JOURNAL OF APPLIED PHYSICS
VOLUME 93, NUMBER 6
15 MARCH 2003
Spectra and energy levels of Nd3¿ in LaSc3 „BO3 … 4 John B. Grubera) Department of Physics, San Jose´ State University, San Jose´, California 95192-0106
Dhiraj K. Sardar Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas 78249-0663
Bahram Zandi ARL/Adelphi Laboratory Center, 2800 Powder Mill Road, Adelphi, Maryland 20783-1197
Thomas A. Reynolds Rey Tech Corporation, 742 SE Glenwood Drive, Bend, Oregon 97702
Theodore Alekel In Phase Crystal Corporation, P.O. Box 230605, Portland, Oregon 97223
Douglas A. Keszler Department of Chemistry, Oregon State University, Corvallis, Oregon 97331-4003
共Received 14 November 2002; accepted 6 January 2003兲 We report a detailed spectroscopic analysis of Nd3⫹ (4 f 3 ) as a dopant in single crystals of LaSc3 (BO3 ) 4 共LSB兲. Absorption spectra were obtained between 570 and 1750 nm at temperatures as low as 8 K. Fluorescence spectra and lifetimes were obtained at similar temperatures from 4 F 3/2 to 4 I 9/2 , 4 I 11/2 , and 4 I 13/2 multiplet manifolds. The observed spectra are similar to spectra reported earlier for Nd3⫹ as a dopant in the alpha phase of LSB. The observed crystal-field splitting of the 2S⫹1 L J multiplet manifolds of Nd3⫹ was modeled using a Hamiltonian, which includes atomic and crystal field terms. A least-squares fitting between 57 calculated-to-observed energy 共Stark兲 levels gave a root mean square deviation of 8 cm⫺1 for the 13 lowest-energy multiplet manifolds. With wave functions obtained from the modeling studies, multiplet-to-multiplet and line-to-line branching ratios were calculated as well as the radiative lifetime for emission from 4 F 3/2 . The results are compared with experimental values obtained in the present study and also with results reported for Nd3⫹ in the beta phase of LSB. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1556185兴 are similar to the spectra reported by Meyn and co-workers3 for Nd3⫹ in the alpha phase of LSB,10 we conclude that a similar environment is also found for Nd3⫹ in our crystal samples. Absorption spectra were obtained between 570 and 1750 nm. Fluorescence spectra and measured fluorescence lifetimes were obtained for transitions from 4 F 3/2 to 4 I 9/2 , 4 I 11/2 , and 4 I 13/2 , multiplet manifolds. The observed splitting of the
I. INTRODUCTION
Lanthanum scandium borate, LaSc3 (BO3 ) 4 , 共LSB兲 as a host lattice for trivalent rare earth ions, R 3⫹ , can be grown in crystal phases that have different spectroscopic and nonlinear optical properties.1 Early spectroscopic measurements of LSB with Nd3⫹ as a dopant were reported by several groups2,3 and summarized by Kaminskii,4 who lists the crystal-field splitting of several multiplet manifolds of Nd3⫹ (4 f 3 ) in the crystal. Further interest in the optical properties of this material became evident when it was discovered that LSB can accommodate relatively high concentrations of Nd3⫹ without observing significant fluorescence concentration quenching.5,6 Spectroscopic properties of diode-pumped Nd3⫹ :LSB have been reported by Meyn, Jensen, and Huber,3 and luminescence concentration quenching and upconversion were quantitatively investigated by Ostroumov et al.7,8 Recently, we reported a Judd–Ofelt analysis of the room temperature absorption spectra of Nd3⫹ :LSB.9 The crystals used in that study were also used in the present study to obtain the detailed crystal-field splitting of the energy levels of the multiplet manifolds of Nd3⫹ (4 f 3 ) by analyzing the absorption and fluorescence spectra of the crystals at temperatures as low as 8 K. Since our low temperature spectra a兲
Author to whom correspondence should be addressed; electronic mail:
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FIG. 1. Absorption spectrum of 4 I 15/2 obtained near 8 K. 3345
© 2003 American Institute of Physics
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J. Appl. Phys., Vol. 93, No. 6, 15 March 2003
TABLE I. Absorption spectrum of Nd3⫹ :LSB 共8 K兲. 2S⫹1
L Ja
4
I 15/2 共6029兲
4
F 3/2 共11 424兲 7 F 5/2 共12 433兲 2
H 9/2 共12 547兲
4
F 7/2 共13 383兲
4
S 3/2 共13 501兲 4 F 9/2 共14 684兲
2
H 11/2 共15 842兲
4
G 5/2 共17 009兲
2
G 7/2 共17 214兲
共nm兲b
␣(cm⫺1 ) c
E obs(cm⫺1 ) d
E calc(cm⫺1 ) e
1713 1698 1694 1661 1652 1643 1613 1599 878 873 808 806 802.25 801.5 799.5 795.25 792.75 786.25 749.75 748 746.5 743.7 741.25 740.5 684.25 683.25 682.5 679.5 673.75 631.9 630.8 630.25 627.5 625.75 624.75 592.5 588.75 585.75 581 580 578.5 577
0.05 0.70 0.75 0.67 0.86 0.05 0.65 0.60 5.05 7.90 41.0 5.23 15.9 34.6 6.79 4.29 4.71 4.49 9.97 34.6 2.60 2.50 12.0 34.6 0.93 1.39 1.42 0.91 0.84 0.37 0.53 0.71 0.76 0.96 0.83 20.2 21.2 12.7 6.26 4.47 5.02 5.04
5837g 5888 5902 6019 6052 6080g 6198 6252 11 386 11 452 12 368 12 404 12 462 12 473 12 504 12 568 12 611 12 715g 13 334 13 365 13 400 13 455 13 487 13 501 14 611 14 632 14 650 14 720 14 830 15 821 15 849 15 862 15 932 15 997g 16 003g 16 873 16 980 17 067 17 207 17 237 17 281 17 330
5833 5890 5907 6015 6056 6090 6192 6255 11 374 11 446 12 351 12 411 12 471 12 489 12 507 12 560 12 606 12 686 13 320 13 355 13 408 13 466 13 488 13 501 14 609 14 637 14 665 14 727 14 818 15 814 15 850 15 866 15 914 15 951 15 964 16 872 16 980 17 072 17 212 17 241 17 272 17 325
Percent free-ion statesf 99.7 99.7 99.7 99.9 99.8 99.6 99.5 99.7 99.1 98.3 87.4 80.1 61.2 61.6 90.4 91.0 95.1 92.5 98.6 98.3 98.3 98.2 99.1 99.1 99.4 98.8 99.3 99.3 99.6 99.7 99.7 99.7 99.6 99.7 99.9 92.9 87.5 64.0 98.3 94.4 89.1 62.4
I 15/2⫹0.174 I 13/2⫹0.044 F 9/2 I 15/2⫹0.244 I 13/2⫹0.034 F 9/2 4 I 15/2⫹0.254 I 13/2⫹0.024 F 9/2 4 I 15/2⫹0.104 I 13/2⫹0.024 F 9/2 4 I 15/2⫹0.134 I 13/2⫹0.014 F 7/2 4 I 15/2⫹0.334 I 13/2⫹0.034 F 11/2 4 I 15/2⫹0.424 I 13/2⫹0.014 F 9/2 4 I 15/2⫹0.204 I 13/2⫹0.024 I 11/2 4 F 3/2⫹0.574 F 5/2⫹0.144 F 7/2 4 F 3/2⫹0.924 F 5/2⫹0.334 F 7/2 4 F 5/2⫹11.52 H 9/2⫹0.554 F 7/2 4 F 5/2⫹18.32 H 9/2⫹0.964 F 7/2 4 F 5/2⫹38.02 H 9/2⫹0.524 F 3/2 2 H 9/2⫹37.74 F 5/2⫹0.394 F 3/2 2 H 9/2⫹9.164 F 5/2⫹0.274 F 7/2 2 H 9/2⫹8.454 F 5/2⫹0.354 F 7/2 2 H 9/2⫹4.614 F 5/2⫹0.124 F 7/2 2 H 9/2⫹7.344 F 5/2⫹0.054 F 7/2 4 F 7/2⫹0.294 S 3/2⫹0.292 H 9/2 4 F 7/2⫹0.494 S 3/2⫹0.294 F 5/2 4 F 7/2⫹0.784 F 9/2⫹0.424 F 5/2 4 F 7/2⫹0.744 F 5/2⫹0.514 F 9/2 4 S 3/2⫹0.514 F 7/2⫹0.204 G 5/2 4 S 3/2⫹0.584 F 7/2⫹0.092 H 11/2 4 F 9/2⫹0.214 F 7/2⫹0.194 F 5/2 4 F 9/2⫹0.864 F 7/2⫹0.152 H 11/2 4 F 9/2⫹0.292 H 11/2⫹0.152 G 7/2 4 F 9/2⫹0.404 F 7/2⫹0.072 H 11/2 4 F 9/2⫹0.094 F 7/2⫹0.062 G 7/2 2 H 11/2⫹0.184 F 9/2⫹0.112 G 7/2 2 H 11/2⫹0.142 G 7/2⫹0.134 F 9/2 2 H 11/2⫹0.114 F 9/2⫹0.092 G 7/2 2 H 11/2⫹0.174 F 9/2⫹0.092 G 7/2 2 H 11/2⫹0.124 F 9/2⫹0.064 S 3/2 2 H 11/2⫹0.054 F 9/2⫹0.032 G 7/2 4 G 5/2⫹6.632 G 7/2⫹0.124 F 7/2 4 G 5/2⫹12.22 G 7/2⫹0.134 S 3/2 4 G 5/2⫹35.52 G 7/2⫹0.144 F 9/2 2 G 7/2⫹1.304 G 5/2⫹0.192 H 11/2 2 G 7/2⫹5.222 G 5/2⫹0.172 H 11/2 2 G 7/2⫹10.62 G 5/2⫺0.152 H 11/2 2 G 7/2⫹37.42 G 5/2⫹0.072 H 11/2 4 4
a
States of Nd3⫹ (4 f 3 ) electronic configuration; number in parentheses is the calculated centroid for the manifold split by the crystal field. Wavelength in nanometers. c Absorption coefficient in cm⫺1 . d Experimental energy in vacuum wave numbers. e Calculated crystal-field split energy levels; parameters, B nm (cm⫺1 ) obtained from least-squares fitting between 57 calculated and observed Stark levels; rms⫽8 cm⫺1 ; B 20 ⫽⫺330, B 22⫽⫺284, B 40⫽⫺889, RB 42⫽⫺702, IB 42⫽12.0, RB 44⫽⫺46.1, IB 44⫽⫺807, B 60⫽178, RB 62⫽⫺273, IB 62⫽25.0, RB 64 ⫽138, IB 64⫽⫺189, RB 66⫽152, IB 66⫽⫺229, all in cm⫺1 . f Percent mixture of free-ion state due to J mixing. g Experimental levels not used in final calculations. b
manifolds, 2S⫹1 L J , by the crystal field was modeled using a Hamiltonian which included both atomic and crystal-field terms. A least-squares fitting between 57 calculated-toobserved energy 共Stark兲 levels gave a root-mean-square 共rms兲 deviation of 8 cm⫺1 for the 13 lowest-energy multiplet manifolds. With the wave functions obtained from modeling the data, branching ratios and radiative lifetimes were calcu-
lated and compared to experimental values obtained for Nd3⫹ in both alpha and beta phases of LSB. II. EXPERIMENTAL DETAILS
Rectangular samples were cut from crystals used in reporting the spectroscopic analysis given in Ref. 9. The
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Gruber et al.
J. Appl. Phys., Vol. 93, No. 6, 15 March 2003
FIG. 2. Absorption spectrum of 4 F 5/2 and 2 H 9/2 obtained near 8 K.
samples were of good optical quality and had a thickness of about 0.32 cm. The concentration of Nd in the crystal samples investigated spectroscopically was about 5 at. wt% (4.5⫻1020 Nd/cm3 ). Absorption spectra were obtained between 570 and 1750 nm with an upgraded Cary Model 14R spectrophotometer controlled by a desktop computer. The spectral bandwidth was set at 0.2 nm and the instrument was internally calibrated to an accuracy better than 0.4 nm. Spectra were analyzed and plotted by using the computer software package SIGMA plot. Fluorescence spectra were observed between 800 and 1600 nm by exciting the sample with the 514.5 nm laser
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FIG. 3. Absorption spectrum of 4 F 7/2 and 4 S 3/2 near 8 K.
emission from a Spectra Physics Model 2005 argon ion laser. The emission bandwidth was 0.12 nm, the maximum laser power was 2 W, and the beam diameter at 514.5 nm was 1.25 mm. Fluorescence was analyzed by a SPEX Model 340E monochromator equipped with a liquid nitrogen cooled Ge detector, Model J16D-M204-R05M-60 from EG&G Judson. We obtained spectral resolution better than 0.8 nm by using a reflection grating with 600 grooves/mm blazed at 1 m. Fluorescence decay was measured by chopping the 514.5 nm emission line from the argon ion laser at 20 Hz and observing the decay signals that were displayed on a 150 MHz Tektronix Model 2445A oscilloscope. The fluorescence decays from the 4 F 3/2 to the 4 I 9/2 , 4 I 11/2 , and 4 I 13/2 , multip-
TABLE II. An 8 K fluorescence spectrum from 4 F 3/2 to 4 I J . Mulitplet Trans.a 4
F 3/2→ 4 I 9/2
共162兲
4
F 3/2→ 4 I 11/2
共2038兲
4
F 3/2→ 4 I 13/2
共4032兲
Line Transb
共nm兲c
Id
E(cm⫺1 ) e
E(cm⫺1 ) f
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
878.0 884.8 887.6 893.2 903 1057.4 1061.6 1065.6 1070.8 1077 1082.2 1336.8 1344.0 1349.6 1357.6 1365.6 1376 1384
0.55 9.80 9.66 5.71 0.71 0.22 9.80 1.15 2.08 1.61 0.43 0.18 9.80 3.54 0.62 0.72 0.18 0.20
11 386 11 297 11 260 11 193 11 068 9455 9417 9382 9336 9283 9238 7479 7438 7408 7364 7321 7265 7223
0 89 126 193 318 1931 1969 2004 2050 2103 2149 3907 3948 3978 4022 4065 4121 4163
E calc共 cm⫺1 ) g ⫺4 91 128 193 331 1935 1967 2000 2058 2091 2152 3911 3944 3974 4030 4057 4115 4169
Percent free-ion statesh 99.74 I 9/2⫹0.254 I 11/2⫹0.024 F 5/2 99.74 I 9/2⫹0.244 I 11/2⫹0.044 I 13/2 99.54 I 9/2⫹0.474 I 11/2⫹0.024 F 3/2 99.54 I 9/2⫹0.434 I 11/2⫹0.024 I 13/2 99.64 I 9/2⫹0.354 I 11/2⫹0.034 I 13/2 99.64 I 11/2⫹0.224 I 9/2⫹0.154 I 13/2 99.44 I 11/2⫹0.374 I 13/2⫹0.204 I 9/2 99.44 I 11/2⫹0.404 I 13/2⫹0.184 I 9/2 99.64 I 11/2⫹0.184 I 13/2⫹0.164 I 9/2 98.84 I 11/2⫹0.664 I 9/2⫹0.444 I 13/2 99.44 I 11/2⫹0.304 I 9/2⫹0.214 I 13/2 99.64 I 13/2⫹0.214 I 11/2⫹0.144 I 15/2 99.54 I 13/2⫹0.284 I 15/2⫹0.204 I 11/2 99.54 I 13/2⫹0.364 I 15/2⫹0.114 I 11/2 99.24 I 13/2⫹0.414 I 15/2⫹0.304 I 11/2 99.74 I 13/2⫹0.164 I 15/2⫹0.124 I 11/2 99.04 I 13/2⫹0.594 I 11/2⫹0.334 I 15/2 99.64 I 13/2⫹0.214 I 11/2⫹0.144 I 15/2
Emission from lower energy Stark level of the 4 F 3/2 manifold 共11 386 cm⫺1 ); number in parentheses is the calculated centroid for the manifold. Transition to individual Stark level from level at 11386 cm⫺1 . c Wavelength in nanometers. d Intensity in arbitrary units for each manifold separately with 9.80 representing the most intense peak in that manifold. e Energy in vacuum wave number. f Energy difference relative to emitting level at 11 386 cm⫺1 . g Calculated crystal-field splitting with parameters, B nm given in Table I, footnote e. h Percent mixture of free-ion states due to J mixing.
a
b
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J. Appl. Phys., Vol. 93, No. 6, 15 March 2003
FIG. 4. Absorption spectrum of 4 G 5/2 and 2 G 7/2 near 8 K.
let manifolds appear as a single exponential decay at all temperatures investigated, suggesting that the concentration quenching does not contribute significantly. For all spectroscopic studies the sample was mounted on the cold finger of a CTI Model 22 closed-cycle helium cryogenic refrigerator that could provide a controlled sample temperature between 8 and 320 K. The sample temperature was monitored with a silicon-diode sensor attached to the base of the sample holder and was maintained by using a Lake Shore control unit. While we report data at a nominal temperature of 8 K, our experience indicates that spectra may be recorded at a somewhat higher temperature since the sample is not directly immersed in the coolant. However, this difference does not limit our ability to carry out a spectroscopic analysis.
Gruber et al.
FIG. 6. Fluorescence spectrum from 4 F 3/2 to 4 I 9/2 obtained at 8 K. Transitions from the lowest-energy Stark level of 4 F 3/2 are observed to all Stark levels of the 4 I 9/2 manifold. Laser excitation wavelength, 514.5 nm.
The absorption spectrum obtained near 8 K between 570 and 1750 nm is given in Table I. The spectrum of individual multiplet manifolds is presented in Fig. 1 ( 4 I 15/2), Fig. 2 ( 4 F 5/2 and 2 H 9/2), Fig. 3 ( 4 F 7/2 and 4 S 3/2) and Fig. 4( 4 G 5/2
and 2 G 7/2). The most intense spectra are observed in the 4 F 5/2 , 2 H 9/2 , manifolds 共Fig. 2兲 and the 4 F 7/2 and 4 S 3/2 manifolds 共Fig. 3兲. What appears as a doublet at 808 nm in Fig. 2 is actually an intense, sharp single peak having an absorption coefficient of 41 cm⫺1 . The scale in the figure was chosen in order to compare this peak with other weaker peaks in the same manifold. The 808 nm peak is of special interest in that it can be pumped directly with certain diode lasers. Several groups have reported yellow emission from Nd3⫹ -doped crystals that have been diode pumped at 808 nm.6,7 They have attributed their observations to excitedstate absorption, to energy transfer upconversion, or to both mechanisms, depending on the pumping conditions.6,7 These mechanisms compete directly with rapid relaxation from the 4 F 5/2 to the 4 F 3/2 manifold from which stimulated emission is possible to the 4 I 11/2 manifold 共1.062 m兲 and to the 4 I 13/2 manifold 共1.344 m兲.5– 8 At 8 K we observe J⫹1/2 absorption peaks for each multiplet manifold in the spectrum. This number represents
FIG. 5. Absorption spectrum of 2 P 1/2 obtained at 85 K. To the higher wavelength side of the most intense peak are three hot bands that identify transitions from Stark levels within the ground-state multiplet manifold, 4 I 9/2 .
FIG. 7. Fluorescence spectrum from 4 F 3/2 to 4 I 11/2 obtained at 8 K. Transitions from the lowest-energy Stark level of 4 F 3/2 are observed to all Stark levels of the 4 I 11/2 manifold. The most intense peak is found at 1061.6 nm. Laser excitation wavelength, 514.5 nm.
III. OBSERVED SPECTRA
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Gruber et al.
J. Appl. Phys., Vol. 93, No. 6, 15 March 2003
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TABLE III. Branching ratiosa.
4
Manifold transition
Line transitionb
F 3/2→ 4 I 13/2
18 17 16 15 14 13 12
7223 7265 7321 7364 7408 7438 7479
11 10 9 8 7 6
9238 9283 9336 9382 9417 9455
5 4 3 2 1
11 068 11 193 11 260 11 297 11 386
Manifold total F 3/2→ 4 I 11/2
4
Manifold total 4 F 3/2→ 4 I 9/2
Manifold total
E (cm⫺1 )
 i j calc.c
 d3/2→J
0.03 0.01 0.05 0.03 0.15 0.71 0.02 1.00 0.05 0.07 0.08 0.05 0.68 0.07 1.00 0.01 0.20 0.40 0.35 0.04 1.00
0.12 共0.087兲
0.46 共0.47兲
0.41 共0.44兲
Emitting Stark level 4 F 3/2 共11 386 cm⫺1 ), see Table II. Line transition identified in Table II. c Calculated line-to-line branching ratios for 8 K spectra normalized to unity for that manifold for comparison with fluorescence given in Figs. 6 – 8. d Calculated multiplet-to-multiplet branching ratios obtained in the present study; values in parentheses are reported in Ref. 9. a
b
the expected number of transitions from the ground-state Stark level to J⫹1/2 Stark levels of excited state manifolds of Nd3⫹ (4 f 3 ). The spectra shown in Figs. 1– 4 show evidence of broadening similar to the spectra observed in lanthanum 共yttrium兲 scandium garnets.11 Site-selective excitation experiments indicated that a single Nd3⫹ site was involved in the fluorescence.12 The crystal-field splitting of the ground-state manifold, 4 I 9/2 , was determined from an analysis of the 85 K and room temperature absorption spectra. The temperature-dependent ‘‘hot band’’ spectra represent transitions from excited Stark levels of the 4 I 9/2 manifold to the excited Stark levels reported in Table I. The splitting obtained for 4 I 9/2 共0, 90, 128, 191, and 323 cm⫺1 ) agrees to within experimental error with values obtained from the fluorescence data reported in Table II. Representative of the hot band absorption spectra observed at 85 K is the spectrum shown in Fig. 5 for transitions to the 2 P 1/2 . Beginning with the strongest peak, to the left in the figure, which represents the transition from the groundstate Stark level, we find three temperature-dependent absorption peaks that represent transitions from excited Stark levels at 90, 128, and 191 cm⫺1 , respectively. The fluorescence spectrum obtained near 8 K and observed between 800 and 1600 nm represents transitions from 4 F 3/2 to 4 I 9/2 共Fig. 6兲, 4 I 11/2 共Fig. 7兲, and 4 I 13/2 共Fig. 8兲 multiplet manifolds and is reported in Table II. The fluorescence spectrum observed between 878 and 903 nm 共Fig. 6兲 consists of five peaks 共two that are relatively weak and three stronger peaks兲 that represent transitions from the lowest-energy
FIG. 8. Fluorescence spectrum from 4 F 3/2 to 4 I 13/2 obtained at 8 K. Transitions to all Stark levels of 4 I 13/2 are observed. The most intense peak is found at 1344 nm. Laser excitation wavelength, 514.5 nm.
Stark level of the 4 F 3/2 manifold 共Table I兲 to the five crystalfield split 共Stark levels兲 of the ground state, 4 I 9/2 , that have been identified from the absorption hot band spectra obtained at 85 K and room temperature. The splitting of the 4 I 9/2 manifold obtained from the fluorescence spectrum 共0, 89, 126, 193, and 318, all in cm⫺1 ) is given in Table II. The fluorescence spectrum from 4 F 3/2 to the 4 I 11/2 manifold observed between 1057 and 1082 nm 共Fig. 7兲 consists of six peaks of which the transition having a wavelength of 1061.6 nm represents more than half the emission to the 4 I 11/2 manifold. The expected number of transitions observed (J⫹1/2) to the 4 I 11/2 manifold gives rise to a manifold splitting of 1931, 1969, 2004, 2050, 2103, and 2149, all in cm⫺1 , listed in Table II. The 8 K fluorescence spectrum, representing transitions from 4 F 3/2 to the 4 I 13/2 manifold 共Fig. 8兲, is dominated by a single intense peak at 1344 nm that represents nearly 60% of the fluorescence to that manifold. Although other expected transitions to this manifold appear as very weak peaks in Fig. 8, we observe the full number (J⫹1/2) of expected transitions that allow us to establish the splitting of the 4 I 13/2 manifold in Table II. IV. ANALYSIS OF SPECTROSCOPIC DATA
The experimental Stark levels reported in Tables I and II have been modeled using codes developed by Morrison and his co-workers some years ago.13–16 These codes are the result of their work on lattice-sum calculations that describe the crystal field at the site of a rare earth ion in a host crystal. Model lattice-sum components A nm at the rare earth ion site are related to crystal-field parameter B nm through a set of terms n that account for lattice phenomena that modify the local electric field.13,14 Based on structural data,12 an initial set of B nm was determined for the present analysis. The crystal-field splitting Hamiltonian can be written as ˆ ⫽ H CF
* 兺 C nm 共 rˆ i 兲 , B nm 兺 n,m i
共1兲
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J. Appl. Phys., Vol. 93, No. 6, 15 March 2003
* ⫽(⫺1) m B n⫺m , and the one-electron tensor opwhere B nm erators, C nm (rˆ i ), transform like the standard spherical harmonics.13,14 The sum on n covers the even integers 2, 4, and 6, and the sum on i covers the three equivalent 4f electrons of the ground-state electronic configuration of Nd3⫹ (4 f 3 ). We chose the symmetry C2/c to describe the environment of the Nd3⫹ ions in the samples investigated. Equation 共1兲 is diagonalized, together with an effective free-ion Hamiltonian over the 13 lowest-energy manifolds given in Tables I and II. The combined model Hamiltonian includes adjustable centroids which represent the center of gravity of the crystal-field-split manifold as affected by J mixing between states.11,15 The initial set of centroids was calculated using the free-ion wave functions reported by Carnall, Fields, and Rajnak.17 Thirteen centroids and 14 initial B nm parameters (C 2 symmetry兲 were allowed to vary in a least-squares fitting analysis between 57 calculated-toobserved Stark levels. With modest adjustment to these parameters, we obtain a final root-mean-square deviation of 8 cm⫺1 . The calculated splitting is reported in Tables I and II. With wave functions established from the modeling studies we calculated individual line strengths for both electric-dipole and magnetic-dipole transitions.14,18 Branching ratios for line-to-line transitions (  i j ) were calculated from the lower of two Stark levels of 4 F 3/2 共the emitting Stark level given in Table II as 11 386 cm⫺1 ) to individual Stark levels within the 4 I J multiplet manifolds. A partition function was included so that results could be compared with the 8 K fluorescence spectra shown in Figs. 6 – 8. The branching ratio as a function of temperature is given as i j⫽
Zi /ij
兺
,
共2兲
i jZi /i j
where i j is the calculated radiative lifetime, and the partition function, assuming thermal equilibrium, is expressed as
Z i⫽
exp共 E i /kT 兲 . 兺 i exp共 E i /kT 兲
共3兲
Branching ratios to a given manifold are normalized to unity for that manifold so that the results can be compared with the relative intensities observed in Figs. 6 – 8. The calculated values of  i j at 8 K are reported in Table III 共column 4兲 with individual transitions between Stark levels identified in column 2 and also in Table II 共column 2兲. The calculated  i j have relative values within each manifold that are consistent with the relative intensity patterns shown in Figs. 6 – 8. Of special interest is transition 7 which represents 68% of the emission to the 4 I 11/2 manifold and transition 13 which represents 71% of the emission to the 4 I 13/2 manifold. Stimulated emission has been reported for these two transitions at 1062 and 1344 nm, respectively.3,4,6 At room temperature (T⫽300 K兲, with the partition function reflecting the populations at that tempera-
ture, we found that these same transitions retain their dominant line-strength values relative to other transitions within a given manifold. Multiplet branching ratios were calculated by summing contributions from line-to-line transitions, each weighted equally. This step corresponds to infinite temperature or Z i ⫽1.0 for all i in Eq. 共3兲. These values are given in column 5 of Table III and are compared with branching ratios we reported earlier9 using the Judd–Ofelt approximation.19,20 The results obtained by these two separate approaches give consistent agreement, and are found to be similar for multipletto-multiplet branching ratios for Nd3⫹ in the beta phase of LSB as reported by Chen et al.10 The measured room temperature fluorescence lifetime for 4 F 3/2→ 4 I 11/2 is 140⫾10 s, which gives a quantum efficiency of 56% for this transition. The calculated radiative lifetime from the present modeling study, assuming T⫽300 K in Eqs. 共2兲 and 共3兲 and an index of refraction from Ref. 9, gives a radiative lifetime for transition 7 of 210 s. This value leads to a quantum efficiency of 67%, which suggests this material has possible laser applications around 1062 nm. The quantum efficiency we report is roughly 10% higher than the value reported for Nd3⫹ in the beta phase of LSB.10 A second calculation for the line-to-line transition 13 at 1344 nm, also at T⫽300 K, gives a calculated value of 187 s, which also suggests that possible interest may be directed toward this transition in the future because of stimulated emission observed at this wavelength. In summary, we report a detailed crystal-field splitting analysis of the 13 lowest-energy multiplet manifolds of Nd3⫹ in LSB. With wave functions obtained from our modeling studies, branching ratios and radiative lifetimes were calculated and compared with earlier reports9,10 and with our fluorescence spectra reported at 8 K. The observed spectra and the analysis of the data are consistent with spectra reported earlier for Nd3⫹ as a dopant in the alpha phase of LSB. The results provide additional spectroscopic information on this material as a possible laser host crystal for stimulated emission at 1062 and 1344 nm.
1
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