr3+ by Coulomb direct interaction (HCdir), Coulomb interaction (HCdir+HCexch) and crystal field (HCF).
50000
Fig. 3. Experimental excitation spectrum (a) and calculated ground state absorption spectrum (b) of Pr3+ in YPO4. Crystal field parameters Bkq in [2] were used in the calculation.
In summary, for Pr3+ in crystal, HCF(d) and HCF(d) are larger than HSO, HCF(d)+HC (fd) may be taken as an approximate Hamiltonian. For triplet 4f5d states, split by HC (fd) is smaller than that by HCF(d), the feature of 5d crystal field is well preserved. Absorption spectra calculated with wave functions obtained by diagonalizing HCF(d)+HC (fd) are comparable to experimental ones. Acknowledgments We are grateful to Prof. Shanda Xia of University of Science and Technology of China for valuable discussion. The work was supported by the Natural Science Foundation of China (Grant no. 10204001). References [1] M. Laroche, A. Braud, S. Girard, J.L. Doualan, R. Moncorge, M. Thuau, J. Opt. Soc. Am. B 16 (1999) 1. [2] L. van Pieterson, M.F. Reid, R.T. Wegh, S. Soverna, A. Meijerink, Phys. Rev. B 65 (2002) 045113. [3] C.K. Duan, M.F. Reid, J. Solid State Chem. 171 (2003) 299. [4] R.C. Pappalardo, J. Lumin. 14 (1976) 159.
Journal of Luminescence 122–123 (2007) 25–27 www.elsevier.com/locate/jlumin
The 4f5d configuration and VUV absorption of Pr3+ in YPO4 Shihua Huanga,, Fangtian Youa, Chunxia Menga, Dawei Wanga, Ye Taob, Guobin Zhangc a
Key Laboratory of Luminescence and Optical Information, Institute of Optoelectronic Technology, Beijing Jiaotong University, Beijing 100044, China b Institute of High Energy Physics, CAS, Beijing 100039, China c NSRL, University of Science and Technology of China, Heifei 230026, China Available online 20 March 2006
Abstract Crystal field interaction of the 5d electron [HCF(5d )] and the Coulomb interaction between the 5d and the 4f electrons [HC(fd )] are the most important interactions in determining the structure of the 4f5d configuration of Pr3+ in solids. Energy levels of the 4f5d configuration in YPO4:Pr were calculated by diagonalizing the simplified Hamiltonian HCF(5d )+HC(fd ). Coulomb exchange interaction compresses the extension of the triplet states, while expands that of the singlet states. Thus, for the triplet states, HC(fd ) could be considered approximately as a perturbation to HCF(5d ). Since the ground state of the 4f 2 configuration is a triplet, the triplet state structure in the 4f 5d configuration determines the spectroscopic properties of the ground state absorption. Absorption spectrum calculated by using the obtained 4f5d wave functions is comparable with the experimental ones. r 2006 Elsevier B.V. All rights reserved. Keywords: Pr3+; 4f5d configuration; VUV spectrum
1. Introduction For rare-earth ions in solids, Hamiltonian of the 4f n15d configuration can be expressed as H ¼ ½H 0 þ H C ðff Þ þ H SO ðf Þ þ H CF ðd Þ þ H C ðfd Þ ¼ Hð4f n1 Þ þ H CF ðd Þ þ H SO ðd Þ þ H C ðfd Þ,
ð1Þ
where H0 is the kinetic energy of the electrons and the potential energy between electrons and the nucleus, HC, HSO and HCF are, respectively, Coulomb, spin–orbit, and crystal field interactions; H(4f n1) is the Hamiltonian of the 4f n1 core. In comparison with the 4f n configuration, less spectroscopic data of the 4f n15d configuration can be obtained experimentally. Hamiltonian (1) requires so many parameters that are difficult to obtain by fitting the experimental data, which is the usual procedure for the 4f n configuration. Even though the parameters can be obtained with the help of ab initio calculation, the characteristics of the wave functions obtained by diagonalizing the complete Hamiltonian or with HSO(d ) and Corresponding author. Tel.: +86 10 5168 3414; fax: +86 10 5168 3933.
E-mail address: [email protected] (S. Huang). 0022-2313/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2006.01.071
HCF(f ) neglected are generally unclear. To further simplify the Hamiltonian is necessary. There are basically three models in doing so. The simplest model includes only n1 H (d ). H ð5d Þ b Hð4f Þ , H C ðfd Þ (we denote CF CF 4f 5d jH j4f 5d by jH j) is required to ensure the approximation reasonable. For it does not hold in most cases, applicability of such simplified Hamiltonian is rather limited. Second model describes the 4f n15d states with j5dGa ij4f n1 SLJ coupling scheme, and simplifies the Hamiltonian by neglecting HC(fd) [1,2]. Certainly, its availability depends on if the inequality Hð4f n1 Þ; H CF ð5dÞbH C ðfdÞ (2) holds. An improvement was made in the third model by introducing a simplified HC(fd) [3] as a perturbation. This model is acceptable and workable, since it requires less parameters in the calculation and was successful in assigning transition bands and calculating transition intensities. H C ðfd Þ is An exception occurs in Pr3+ ion, where 1 10 000–20 000 cm , comparable to H CF ðd Þ , while H SO ðf Þ [for 4f5d with HCF( f ) neglected, it is right H(4f n1)] is no more than 3000 cm1. Instead of (2), the
ARTICLE IN PRESS S. Huang et al. / Journal of Luminescence 122–123 (2007) 25–27
26
inequality H CF ð5dÞ; H C ðfdÞbHð4f n1 Þ
(3) Triplets
holds. Thus, with neglecting HSO(f ), the basic properties of the 4f5d configuration might still be well described. In this paper, the features of the 4f5d configuration are discussed with the state densities obtained by diagonalizing the simplified Hamiltonian HCF(d )+HC(fd ), then the ground state absorption is calculated and compared with the experimental excitation spectrum.
T B1
ions in crystals
E
As mentioned above, the Hamiltonian for the 4f5d configuration of Pr3+ ions in solids can be simplified by H H CF ðdÞ þ H C ðfdÞ,
(4)
where H0 determines the center of gravity of the configuration, and can be absorbed into the parameter F0. 4fm; 5dGa i was chosen as the basis for expressing the 4f5d wave functions. Since all the wavefunctions must change their sign under permutation of both spin and orbital coordinates of the f and d electrons, and the spin wave function of the singlet is antisymmetric while that of the triplets is symmetric, orbitals of the singlets and triplets must be, respectively, symmetric and antisymmetric com binations of 4fm; 5dGa i and j5dGa ; 4fm . They are distinguished by total spin S, and split under Coulomb exchange interaction. Neglecting HSO makes S a good quantum number. The 4f5d energy levels and wave functions were calculated by diagonalization of the Hamiltonian in Eq. (4). In YPO4, Pr3+ ions replace Y3+ with D2d site symmetry. Crystal field parameters Bkq(d) and Coulomb interaction parameters F’s and G’s, except F0, were taken from Ref. [2]. F0 ¼ 56 800 cm1 was chosen to fit the excitation spectrum in III. In Fig. 1, curves T and S denote the calculated state densities of triplets and singlets. Huang–Rhys factor of the f–d transition is S E 2–4; the 1/e half-width of the phonon sideband is dE (2So1+ 2n4)1/2 _o, where hni is the average phonon population at given temperature, _o is the phonon energy. d ¼ 1000 cm1 and a Gaussian profile g(EEj, d) were assumed for each state j in the 4f5d configuration of YPO4:Pr at room temperature. The density of j5dGa i in a state j with energy Ej is calculated by DðGa ; EÞ ¼ ð2S þ 1Þ
3 X X 4fm5dGa j 2 gðE E j ; dÞ: j m¼3
(5) The densities of four crystal field components of the 5d electron are also shown in Fig. 1. Fig. 1 indicates that the j5dGa i feature is well preserved in the triplets, especially, j5dB1 i and j5dB2 i are concentrated at the low and high portion of the configuration, respectively. Mixing occurs mainly in the middle of the
State Density (a. u.)
2. The 4f5d configuration of Pr
3+
A1 B2 Singlets S B1 E A1 B2
40000
50000
60000
70000
Wavenumbers (cm-1) Fig. 1. Total (T, S) and compositional singlet and triplet state densities of the 4f5d configuration of Pr3+ in YPO4. 5dGa components are denoted by Ga.
configuration, where the separation between j5dE i and j5dA1 i is small. For singlets, however, spreads of j5dGa i densities are much wider. It should be noted that in the 4f5d configuration of Pr3+ the values even the signs of the separations between the singlets and the corresponding triplets are different; the approximation in ref. [3] for the f–d interaction is not valid for Pr3+. The difference between the structures of triplets and singlets comes from the difference in Coulomb exchange interaction. Fig. 2 is the energy levels calculated separately with HC(fd) and HCF(d ) for the 4f5d configuration. Coulomb exchange interaction compresses the extension of the triplets while expands that of the singlets. In comparison with the crystal field interaction of the 5d electron, HC(fd ) is smaller for the triplets and hence can be roughly considered as a perturbation. For the singlets, however, HC(fd ) is comparable to HCF(d), state mixing would both be serious, either by choosing the set of 4fm; 5dGa i or 4f ; 5d; LSi as the zero-order wave functions. Based on this consideration, we may expect that 4fm; 5dGa i would be better for describing the triplet 4f5d states of Pr3+ in solids with strong crystal field interaction (such as fluorides); while 4f ; 5d; LSi might be applicable
ARTICLE IN PRESS S. Huang et al. / Journal of Luminescence 122–123 (2007) 25–27
HCdir+HCexch
HCdir(fd )
HCdir+HCexch
27
HCF(fd )
1P 1H
P
65000
B2
60000
(b) H 1F
3D
E
D 55000
3G
A1
1D
F
3H
50000
3F
(a) G
1G
B1 Triplets
Intensity (a.u.)
Energy (cm-1)
3P
40000
for the singlets in solids with weak crystal field strength (such as SrAl12O19). 3. VUV absorption of Pr3+ in YPO4 To check if the 4f5d structure obtained from the simplified Hamiltonian makes sense, VUV excitation spectrum was measured and compared to the calculated one. The measurement was carried out at the Spectroscopy Station of Beijing Synchrotron Radiation Laboratory. The excitation spectrum (Fig. 3a) was measured by monitoring the 4f 5d-4f 23H6 emission at 263 nm and was calibrated with the fluorescence of sodium salicylate for spectral response of the instruments. Because of the lowest state of the 4f 2 configuration is a triplet, with only few percents of singlet components [4], the 4f 5d absorption is dominated by the structure of triplet 4f 5d states. All Stark levels of the ground 3H4 state were assumed to be equally occupied. Absorption from 3H4 to the triplets was calculated and shown in Fig. 3b. It seems to be comparable to the experimental one.
60000
70000
Wavenumbers (cm-1)
Singlets
Fig. 2. Split of the 4f5d configuration of Pr3+ by Coulomb direct interaction (HCdir), Coulomb interaction (HCdir+HCexch) and crystal field (HCF).
50000
Fig. 3. Experimental excitation spectrum (a) and calculated ground state absorption spectrum (b) of Pr3+ in YPO4. Crystal field parameters Bkq in [2] were used in the calculation.
In summary, for Pr3+ in crystal, HCF(d) and HCF(d) are larger than HSO, HCF(d)+HC (fd) may be taken as an approximate Hamiltonian. For triplet 4f5d states, split by HC (fd) is smaller than that by HCF(d), the feature of 5d crystal field is well preserved. Absorption spectra calculated with wave functions obtained by diagonalizing HCF(d)+HC (fd) are comparable to experimental ones. Acknowledgments We are grateful to Prof. Shanda Xia of University of Science and Technology of China for valuable discussion. The work was supported by the Natural Science Foundation of China (Grant no. 10204001). References [1] M. Laroche, A. Braud, S. Girard, J.L. Doualan, R. Moncorge, M. Thuau, J. Opt. Soc. Am. B 16 (1999) 1. [2] L. van Pieterson, M.F. Reid, R.T. Wegh, S. Soverna, A. Meijerink, Phys. Rev. B 65 (2002) 045113. [3] C.K. Duan, M.F. Reid, J. Solid State Chem. 171 (2003) 299. [4] R.C. Pappalardo, J. Lumin. 14 (1976) 159.