Terras Raras Libro

HDL-TM-92-25

September 1992

AADfA259 136

Energy Leveds and Predicted Absorption Spectra of Rare-

ok.)in Pare-1artthcAv.meid

U.S. Army Laboratry,, ommandHarry Diamrnd Laboratories

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1. AGENCY USE ONLY XWW i•b* L REPORT oAT . REPORT WK AM DAT.S COVERED

September 1992 Interim, from 1 July to 30 Sept 1992

4. TITLE AND SUSTITLE L2 FUNDN NUMBERS

Energy Levels and Predicted Absorption Spectra of Rare-Earth Ions in Rare-Earth Arsenides

L. AUrNOR(S)

Donald E. Wortman and Clyde A. Morrison

7. PERFORMING ORGANIZATION NAMES AND ADORESS(E$) L PERPORONG ORGANMATIONREPORT NUMER

Harry Diamond Laboratories HDL-TM-92-252800 Powder Mill RoadAdelphi, MD 20783-1197

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U.S. Army Laboratory Command AGENCY REPWORT -MBER2800 Powder Mill RoadAdelphi, MD 20783-1145

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1I& ABSTRACT llux wen2,*w)

A crystal-field Hamiltonian for octahedral symmetry was used along with free-ion parameters for aqueoussolution to fit the reported optical absorption spectra of Er3* in ErAs. Parameters obtained from this fit were thenused in a model to predict optical absorption spectra of Er3+ for the 4115/2 to 4113/2 multiplets at 5, 74, and 300 K;these predictions showed excellent agreement with the reported experimental data at these temperatures.Consequently, we used an interpolation procedure to predict the crystal-field splittings of the lower multiplets ofthe rare-earth ions Tb3+ through Yb3+ in their respective arsenide compounds. The lowest multiplet energy levelspredicted for Tm3+ and Yb3+ compare favorably with measurements made by inelastic neutron scattering. Inaddition, we calculate the absorption spectra for Tb3+, Dy 3 ', Ho3+, Tm3+, and Yb3+ in their respective arsenidecompounds at 4.2,77, and 300 K. From these calculations, we show the transitions between the levels of the lowesttwo J multiplets for each of the ions.

10. S3110 TERIM NUISM R OF PAGS

29Rare-earth arsenides, rare-earth spectra IC O O

17. SSWIT CLASSIICATIIOLI SECURTY CLASSWICATION 17. SECURMITY CLASSICATION as. L /TATION OF ABSTRACT

OF REPORT OF THIS PAGE OF AISTRACT

Unclassified Unclassified Unclassified ULM•EN -aUo.Ufo Oiderd Foey 2m = OW 2-MI

Piinaib Me ] 51

Contents

1. Introduction .............................................................................................................................. 52. Fitting Experimental Data ................................................................................................ 53. Calculation of M agnetic Dipole Line Strengths .............................................................. 74. Comparison with Experiment ........................................................................................... 8S. Emission Branching Ratios ................................................................................................ 86. Theoretical Predictions ................................................................................................... 107. Predicted Energy Levels, g Values, Absorption Spectra, and Multiplet

Branching Ratios ............................................................................................................ 12

7.1 Tb in ThAs ........................................................................................................................ 127.2 Dy in DyAs ........................................................................................................................ 147.3 Ho in HoAs ........................................................................................................................ 167.4 Tm in TmAs ...................................................................................................................... 187.5 Yb in YbAs ........................................................................................................................ 20

8. Conclusion .............................................................................................................................. 22Acknowledgements ............................................................................................................... 22References ................................................................................................................................... 23Distribution ................................................................................................................................. 25

Figures

1. Predicted absorption spectra of 4115/2 to 4113/2 levels of Er3+ in ErAs, assuming aLorentzian line shape with AE = 3 cm - .............................................................................. 9

2. Four largest line-to-line branching ratios at 300 K for 41,3/2 to 4115/2 transitions for Er3+in ErAs .................................................................................................................................... 10

3. Predicted absorption spectra of 7F 6 to 7F 5 levels of Tb3+ in TbAs, assuming aLorentzian line shape with AE = 3 cm -! ..................................................................................................... 13

4. M ultiplet-to-multiplet branching ratios for Dy3+ in DyAs ................................................ 155. Predicted absorption spectra of 6H15/2 to 6H 13/2 fevels of Dy3÷ in DyAs, assuming

a Lorentzian line shape with AE =3........ ....... ...................................................................... 156. Predicted absorption spectra of 5I to 517 levels of Ho3 in HoAs, assuming a

Lorentzian line shape with AE =3 cm 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177. Predicted absorption spectra of 3H6 to 3F4 levels of Tm3÷ in TmAs, assuming a

Lorentzian line shape with AE = 3 cm- ........................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198. Predicted absorption spectra of 2F/ to 2F5 ,2 levels of Yb3+ in YbAs, assuming a

Lorentzian line shape with E = 3 cm-! ................................................................................. 21

3

Tables

1. Theoretical and experimental energy levels ..................................................................... 62. Magnetic dipole line strengths, Sm, for line-to-line 452 1t ......................3..................... 73. g values of 4115,2 and 4'13/2 levels of Er3+ in ErAs ............................................................... 74. Lattice constants for LnAs for experimental values and interpolated

values for triply ionized rare-earth ions with electronic configuration 4fr ......................... 115. Interpolated crystal-field components, Ak,, and crystal-field parameters, Brn.,

for L nA s ............................................................................................................................... 116. Predicted energy levels and free-ion mixture for TY3 + in ThAs .................................... 127. Predicted g values for 174 and 175 levels of Tb 3Y in TbAs ............................................... 138. Predicted energy levels and free-ion mixture for Dy3+ in DyAs .................................... 149. Predicted g values for 176, 177, and I8 levels of Dy3+ in DyAs ........................................ 16

10. Predicted energy levels and free-ion mixture for Ho3+ in HoAs ................................... 1611. Predicted g values for 174 and 175 levels of Ho3+ in HoAs ............................................... 1712. Predicted energy levels and free-ion mixture for Tm3+ in TmAs .................................. 1813. Predicted g values for 24 and 15 levels of Tm3 + in TmAs ............................................. 1914. Experimental energy levels of Tm3+ in TmAs reported by Hulliger [10] ....................... 1915. Comparison of present work and Hulliger [10] ............................................................... 1916. Predicted energy levels and free-ion mixture for Yb 3+ in YbAs .................................... 2017. Predicted g values for 1`6,127, and 128 of Yb3÷ in YbAs ................................................. 21

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4

1. Introduction

Small, stable, narrow-linewidth lasers built by the doping of rare-earth ionsin HI-V semiconductors are of current interest for optoelectronic componentsand integrated optical circuits. Lasers with these desirable properties can bepumped by photons whose energies are greater than the band gap or by currentinjection into the region occupied by the rare-earth ions. Characteristic,narrow-line frequencies of the 4fv rare-earth ions can provide direct laseroutput or can be used to lock III-V semiconductor laser transitions [1].

In the work reported here, we analyze the absorption spectra [2] of Er3+ in a3300-A-thick layer of ErAs to obtain phenomenological crystal-field param-eters, Bn, for Er3 + in ErAs. The Bn_ were obtained by least-squares fittingthe reported spectra on the 4115/2 and "113/2 multiplets of Er3+, and these werealso used to calculate the magnetic dipole line strengths for all the transitions,as well as the magnetic g factors for each level. The magnetic dipole linestrengths were then used to compute the absorption spectra of Er3+ in ErAs;the computation results compare favorably with experiment. The line-to-lineemission branching ratios were calculated as a function of temperature for the4113/2 to 4115/2 transitions of Er3+ in ErAs. Using these Bn for Er, we nextpredict theBn for the entire triply ionized rare-earth series of arsenides, LnAs(Ln = Ce to Yb). These latter Bn, are then used to predict the energy levelsand the magnetic dipole line strengths for triply ionized Tb, Dy, Ho, Er, Tm,and Yb in their respective arsenide lattices. We present the absorption spectracalculated for transitions between the levels of the lowest two J multi plets ofthese ions, assuming a Lorentzian lineshape with a linewidth of 3 cm-. Muchof the analysis follows the procedure used previously [3] in the investigationof the spectra of triply ionized lanthanides (rare-earth ions), Ln 3+, inCs2 NaLnCl6.

The phenomenological A, for Er3+ in ErAs were obtained from the relationBn = pt 4 where the pn for each rare-earth ion were given in 1979 byMorrison and Leavitt [4]. These phenomenological An for ErAs and the1968 x-ray data of Wyckoff [5] yielded Brn, which were used to compute theenergy levels and multiplet branching ratios for the triply ionized rare-earthions, LnAs, for Tb3+ through Yb3+. The free-ion aqueous parameters ofCarnall et al [6] were used in all these calculations.

2. Fitting Experimental Data

In 1991, Schneider et al [2] reported the absorption spectra of Er3 + in ErAs at5, 74, and 300 K and gave an analysis of the energy levels using theHamiltonian of Lea et al [7] in 1962. The ErAs they investigated was a 3300-A-thick layer grown by molecular beam epitaxy on a substrate of GaAscapped by a thin layer of GaAs.

5

The data of Schneider et al [2] were used along with the crystal-fieldHamiltonian, HCEF, for the 4f electronic configuration in Oh symmetry,given by

N

HcEF = Bdo j C (c4s) + (fK[C44;i) + C4-4^ri)1) +'V 14

i=1 .

to obtain the best least-squares fit between the calculated and measuredenergy levels. In obtaining the best fit to the experimental data, we varied B40and B6o as well as the calculated difference in the centroids of the 4115/2 and4113/2 multiplets. The free-ion wavefunctions were determined from theparameters [6] for aqueous solution. Because we could not convert theparameters B4 and B6 of Schneider et al [2] to the form used in equation (1),we started the fit with the B40 and B60 values given elsewhere [3] for Er3÷ inECsNaErCI6.The reason for this choice is that the point-group symmetry forEr3 + in ErAs and in Cs2NaErC16 is the same in each material (Oh). Again, asbefore [3], we label the states according to their transformation propertiesunder the group 0 rather than Oh. This entails dropping the parity labels (+)or (-), which are determined by the number of f electrons. The irreduciblerepresentations of the 0 group are from Koster et al [8]. The resultingparameters, energy levels, and wavefunction compositions are given intable 1.

Table 1. Theoretical No.b Centroid I. R.d ETho EExp.e Free-ion mixture (%)and experimentalenergy levels (cm-1) 1 61 r. 0.3 0 99.99 415/2and composition for 2 r7 26.4 27.2 99.99 15/2+ 0.01 13/2Er3÷ in ErAsa 3 P. 28.6 27.2 99.99 41i5/2 + 0.01 4132

4 r 6 126.8 129.0 100.00 4115/25 r. 133.5 133.5 99.99 4f

6 6534 r 6 6490.7 6491.3 99.99 417 18 6505.4 6505.7 99.97 41I3/2 + 0.03 4111,28 r7 6515.4 6515.7 99.96 4 0 +00341129 P7 6582.6 6583.0 99.99 113/2 + 0.01 415,a

10 r. 6583.9 6583.0 99.99 4 13/2t+ 0.01 41J5/2

11 10,220 P6 10194.8 - 99.97 41/2 + 0.01 419/2 + 0.01 4F7 /212 r8 10201.2 - 99.95 411/2 + 0.04 419M13 1r7 10236.5 - 99.96 4711t2 + 0.03 4113/214 18 10239.9 - 99.97 41i1U+ 0.02 4113,2

'aB40 704.5, B = 51.07 cnm-, and rms = 0.870 cr"1.bNI.bers used to designate levels used in discussion.CIn absence of experimental data, centroids were calculated from aqueous solution

parameters of Carnall et al [6].dlrreducible representation of 0 group, Koster et al [8].Tsang and Logan (1).

6

3. Calculation of Magnetic Dipole Line Strengths

Since the Er3 + ion occupies a site with 0 h symmetry, the electric dipoletransitions are parity forbidden. However, the magnetic dipole operator haseven parity and should correspond to the experimental absorption, if weassume that the absorption is not vibrationally assisted. Because of theexcellent agreement of the calculated values of the energy levels with theexperimental values, we assume that all the observed levels are magneticdipole. The operator we use for the magnetic dipole, M, is

M = aao (L + geS) , (2)

2

where a is the fine structure constant, ao the Bohr radius, g, the free-electrong-factor, and L and S are the orbital and spin operators, respectively. We thencalculate the line strength given by

snm = I(mrrf nr , (3)i,f

where the sum on i and f is over all the components of ri, and rf. Thewavefunctions [nri) and Imrf) are obtained from the simultaneous diagonal-ization of the crystal field in equation (1) and the free-ion Hamiltonian withthe parameters for Er3+ given by Carnall et al [6]. These results are given intable 2. We also calculated the g values as defined earlier [3] for the 4115/2 and4113/2 energy levels; these results are given in table 3.

Table 2. Magnetic 6, T6 7, r. 8, 17 9, r7 10, r8dipole line strengths,S111, (1or-2 cm2 ), for' _________________

line-to-line 411,2. 1, r. 47.73 30.74 3.139 0.01178 0.38874113/2 2, r 7 0 6.804 8.717 1.060 3.290

3, r.8 0.0015 33.16 14.69 8.120 8.001

4, r 6 0.0028 0.0032 0 0 44.755, r 8 0.0398 0.2482 0.2345 38.43 40.15

Table 3. g values of No. I. R. g1 g2

47i5/ and 4112 levels of 1 r 8 4.945 -11.897Er3+ in ErAs 2 r 7 - 6.777

3 r8 -1.194 9.6974 176 -5.933 -5 .8 -12.174 0.2156 176 5.546 -7 r 8 -2.506 -5.9968 r 7 - -3.6429 r7 - 4.285

10 r8 0.294 9.737

"For an explanation of definitionof notation of g values, seeMorrison et al 13J.

7

4. Comparison with Experiment

The line strengths given in table 2 have been used to calculate the line-to-lineabsorption as a function of energy at 5, 74, and 300 K reported by Schneideret al [2]. The results are shown in figure 1. The quantity plotted, I(E), is

E) o 5 (Ej-Ei)Sij exp [-(Ei-EI)/kT] (4)jff6 i-1 ([E - (Ej - Ei)] + (N2)Zi

where

5ZI= wi exp[-(Ei - E1ikT] (5)i=1

and A is the full linewidth at half maximum value, and, as suggested bySchneider et al [2], we have used A = 3 cm- 1. If this figure is compared withfigure 1 of Schneider et al [2],we find that every line agrees with their results,except for the splittings of the lines they label 1 and 2.

5. Emission Branching Ratios

We calculated the emission branching ratios assuming that the 4113/2 level ispumped and the population of this state is thermalized. That is, we calculate

Pi = exp[- (Ej - E6/kT]Sij (Ej - E)3 (6)SoZ2

forj = 6 to 10, i = I to 5, where

10Z2= wj exp[- (Ej - E6)kT]; (7)

j=6

So is determined such that

5 10

i-=1 j.6

and w. is the degeneracy of each level in the 4 113/2 multiplet (wj =2 for 176 and1r7, and 4 for Ir). The.8ii are shown in figure 2 for the four largest branchingratios at T = 300 K. At all temperatures, the largest branching ratio is fromlevel 6 to level 1 (AE = 6491.3 cn-1 ). However, at room temperatures, thetransition of level 7 to level 3 (AE = 6478.5 cm-1) has a large branching ratio

8

(13.4 percent), but since level 3 is only 27.2 cm-1 above the ground level,population inversion would be difficult. Also, at room temperature, it mightbe possible to achieve population inversion in the transition from level 10 tolevel 4(fi = 12.5 percent) at 129 cm- 1 (AE = 6454.0 cm-').

Figure 1. Predicted (a) 6

absorption spectra of411M to 41 levels Of

Er3* in ErAs, assuming 4a Lorentzian line shape 1with AE a 3 cn-1: 3(a) T- 5 K,(b) r = 74 K, and 2(c) T = 300 K.

6400 6425 6450 6475 6500 6525 6550 6575 660EnerWy (cr-1)

(b) 3.0

2.5

2.0

1.5

064 6425 60 645 6W 62 65 6575 660Eneng (cm-1)

(c) 2.0

1.6

1.2i°S.1.0.4 A k A0.

640 42 650645 650 6525 650 M5W60Energy (cm-1)

9

Figure 2. Four largest 100

line- to-line branching 9oratios at 300 K for 411= 80' 6-1

to 41,, transitions for ..... 7-3Er3+÷ in ErAs. 70 -- - ý .1

7.... 10-4

so,

401

301

20

o10 . ......... ................ .

0 25 50 75 100 125 150 175 200 225 250 275 300

T(K)

6. Theoretical Predictions

In the three-parameter theory of crystal fields proposed in 1975 by Leavitt etal [9], the crystal-field parameters, Bnm, are related to the crystal-fieldcomponents by

B,, = p,A,,,,,, (8)

and it is assumed that the pn are dependent only on the lanthanide ion and theAn,, are host dependent. In the cubic symmetry for the LnAs compounds, weneed only P4 and p6 along with A40 and A60. The values for p. have beentabulated elsewhere [4], and we use these values here. Using the values of p4and p6 for Er3* and the values of B40 and BE0 from the best fit given intable 1, we obtain experimental values of the crystal componentsA4(Er) andA60(Er), which can be used in equation (8) to predict the energy levels of theother lanthanides as impurities in ErAs. However, we wish to find theAn,(Ln)in LnAs. To obtain the A,,(Ln) for LnAs, we assume that the dominantcontribution to the An,(Ln) is given by the monopole contribution to thecrystal-field components. For cubic site symmetry, the monopole Am, can bewritten as

An,(Ln) = Vf/a(Ln)"*l , (9)

where a(Ln) is the lattice constant for LnAs and the VnM are crystal-fieldcomponents for the unit lattice constant and are the same for all cubic LnAs.The a(Ln) for a number of lanthanides are given by Wyckoff [5], and hisresults have been used to interpolate the lattice constants for all the LnAs fromLaAs through LuAs; these results are given in table 4.

10

We obtain the A,,(Ln) for LnAs from equation (9) by using

•,[a (Er +1ALn) = Anj(Er) [ a( E) (10)

with the A.m(Er) determined from the phenomenological B 40 and B 60 for Erin ErAs. These results are given in table 5, along with the B 40 and B 60 for allthe LnAs given in table 4. If the values of B40 and B 60 in table 5 are comparedto the values given earlier [3] (table VI) for Ln3+ in Cs2NaLnCI6, we see thatthe B40 and B60 are much smaller for Ln Xs.

Table 4. Latticeconstants forLnAs N Ion a (A)" a(Ln = La to Lu) for 0 La 6.125 6.103experimental values 1 Ce 6.060 6.060and Interpolated 2 Pr 5.997 6.019values for triply 3 Nd 5.958 5.980Ionized rare-earth ions 4 Pm - 5.943with electronic 5 Sm 5.921 5.908configuration 41N 6 Eu - 5.875

7 Gd 5.854 5.8448 Tb 5.827 5.8149 Dy 5.780 5.787

10 Ho 5.771 5.76211 Er 5.732 5.73812 Tm 5.711 5.71713 Yb 5.698 5.69714 Lu - 5.679"OR. W.G. Wyckoff [5].ba(N) = 6.103273-4.378697X+

9.666212 X2 X = N/1O0 (rms =1.326 x 0"2'A)

Table S. Interpolated N Ion A4O (cm-n/A4) B4o (cnrm) A6o (cm-1/A6) B6o (cm-)crystal-field compo-nents, Ak and crystal. 0 La 1254 - 33.76 -

field parameters, Be,, 1 Ce 1299 979.4 35.47 83.06forLnAs 2 Pr 1344 869.0 37.19 69.75

3 Nd 1388 802.1 38.92 61.874 Pm 1432 764.8 40.65 57.795 Sm 1475 745.0 42.37 55.976 Eu 1517 733.9 44.07 55.107 Gd 1558 725.7 45.74 54.318 Tb 1598 717.6 47.38 53.229 Dy 1636 710.4 48.97 51.98

10 Ho 1672 705.4 50.50 51.1111 Er 1707 704.5 51.97 51.0712 Tm 1739 705.1 53.36 51.4813 Yb 1770 697.0 54.66 49.8514 Lu 1797 - 55.86 -

11

7. Predicted Energy Levels, g Values, Absorption Spectra,and Multiplet Branching Ratios

The B 40 and B6o in table 5 are used in equation (1) along with the free-ion

centroids of Carnall et al [6] from the aqueous data to obtain the energy levels,g values, absorption spectra, and branching ratios for Ln = Tb, Dy, Ho, Tm,

and Yb in LnAs. Only the multiplets that lie in the band gap of GaAs

(-11,000 cm-1) are given.

7.1 Thin TbAs

The energy levels and free ion composition of the wavefunctions for the 7Fjfor J = 6 through 0 are given in table 6. For most values of J, the free-ion

component of the wavefunction exceeds 99 percent, and this result would

indicate that the analysis of the experimental data using the operator equiva-

lent method given by Lea et al [7] would give a good representation of the

crystal-field parameters. The strongest optical absorption would be in the

2000 cm- 1 region (7F 6 -- 7F 5 ), which is the long wavelength limit given by

Schneider et al [2]. Multiplet line strengths of 7F 6 to higher multiplets are two

Table 6. Predicted Nob Centroidc I. R.d Energy Free-ion mixture (%)energy levels and free-ion mixture for Tb3 ÷

In TbAsa 1 74 r, 0.0 99.86 7F 6 + 0.13 7F42 r4 17.8 99.75 7F6 + 0.16 7F5 + 0.08 7F43 175 38.6 99.62 7F 6 + 0.35 7F 5 + 0.02 7F 4

4 172 121.5 99.94 7F6 + 0.06 7F35 175 148.6 99.86 7F 6 + 0.09 7F5 + 0.03 7F46 r3 157.6 99.88 7F 6 + 0.06 7F5 + 0.05 7F4

7 2112 £4 2058.3 99.84 7F 5 + 0.11 7F6 + 0.04 7 F18 r5 2112.1 99.43 7F5 + 0.44 7F6 + 0.10 7F2

9 173 2160.5 99.81 7F 5 + 0.09 7F 2 + 0.06 '7F6

10 r4 2177.3 99.72 7F 5 + 0.19 7F3 + 0.05 7F6

11 3370 171 3309.9 99.56 7F 4 + 0.30 7F0 + 0.13 7F612 174 3334.7 99.59 7F 4 + 0.16 7F1 + 0.13 7F313 173 3354.9 99.89 7F 4 + 0.05 7F6 + 0.05 7F5

14 15 3466.0 99.38 7F 4 + 0.56 7F 3 + 0.05 7F6

15 4344 14 4334.8 99.30 7F 3 + 0.36 7F1 + 0.20 7F5

16 r5 4360.5 97.33 7F3 + 2.03 7F 2 + 0.57 7F417 £2 4395.4 99.94 7F3 + 0.06 7F6

18 5028 r5 5012.1 97.86 7F 2 + 2.05 7F3 + 0.08 7F5

19 r3 5111.1 99.89 "F2 + 0.09 7F5 + 0.01 7F4

20 5481 £4 5502.8 99.43 7F1 + 0.38 7F3 + 0.15 7F4

21 5703 r1 5722.6 99.70 7F0 + 0.30 7F 4

"B4o 717.6 and B60 = 53.22 cm-1.bNwbers to designate levels used in discussion.CAqueous centroids.dlrreducible representation of 0 group, Koster et al [8].

12

orders of magnitude smaller than the 7F 6 - 7F 5 transitions. The absorptionspectra for the transitions between the energy levels of the 7F 6 to the 7F5 werecomputed using equation (4) with 1 s i< 6, 7 sj % 10 (table 6) and are shown

in figure 3 for T= 4.2,77, and 300 K. In addition, the g values for all the states

are given in table 7.

Figure 3. Predicted (a) 24absorption spectra of7F( to 7F. levels of Tb3 2In TbAs, assuming aLorentzlan line shape C

with AE = 3 c ra -: 1"

(a) T= 4.2 K, 12(b) T = 77 K, anJ(c) T = 300. K f

4

01'1850 1900 1950 2000 2050 2100 2150 2200 2250

Energy (crn-1 )

(b) (c)5000 4000'

14000

.130000132000 -2

0

10001000-

0 0o1850 1900 1950 2000 2050 2100 2150 2200 2250 1850 1900 1950 2000 2050 2100 2150 2200 2250

Energy (cm-1) Energy (cm- 1)

Table 7. Predicted g No. I. R. g

values for 14 and r. 2 14 1.5568

levels of Tb3+ In TbAs" 3 r 5 5.6857

5 r.5 1.79817 r4 8.90318 r. 7.4531

10 174 -7.457712 174 1.628114 r. -7.160915 174 -4.6128

aSee Morrison et al [3] 16 r. -1.0517for definition of g 18 r5 2.2372values. 20 r4 2.9733

13

7.2 Dy In DyAs

The energy levels and free-ion wavefunction composition for 6Hj, J = 15/2through 5/2, and 6Fll/2 , 6F 9/2, and 6F 7t2 are given in table 8. Even though thecrystal-field parameters are small, the free-ion levels are mixed by the crystalfield. In some cases the mixture of different states consists of 40 percent of astate. For example, one level of the labeled 6F 9/2 multiplet and one level in themultiplet labeled 6H 7/2 are only 60 percent of their respective multiplets. Themultiplet-to-multiplet branching ratios for each multiplet are shown infigure 4. The absorption spectra for the transitions between the energy levels

Table 8. Predicted No.b Centroidc I. R.d Energy Free-ion mixture (%)energy levels and free- (cm- 1)Ion mixture for Dy-'In DyAs f 1 40 F6 0.0 99.99 6H + 0.01 6Fi 1n

2 F8 12.8 99.98 6H15/2 + 0.02 611t323 F7 85.5 99.90 6H15/2 + 0.09 6H13/24 F8 139.2 99.95 6/ + 003 63 + 0.01 6F9/25 r. 174.0 99.95 H15/2 + 0.03 6F 11/2 + 0.01 6H13/2

6 3505 Fe 3530.2 99.93 6-132 + 0.03 6H15/2 + 0.02 6/-/11/27 17 3532.1 99.88 6HI312 + 0.08 6

15/2 + 0.02 6m8 F7 3566.4 99.68 6H1/2 + 0.23 6H11t2 + 0.06 6F11/29 r 8 3576.4 99.79 6H13/2 + 0.12 6Hl/2 + 0.04 'F, /2

10 176 3589.8 99.95 6H-13/2 + 0.02 6H1 1/2 + 0.02 6H9,"

11 5833 176 5860.9 99.84 6'H11/2 + 0.07 6Fll/2 + 0.03 6H7/212 F8 5867.6 99.72 6H1 1 / +0.096 + 0.08 6F9)213 177 5896.5 99.62 6H/-1 /2 + 0.24 6H1/ + 0.09 6F 1 /214 r 8 5909.0 99.77 6H11/2 + 0.09 6H13 /2 + 0.06 6 Fl/2

15e F8 7707.9 78.72 6H9,2 + 21.04 6F11,2 + 0.13 6F9/216 r8 7729.1 96.45 6H9 ,+3.056F1 1 , +0.26 'F9 217 Fe 7749.0 98.56 6F,1 /2 + 1.31 6H9/2 + 0.05 6H,1 /218 1F6 7754.5 82.88 6/H, + 16.83 6/F11 2 + 0.24 6F9/219 F7 7758.4 99.83 6F 11/2 + 0.09 6H11/2 + 0.07 6H13/220 1F6 7847.3 82.99 6F11 /2 + 16.74 6H9, + 0.13 61H7a

aB40 =710.4 andB60= 21 r 8 7851.6 77.12 6F11/2 + 22.69 Hg2 + 0.12 6 H1l/2

48Nu9 o designate 22 r 8 9080.5 59.91 6F9,2 + 39.95 6Hfra + 0.05 6H9/2levels used in 23 F8 9149.8 99.34 6Fqr2+ 0.40 6H7f2 + 0.11 6H9q-discussion. 24 1F7 9150.1 99.39 6'7a + 0.306 15,2+ 0.28 6F,7 aCAu s n 25 F6 9162.2 88.08 6F9/2 + 11.55 6H7/2 + 0.30 6H9/2dlrreducible r26 16 9196.9 88.06 H/2 + 11.63'Fg,2+0.16 6F7 /2ration of O group, 27 r 8 9214.4 59.02 6H7,2 + 40.10 6F9/2 + 0.43 6Hs52Koster et al [8].'Lewls 15 through 27 28 10169 F8 10200.2 99.22 6AH5 2 + 0.35 6H7/2 + 0.15 6F7/2are mixed, Centroids 29 1`7 10265.9 98.37 6Hff2 + 1.15 6F 7, + 0.24 6H7,are 6H;,12 - 7692,6Fre12- 7692; 30 11025 F77 11061.7 98.54 6F7 2 + 1.09 16H5/2 + 0.34 6Hx/2F1112 -7730; +. ,'W6F9V 2-9087; and 31 F. 11089.9 99.78 6F7/2 + 0.16 6H5 2 + 0.03 H9 2

6#;;/2 9115 Og-i 32 r6 11105.6 99.75 6FTp l 0.19 6H.,ý +0.02 6H9•

14

of the 6/115,2 to the 6H13/2 were computed using equation (4) with 1:% is 5 and6 sjs 10 (table 8) and are shown in figure 5 for T 4.2, 77, and 300 K. Theg values for each state are given in table 9.

Figure 4. Multiplet-to-multiplet branching - . --ratios for Dy3÷ in IQ .!••

SN'.. __ .- ...


absorption spectra of6H ,,/2 to 6H 12 levelsof Dy3 ÷ in DyAs,assuming a

Lorentzlan line shape 2

with AE = 3 cr- 1:I

(a) T = 4.2 K,

(b) T = 77 K, and _ 1(c) T = 300 K.

3320 3360 3400 3440 3480 3520 3560 3600Energy (cm-1)

(b) (c)12 8

10

8-

'4 12-

0 0.3320 3360 3400 3440 3480 3520 3560 3600 3320 3360 3400 3440 3480 3520 3560 3600

Energy (c="') Energy (cmnI)

15

Table 9. Predicted g No. 1.R. g1 g2 No. I.R. g1 92

values for r., D7, and 1 1 6 -6.624 - 17 0.314 -10.742

DyAss 2 r. -12.035 -0.908 18 r 6 2.415 -

3 r7 - 7.514 19 P7 - -5.2884 r. -5.335 10.394 20 r 6 -3.668 -

5 r. 8.074 -11.703 21 r. 8.544 2.6686 18 0.525 11.245 22 r. -6.729 1.4907 r 7 - 4.599 23 P8 8.363 0.3828 r 7 - -3.723 24 r 7 - 2.3039 r. -3.074 -6.908 25 P6 4.330 -

10 r 6 6.339 - 26 P6 -1.159 -11 P6 -4.387 - 27 r. -5.507 0.05112 r 8 7.100 3.166 28 r 8 0.078 1.32013 r 7 - -4.442 29 r 7 - -0.264

"aSee Morrison et al [3] 14 r 8 0.938 -9.698 30 r 7 - 4.124for definition of g 15 r 8 5.879 2.836 31 P8 -5.101 -1.358values. 16 P. -5.722 -0.403 32 P6 -3.230 -

7.3 Ho in HoAs

The energy levels and free-ion wavefunction composition for the 51j multipletof Ho 3 + in HoAs for J = 8 to 5 are given in table 10. For each 5I level, thecomposition of that state is practically 100 percent. The absorption spectra forthe transitions between the energy levels of the 518 to 517 were computed usingequation (4) with 1 s i s 7 and 8 sj js 13 (table 10) and are shown in figure

6 for T = 4.2, 77, and 300 K. The g values for each state are given in table 11.

Table 10. Predictedenergy levels and free. Nob Centroidc !. R.d Energy (cm-) Free-ion mixture (%)Ion mixture for Ho3+ 1 80 r 3 0.0 99.99 518In HoAsd 2 r 4 2.3 100.00 518

3 r, 7.5 100.00 SIS4 r 4 88.0 99.98 518 + 0.01 5175 r 5 93.6 99.99 518+0.015 176 P3 116.3 99.99 5187 P5 117.9 99.99 518

8 5116 P4 5065.7 99.98 517 + 0.01 5189 P5 5068.9 99.99 517 + 0.01518

10 r 2 5110.2 99.97 517 + 0.02 sI611 r 5 5120.6 99.97 517 + 0.02 51612 r 3 5127.0 99.97 517+0.0251613 r 4 5139.7 99.99 517 + 0.01 5F5

14 8614 r 3 8570.7 99.97 5I6 + 0.02 17

aB = f 705.4 and B6E 15 r 5 8574.6 99.% 5I6 + 0.02 517 + 0.01 51551.11 c-'1. 16 r 2 8590.8 99.97 516 + 0.02 517bNumbers to designate 17 r 5 8615.4 99.92 516 +0.07515levels used in 18 r 4 8625.7 99.94 516 + 0.04 515discussiopL 19 r, 8634.6 99.98 516 +0.01 514 + 0.01 5F4cAqueous centroids. 20 11164 r 4 11127.2 99.94 515 + 0.04 516dfrreducible represen. 21 r 5 11144.8 99.92 515 + 0.07 516

tio oof0 group, 22 P3 11166.5 99.88 515 + 0.11 5 44÷0.014F+Koser et al 8. 23 r 4 11174.1 99.9 515+o0.07514.o+015,6

16


absorption spectra ofSlS to 417 levels ofHoU In HoAs,

assuminga 2

Lorentzlan line shapewith AE = 3 cn3-: 1

(a) T = 4.2 K,

(b)T=77 K, and 0(c)T=300K. 4920 4980 50o0 5040 5080 5120 5160

Energy (c-1)

(b) (c)24 15.0

~20 112.5

16

121 7.5

4.~ 2.5

0 0.04920 4960 5000 5040 5080 5120 5160 4920 4960 5000 5040 5080 5120 5160

Energy (cmn-) Energy (m4-1)

Table 11. Predicted g No. I. R. gvalues for r and rlevels of Ho' .in 2 T, -0.4529

HoAs 4 1r4 -8.2455 r. -9.62287 r. 839988 rI 4.20799 175 -7.4662

11 r7 -3.139613 r"4 9.376315 15 2.047617 r. 3.285518 ['4 1.061620 r4 5.436321 r. 4.612523 r4 -4.4706

"dSee Morrison et al 131for doitions of gvalues.

17

7.4 Tm in TmAs

The energy levels and free-ion wavefunction composition for the 3H6, 3F4,and 3H5 multiplet of Tm3+ in TmAs are given in table 12. Each of the 3Hj and3F 4 consist of 100 percent of the free-ion level. These results indicate that themethod of Lea et al [7] would be applicable to all the multiplets. Theabsorption spectra for the transitions between the energy levels of 3H6 to the3F4 were computed using equation (4) with 1 i i: 6 and 7:sj s 10 (table 12)and are shown in figure 7 for T = 4.2, 77, and 300 K. The g values for all thelevels are given in table 13.

In 1979, Hulliger [10] listed four different sets of experimental energy levelsfor the 3H6 multiplet as given in table 14. Table 15 compares our results withHulliger's. In almost all cases, our predicted values lie within the variance ofthe experimental energy levels given in table 14.

Table 12. Predictedenergy levels and free- No.b Centroidc I. R.d Energy Free-ion mixture (%)ion mixture for Tm3+ (cm-1)in TmAsa 1 202 1i 0.0 99.91 3H6 + 0.08 3F4

2 r'4 28.7 99.95 !H6 + 0.04 3F43 ]r5 62.9 99.98 3H6 + 0.01 3F4 + 0.01 3H54 r2 145.7 100.00 3H65 1. 201.9 99.99 3H166 1[3 215.5 99.98 3H6 + 0.01 3F4

7 5812 r,, 5620.6 99.98 3F 4 + 0.01 3H6 + 0.01 3H48 r 3 5750.3 99.91 3F4 + 0.07 3H5 + 0.01 3H6

9 14 5778.2 99.91 3F4 + 0.05 3H5 + 0.0410 [' 5815.6 99.91 3F4 + 0.08 6

11 8390 F9 8225.6 99.90 3H5 + 0.05 3F4 + 0.03 3H412 [3 8244.8 99.83 3H5 + 0.08 3H4 + 0.07 3F413 r5 8331.5 99.96 3H5 + 0.01 3F2 + 0.01 3H614 14 8380.2 99.97 5 + 0.02 W114

15 12720 r., 12569.9 99.63 3H4 + 0.33 3F3 + 0.04 3F216 r3 12622.4 99.81 3H4 + 0.11 3F2 + 0.083 1j17 r4 12664.3 99.85 3H4 + 0.10 3F3 + 0.05 3f518 r1 12724.4 99.99 3H4

a = 705.1 and B60 = 51.48 cm- 1.bkwdbers to designate levels used in discussion.'Aqueous centroids.dlrreducible representation of 0 group, Koster et al [8].

18


absorption spectra of3H6 to 3F 4 levels of 6Tm3 ÷ in TmAs, 12

assuming aLorentzian line shapewith AE = 3 cmn1 : f(a) T = 4.2 K,(b) T = 77 K, and 4

(c) T = 300 K. 1560 5640 5680 5720 5760 580 584

Energy (cn-1)

(b) (c)150- 160

125

0 40

25 14

0 05600 5640 5680 5720 5760 5800 5840 5600 5640 5680 5720 5760 5800 5840Energy (cn-r) Energy (c=-4)

Table 13. Predicted gvalues for r and 1r. Table 14. Experimental energy levels (cur 1 ) Table 15. Comparison of presentlevels of Tmn+ in Tm"As of Tm3+ in TmAs reported by Hulliger [10ja work and Hulliger (10]

No. I. R. g No.b 1. R. 1 2 3 4 Energy levels (cm- 1)

2 174 1.1755 2 r24 21.5 21.5 19.5 23.6 Level Present work 1979, Hulliger3 r. 3.5743 3 r 5 46.5 48.7 41.7 50.7 2 (14) 28.7 19.5-23.65 r 5 2.2514 4 1"2 139 101 124 152 3 (1s) 62.9 41.7-50.77 r. -5.6900 5 f15 165 162 148 181 4 (12) 145.7 101-1529 r 4 1.1394 6 173 174 174 156 190 5 (15) 201.9 148-181

11 174 -5.0612 OSee Hulliger [101 for references to experi- 6 (13) 215.5 156-19013 r5 5.1658 mental data. Hulliger's data are multiplied14 124 6.0613 by 0.6950 cm- 1/KaSee Morrison et al [3J bNumbers correspond to table 12: groundfor definitions of g values, state is r,.

19

7.5 Yb in YbAs

The energy levels and free-ion wavefunction composition for the two multi-plets, 2F7/2 and 2F 5/2, of Yb 3+ in YbAs are given in table 16. TheJ mixing bythe crystal field is negligible, and each level is practically 100 percent of thatmultiplet (99.99 percent). The absoTtion spectra for the transitions betweenthe energy levels of the F7/2 to the F512 were computed using equation (4)with 1 s i :s 3 and 4 sj j: 5 (table 16) and are shown in figure 8 for T= 4.2,77, and 300 K. The g values for each level are given in table 17. The energylevels of the 4F7/2 have recently been determined by inelastic neutronscattering in 1990 by Kohgi et al [11]. They report the first excited state, F8,at 144 cm-1 at T= 14 K, and at 200 K they report the r8 at 152 cm-1 and theF7 at 340 cm- 1. In 1991, Donni et al [12] reported the "8 at 141 cm- 1 and theF7 at 331 cm-l; these measurements were made over a temperature range of40 to 295 K. Both Kohgi et al [11] and Donni et al [12] found theirexperimental data consistent with a r6 ground level. We calculated the linestrength for the F6 -- F8 to be 558 x 16-23 cm 2 and the F 8 -. F8 line strengthto be 358 x 10-23 cm2 , which qualitatively agrees with the plots of Donni etal [12].

Table 16. Predictedenergy levels and free- N' Ceniroidc I.R.' Energy Free-ion mixture (%)ion mixture for W4 (cm-)in YbAs4 1 250 r 6 0.0 100.00 2F

2 r8 128.6 99.99 2F/2 + 0.01 2F5/23 r 7 293.7 99.99 2F7 2 + 0.01 2F5 2

4 10450 r. 10272.9 99.99 2F5/2 + 0.01 2F7/25 r 7 10471.8 99.99 2F5/2 + 0.01 2F7/2

aB40 = 697.0 andB6o = 49.85 cm-1.bNWmbers to designate levels used in discussion.cAqueous centroids.dlrreducible representation of 0 group, Koster et al [8].

I

20!

Figure S. Predicted (a) 4

absorption spectra of2 v to 2F. levels ofYb 3 I÷n YbAs,

assuming a 2

Lorentzian line shapewith AE = 3 cm-1 :

(a) T = 4.2 K, 1

(b) T= 77 K, and S(c) T-- 300 K. 0 4---99 100 1601 102 103 104 105

Energy (cm-n)

(b) 30' (C) 15.0

25 12.5

0 10.0o

15. 7.5

10. 5.0

-5. -S 2.5.

99 100 101 102 103 104 105 99 100 101 102 103 164 10Energy (c-1) Energy (cm-1)

Table 17. Predicted g No 1. R. 91values for I'r, 177, and No.__.R. __l __2

18 of Yb3+ in YbAsO 1 176 -2.667 -2 178 -4.179 -1.1553 "7 - 3.4194 178 0.8442 3.1535 r7 - -1.417

"aSee Morrison et al [3] fordefinitions of g values.

21

8. Conclusion

We have used a crystal-field Hamiltonian appropriate for a rare-earth ion inoctahedral cubic symmetry and varied two crystal-field parameters, B4o andB60, to obtain the best fit to the experimental data of Schneider et al [2] takenon Er3* in ErAs. We also calculated the optical absorption data and obtainedexcellent agreement with the results of their traces taken at 5, 74, and 300 K.

Using scaling and interpolation procedures, we obtained phenomenologicalAn, for the entire LnAs series (Ln = La to Lu). No attempt at a morefundamental theory of the A,. (such as given in 1991 by Stevens andMorrison [13]) was considered. The phenomenologicalAnm then yielded Bnfor the LnAs series from which energy levels below the band gap of GaAs, gvalues, and multi[let branching ratios were calculated for the rare-earth ionsTb3, through Yb +. The energy levels of the ground multiplet of Tm3 ÷ andYb3+ in their respective arsenide compounds are in reasonable agreementwith the energy levels determined by inelastic neutron scattering experi-ments. Calculated absorption sfectra at 4.2 to 300 K are also given for thelowest lying multiplets for Tb + through Yb3+ in their respective arsenidecompounds. The g values for all the levels in all the compounds are calculated.

Acknowledgements

Greg Turner, Wayne Lee, and Baruch Sheinson are thanked for their help withthe calculations and graphing.

22

References

1. W. T. Tsang and R. A. Logan, Appl. Phys. Lett. 49 (1986), 1686.

2. J. Schneider, H. D. Miller, J. D. Ralston, F. Fuchs, A. D6rnen, and K. Thonke,Crystal-Field Splittings ofEr3 + (4# 1) in Molecular Beam Epitaxially GrownErAs/GaAs, Appl. Phys. Lett. 59 (1991), 34.

3. C. A. Morrison, D. E. Wortman, and R. P. Leavitt, J. Chem. Phys. 73 (1980),2580. (This paper should be consulted for a complete detailed description ofthe methods used in the analysis presented here.)

4. C. A. Morrison and R. P. Leavitt, J. Chem. Phys. 71 (1979), 2366.

5. R.W.G. Wyckoff, Crystal Structures, vol.1 (1968), 85-91.

6. W. T. Carnall, P. R. Fields, and K. Rajnak, J. Chem. Phys. 49 (1968), 4412,4424, 4443, 4447, and 4450 (five consecutive papers).

7. K. R. Lea, M.J.M. Leask, and W. P. Wolf, J. Phys. Chem. Solids 23 (1962),1381.

8. G. F. Koster, J. 0. Dimmock, R. G. Wheeler, and H. Statz, Properties of theThirty-Two Point Groups, MIT Press, Cambridge, Massachusetts (1963).

9. R. P. Leavitt, C. A. Morrison, and D. E. Wortman, Rare Earth Ion-HostCrystal Interactions 3. Three Parameter Theory of Crystal Fields, HarryDiamond Laboratories, HDL-TR-1673 (June 1975).

10. F. Hulliger,RareEarthPnictides, inHandbook on the Physics and Chemistryof Rare Earths, ed. K. A. Gschneidner, Jr., and L. Eyring, vol. 4 (1979), 153.

11. M. Kohgi, K. Ohoyama, A. Oyamada, T. Suzuki, and M. Arai, Physica B163(1990) 625.

12. A. Donni, A. Furrer, P. Fischer, F. Hulliger, and P. Wachter, Physica B171(1991), 353.

13. Sally B. Stevens and Clyde A. Morrison, Theoretical Crystal-Field Calcula-tions for Rare-Earth Ions in III-V Semiconductor Compounds, Harry Dia-mond Laboratories, HDL-TM-91-16 (October 1991).

23

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Attn: AMSLC-DL, Dir Corp Labs Atn: SLCHD-ST-AP, R. TeaitAttn: SLCHD-ST-AP, R. Leavitt

Installation Support Activity Attn: SLCHD-ST-AP, R. ToberAttn: SLCIS-CC-IP, Legal Office Attn: SLCHD-ST-AP, T. Bahder

USAISC Attn: SLCHD-ST-OP, C. Garvin

Attn: AMSLC-IM-VA, Admin Ser Br Attn: SLCHD-ST-OP, J. GoffAttn: SLCHD-ST-R, A. A. BencivengaAttn: AMSLC-IM-VP, Tech Pub BrAn:LHDT-PChe

(2 copies) Attn: SLCHD-ST-SP, ChiefAttn: SLCHD-ST-SP, J. Nemarich

Harry Diamond Laboratories Attn: SLCHD-ST-SS, ChiefAttn: Laboratory Directors Attn: SLCHD-TA-AS, G. TurnerAttn: SLCHD-CS, Chief Scientist Attn: SLCHD-TA-ET, B. ZabludowskiAttn: SLCHD-NW-EH, Chief

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