The spectrum of Nd3+ in rare earth orthoaluminates. The trigonal to orthorhombic transition study of the 2H112 level

.I. Phys. Chem. Solids Vol. Printed in Great Britain.

50, No.

12, pp. 1227-1235,

0022-3697/89 $3.lNl+ 0.00 0 1989 Pergamon Press plc

1989

THE SPECTRUM OF Nd3+ IN RARE EARTH ORTHOALUMINATES. THE TRIGONAL TO ORTHORHOMBIC TRANSITION STUDY OF THE 2H,,,2 LEVEL M. FAUCHER, D. GARCIA, E. ANTIC-FIDANCEV and M. LEMAITRE-BLAISE ER 60210, CNRS, 1 Pl. A-Briand, 92195 Meudon-Ctdex, (Received

France

17 April 1989; accepted in revised form 13 July 1989)

Abstract-Some structural and spectroscopic features of rare earth orthoaluminates are examined. The trigonal+orthorhombic transition is studied in a series of Nd,Sm,_,AlO, compounds. The evolution of the crystal structure is followed by X-ray analysis and optical absorption. The free ion and crystal field parameters of Nd3+ (4f3 configuration) are determined in LuAlO,:Nd)+. The anomaly of the calculated splitting of the *H(2),,,, levels is slight, but well characterized in NdAlO, The spin correlated crystal field and orbitally correlated crystal field models are tested as well as an empirical correction which was proposed earlier. Keywords: Neodymium spectroscopy, absorption spectrum, crystal field analysis, 2H,1,2 level, rare earth aluminates, phase transition, correlated crystal field.

1. INTRODUCTION and the compounds YAlO, : Ln3+ have stimulated interest as potential laser materials with special regard for their anisotropic optical properties. The LnAlO, compounds can be synthetized by solid state reaction of the oxides at high temperature. Some care must be taken to avoid the formation of the garnet when dealing with the smallest rare earths (Yb, Lu) [l]. LaAlO,, the first compound in the series, belongs to the D$-Rye space group at room temperature [2,3]. The compounds following along the series down to NdAlO, display the same structure, but are somewhat more distorted than LaAIO,. A structural change occurs between NdAlO, and SmAlO,. The latter is orthorhombic (space group Dig-Pfmm) as are the compounds following the series down to Lu. This second group also includes YAlO,. Structural data are available at room temperature for NdAlO, and SmAlO, [4,5], and YAIOj [6]. Optical studies of neodymium-doped orthoaluminates have already been reported for LaAlO, [7,8], NdAlO, [9, lo], GdAlO, [l 11,YA103 [12, 131, and LuAlO, [14,15]. One purpose of this paper is to present some structural features of the trigonal-+orthorhombic transition studied in a series of Nd,Sm, _,AlO, compounds with 0 < x < 1 (Section 2). The evolution of the 2H(2),1,2 and 4F9,2 levels from LuA10,:Nd3+ to NdA103 is shown in Section 3. In Section 4, we focus on the last compound in the series, i.e. LuAlO, :Nd3+. Ninety-eight spectral lines Rare earth

aluminates

LnAlO,

are utilized in a crystal field refinement of the oneelectron crystal field parameters within the C.Vpoint symmetry group. The empirical correction we proposed earlier [16, 17] in order to match experimental and calculated 2H(2),,,, energy levels proves to be effective in this particular case as well. NdA103, quite close to the cubic structure, is used in Sections 5 and 6 to test possible corrections to the one-particle crystal field Hamiltonian in order to remove the discrepancy of the calculated 2H(2),,,2 levels. The configuration interaction is investigated as a possible physical mechanism. The two-electron SCCF (spin correlated crystal field) and LCCF (orbitally correlated crystal field) parameterizations [18-201 are also applied with success. However, the order of magnitude of the correction, if satisfactory in NdA103 is not sufficient when the same procedure is applied to Nd,O, where the discrepancy is far more pronounced.

2.

TRIGONAL + ORTHORHOMBIC TRANSITION

The distortion of trigonal orthoaluminates with respect to the ideal cubic structure decreases when the temperature is raised or when the rare earth radius increases. LaAlO, becomes cubic (space group Pm3m with an Oh site for the rate earth) at 700 K. In the same way, the rhombohedral distortion of NdAlO, diminishes as the temperature rises. The compounds following in the series, from Sm to Lu are orthorhombic.

1227

1228

M. FAUCHER et al.

Following Glazer’s classification of octahedral tilting in perovskites [21], Piriou et al. [22], studying the LaAlO,/EuAlO, system, assumed that in the trigonal+orthorhombic transition, two elementary octahedral rotations would be unchanged while only the third one would flop over. This mechanism could possibly explain the smooth variation of some Eu’+ fluorescence lines as in a second order transition. In order to follow the phase transition between Nd and SmAlO,, polycrystalline Nd,Sm, _. AlO, samples with x = 0.08, 0.20, 0.65, 0.80 and 1.00 were prepared by solid state reaction of the oxides at about 2000 K during 12 h in a zirconia furnace [23]. We assume that neodymium and samarium ions statistically distributed throughout the samples behave like cations with a mean radius equal to x .rNd+(l -x).rSm. On the whole, the Guinier X-ray diffraction patterns seem to change smoothly from x = 0 to x = 1. Only a few details reveal a jump of the structure and not a gradual change. For compositions with x ranging between 0.80 and 1.00, the X-ray patterns seem to correspond to a pure rhombohedral phase, and for x lower than 0.65 to a pure orthorhombic phase. The transition takes place at room temperature between x = 0.8 and x = 0.65. For these compositions, the powder patterns exhibit a few more lines than can be refined on a unique cell basis.

Equivalent related by:

trigonal and orthorhombic

h,=

1

k, = I, =

1

0

h,

l/3

l/3

k,

-213

l/3

-l/3 i

213

indices are

I

I,.

For x = 0.80, orthorhombic line (022) appears weakly, close to the trigonal line (006), which fades away for x = 0.65. In the same way, orthorhombic (132) which is faint for x = 0.8 strengthens and supersedes trigonal (018) for 0.65. Except for these two couples of lines, all the other observed lines display quite similar positions and strengths in both patterns. We deduce: firstly that the orthorhombic and rhombohedral phases co-exist between x = 0.80 and 0.65, the trigonal phase being prominent for x = 0.8 whereas the orthorhombic phase prevails for x = 0.65, and secondly that the two-dimensional arrangement of atoms in both structures in a (001) (trigonal) or (011) (orthorhombic) plane must be quite similar. Figure 1 shows the atoms which are located in, or close to, a trigonal (001) plane containing rare earths. The atomic positions are those determined by Marezio et al. [5]. The trigonal and orthorhombic cell

oxygen rare earth

orthorhombic

phase

oxygen trlgonal phase rare earth

0

Q Fig. 1. Atomic positions in NdAlO, with x = 0.8 (trigonal phase) and x = 0.65 (orthorhombic phase). The projection is made on a (001) trigonal or (011) orthorhombic plane containing rare earths. The height of the atoms above the plane is indicated. The periodic two-dimensional pattern is outlined as well as the part of the rare earth coordination polyhedron which lies in the plane.

1229

The spectrum of NdS+ in rare earth orthoaluminates

147ooc

La

1 1.

0.92

1

t

1.270

0.6

0.65 t

,I 1.265

1.260

0.5

t 1.255

0.35 t 1.250

0.20 t &Al 1.245

Fig. 2(b)

Fig. 2(a)

Fig. 2. (a) Experimental “Fgi2levels in LuA10,:Nd3+, YA10,:Nd3+, GdAlO,:Nd’+, the Nd,Sm, _,AlO, compounds and LaAIOj:Nd’+ (indicated for short as Lu, Y, Gd, Nd and La at the top of the arrows). The x coordinate gives the mean cationic radii of the samples. The magnification of the transition area is given in (b). (b) Experimental “Fgi2levels in the Nd,Sm, _,AlO, compounds (transition area). The x values are indicated at the top of the arrows.

parameters refined the following:

from X-ray

for x = 0.8 (trigonal a = 5.325(4) A;

powder

are

phase):

c = 12.913(S) A;

for x = 0.65 (orthorhombic

a = 5.319(4) A;

patterns

phase):

b = 5.296(4) A;

c = 7.482(6) A. The dimensions of the rectangular periodic pattern on the trigonal (001) plane are similar: 5.325(5) A x 9.223(8) A for the trigonal phase, and 5.319(5) A x 9.166(8) A for the orthorhombic

phase.

The rare earth frames of both structures projected on a (001) trigonal plane are practically coincident over large distances which suggests for these x values, a possible epitaxial crystal growth of the two phases along the trigonal [OOl] direction.

3. ELECTRONIC

ENERGY LEVELS

The optical absorption spectra at 4K of LuA10r:Nd3+, YA10X:Nd3+, GdA10r:Nd3+ and Nd, Sm, _. AlO, samples were recorded between 11,000 and 33,000 cm-‘. The spectral lines are essentially transitions originating from the lowest sub-level of 4I9,2. As an example, the evolution of the 4F9,2 and 2H(2),,,2 energy levels with respect to the ground state is represented on Figs 2 and 3, respectively, as a function of the mean rare earth radius. In addition to the above quoted compounds, we have also plotted the levels of LaA10,:Nd3+ from Ref. 7. Figures 2(a) and 3(a) display a global view across the rare earth series while Figs 2(b) and 3(b) show a magnification of the transition zone between SmalO, and NdA103. The 4Fsi2levels are more affected than the ‘H(2),,,, set by the phase transition. Only one sub-level crosses the boundary smoothly, whereas the four other energy positions change abruptly. The Sm3+ transitions appearing in the Nd,Sm,_,AlO~ spectra were identified and not taken into account. The ionic radii chosen for La3+, Nd3+, and Sm3+ are Shannon’s values for a coordination number equal to 12 [24]. The structural data of YAlO, were used to estimate the ionic radii of Y3+ in a twelve-fold coordination (1.19 A), on the basis of the empirical relationship between interatomic distances and bond

M. FAUCHER et al.

1230

strengths described in Ref. 25. Finally, the ionic radii of Gd3+ and Lu3+ were reasonably extrapolated to CN = 12 yielding the values 1.22 and 1.15 A, respectively. The ionic radii in Figs 2 and 3 are mean values taking into account the global composition of the samples. The X-ray patterns of the mixed oxides seem to show that the phase transition occurs between x = 0.65 and 0.8 (for x = 0.8, the mean rare earth radius is equal to 1.264 A) but the spectroscopic data at 4 K suggest that for x = 0.8, the major part of the Nd,Sm, _ .A103 compound is already orthorhombic. This is consistent with the fact that a lowering of the temperature favours the orthorhombic phase. 4. CRYSTAL

FIELD PARAMETERS LuAIO, : Nd3+

OF

The LuA103:Nd3+ polycrystalline sample was obtained by over-heating a liquid droplet of the stoichiometric mixture in an aerodynamic levitation device associated with a 350 w CO, laser. The apparent temperature was about 2900 K and the melting time was about 2min for a 5@-100mg sample [26]. The absorption spectrum was recorded at 4 K from 11,000 cm-’ up to 33,000 cm-’ by means of a 3.4 m Jarrell Ash spectrograph. The experimental data are listed in Table 1 together with the values of the low lying 41i,1,and 4I,3,2energy levels from Ref. 13 which were also used in the refinement process.

Free-ion and crystal field parameters (cfp) were refined by means of IMAGE [27]. Fourteen free ion parameters were varied, i.e. the electrostatic ED, El, E*, E3 Racah parameters, tl, p, and y Trees parameters, T2, T3, T4, T6, T’and T* Judd parameters and the spin-orbit coupling parameter 5. Further, the point site symmetry allows 15 crystal field parameters, i.e. Bi, Bi, S:, Bi, B:, S:, B:, S:, Bi, Bi, $9 B:, Sk B:, and Sz. The free-ion parameters of NdAlO, were used as a starting set for LuA103:Nd3+. A set of starting cfp values was obtained using the structural data of YAIO, [6] and the point charge electrostatic model. A 35.6 degrees rotation was performed around the z crystallographic axis in order to cancel Sz. The calculated parameters were multiplied by the adequate correction factors for NdAlO, (R, = 0.43, R, = 1.38 and R, = 3.29) [28]. The experimental and calculated energy levels are listed in Table 1, and the final free-ion and crystal field parameter values are gathered in Table 2. The overall mean deviation is equal to 11.5 cm-’ for the 98 levels. We have grouped in Table 3, cfp of various origins: ab initio electrostatic values for YAIO,:Ln’+ [29]; two refined sets for YA103:Ln3+ [30, 311; our ab initio starting set; and lastly our final refined values for LuA103:Nd3+. The five sets of values diverge. There is a large difference between one fitted set for

16100 -

16100

16000

t

15900-

La 1.270

Fig. 3(a)

1.285

1.260

1.255

1.250

Fig. 3(b)

Fig. 3. (a) Experimental *H(2),,,, levels in LuA103:Nd3+, YA103:Nd3+, GdA103:Nd3+, the Nd,Sm, _ ,AlO, compounds and LaA103:Nd3+. (b) Experimental ‘H(2),,,, levels in the Nd,Sm, _ ,AlO, compounds (transition area).

1.245

1231

The spectrum of Nd3+ in rare earth orthoaluminates

[30] and our set for LuA103:Nd’+. The parameters refined by Deb [31] seem closer but some opposite signs in fact give rise to quite different energy values. However, the crystal field strengths are not too different: 188,272 and 295 cm-’ (k = 2,4 and 6, respectively) for YA10,:Ln3+ in Ref. 30, and 170, 246 and 288 cm-’ for the same compound in Ref. 31, whereas for LuA10s:Nd3+, we find 200, 261 and 318 cm-‘.

5. THE

YAI0,:Ln3+

Exp. 0

Calc.

Exp.-Calc.

12 124 225 490 661

-12 -4 2 -3 1

2159t 2241t 2317f 2378t

2019 2106 2l51 2254 2319 237%

39577 4022t 4102t 4202t 4287f 4327f 4442t

3956 4033 408% 4189 4281 4336 443%

-11 14 13 6 -9 4

11391 11530

11379 11485

12 45

12393 12440 12494 12544 12578 12699 12736 12868

12374 12435 12501 12543 12580 12702 12760 12884

19 5 -7 1 -2 -3 -24 -16

‘4,~

13294 13430

13310 13439

-17 -9

“‘G

I3538 13560

13546 13556

%*

13577 13633

13575 13633

4F,,

14634 14698 14717 14780 14912

14652 14702 I4724 14794 14932

15841 1587% 15883 15979 1598% 16071

15839 1586% 15880 15954 is977 16078

16921 16996 17102

16925 1700% 1709%

17265 I7285 I7335 17441

17254 17292 17327 1742%

4f,i,

120 227 487 65.5 2020t 2097t

%I,2

4F5!2 + 2w2)9:z

-6 -9

The set of 2H(2),,,2 calculated values is usually a miniature reproduction of the experimental set. This unexplained phenomenon is all the more pronounced as the fourth order crystal field parameters are strong with respect to the second and sixth Table l-continued EXP.

Calc.

%,2

18809 18855 18930 19046

18796 1885I 18941 19060

13 4 -11 -14

19189 19278 19325

19180 19282 19340

9 -4 -15

19390

19394 19417 19476 19516 19538

-4

19619 19723 19865 19901

19616 19707 19844 19916

3 16 21 -15

20815 20844 20876 20912 20956 20992 21069 21185 21269 21331 21442 21499 21554 21620 21725 21826 21869 21902

20812 20837 20867 20922 20946 21000 2lO68 21205 21257 21320 21425 21495 21563 21620 2I743 21808 21874 21896

3 7 9

23313

23105

8

23576 23705

-10 12

25927 26073

23586 23693 23847 25933 2607 1

27583 27669

27601 27674

-1% -5

278.51 27933 28212

27830 27933 2819%

+ 24z 2&3,*

-2 “Gw

19473 19522

1

243/2

*G,2

+4G,,,,

-8 4

-1% -4 -7 -14 -20

432. 2P,,2

2 10 3 25 11 -8 -4 -12 4 II -7 8 I3

Exp.-Calc.

Enersv level

8 7 0

NdAIO,

AND LuA10,: Nd3+

5.1. NdA103

Table 1. Experimental and calculated energy levels Energy level

‘W),,,z LEVELS IN

%,z

28386

28396

ZL1512

29747

29743

32905 33001

32905 33017

‘D(2)3,2

t Experimental levels from Ref. 13.

-3 6

-10 10 -8

1 -20 I2 11 17 4 -9 0 -18 18 -5 6

-6 2

21 0 14 -10 4 0 -16

M. FAUCHER et al.

1232

order parameters [16, 171. For B4/(B2 + B6), with

NdA103,

calculated and experimental 2H(2),,,2 energy values reported in Ref. 10 fit passably well [Fig. 4(a)]: the experimental splitting of the levels amounts to 190cmand the calculated one to 156cm-‘. The discrepancy is far from being as flagrant as for Nd,O, where calculated and experimental splittings amount to 97 and 280cm-‘, respectively [32]. However, NdA103 is a good test material to analyse the discrepancy. Its point symmetry is close to 0, and the experimental energy spectrum, characteristic of a distorted cubic environment, permits an unambiguous identification of singlets and weakly split doublets, designated by A and E for convenience. A detail in the energy sequence of the 2H(2),,,, level shows precisely where the failure of the calculation is: it proposes for the six 2H(2),,i, levels the succession of E, A, E, and A representations, while the experimental scheme imposes A, E, E, A. This anomaly seems to be unique throughout the analysed range of the spectrum. Any theoretical or empirical modification of the salculation must not only ensure a 20% increase of the overall splitting, but also reproduce the correct experimental representation sequence. Among the physical processes which are not taken into account by the one-electron parameterization of the crystal field, we had the feeling that configuration interaction could be responsible for a great part of the calculated discrepancy of the 2H(2),,;2 levels. In fact this assumption seems to be invalidated by two evidences, the first due to computer simulation, the second one to direct experimental observation: (a) A full calculation involving the 4f3 configuration and the nearest excited configuration 4f25d’ mixed together by odd cfp chosen within a “reasonable” range of values (see the Pr3+ example in Ref. 33) did not invert the A and E misplaced representations.

the ratio

is equal to 0.28 which is the smallest value we found for all the compounds we investigated so that Table 2. Refined crystal field parameters of LuAlO,:Nd’+

Parameters

Value (cm-‘) 13,023 4879 23.02 476.0 20.18 -595.5 742.5 294.4

+1 0.6 0.01 0.1 0.03 0.8 2.4 2.1 2.1 5.0 5.9

41.1 97.6 - 269.2 312.4 221.6 873.5

sg

0.5

-265 584 0

24 I1

- 384 928 -141 -356 -777

44 27 24 23 38

-606 555 -121 1509 - 147 -51

46 48 44 64 20 53

-87

38

Number of Stark levels: 98. Mean deviation (cm-‘): 11.5

Table 3. Crystal field parameters of Nd’+ in orthoaluminates Parameters (cm- ‘)

(3)

(2) YA10,Nd3+

(1)

Ab-initio

(4) (5) LuAlO,:Nd’+ Ab inifio Refined

Refined .A

51 sf

-6320 -174

B: B: ;:

-588 -184 364 -6

S;

337

’

-177 504 ’ 0

-128 464 0

-265 584 0

-1345 521 -214 525

-436 710 -388 208

-305 697 - 748 -433

-384 928 -356 -141

575

843

-709

-777

-928

- 606

405 66 1478 -1189 -115

- 555 121 1509 - -51 147

-127

-87

814 18 0

B:

-789

-1110

-813

;a 8: ;:

-221 138 -1529 -884 120

-155 348 1214 -22182

-55 512 1251 - 344 143

St

70

370

81

(1) Ab initio values for YAlO,Nd )+ from Ref. 29; (2) and (3) refined cfp of YA101:Nd3+ from Refs 30 and 31: (4) electrostatic values for LuAlO,:Nd’+ multiplied by 0.43, 1.38, and 3.29 for k = 2, 4 and 6, respectively; (5) refined values for LuAIOX:Nd”+ (this work).

____ ____ ----__ -----._ -----_ 1____ 1233

The spectrum of NdS+ in rare earth orthoaluminates

(b)

(4

T

. NdAlO 3

. LuA103:Nd"

__--

_-’

‘*

__--

---.__

--_

-.

--.

*-_.

--._

‘.

--.

---.__

a.

--....1_

_____---------_____

;.i

.‘_-

__--,

8’

____.----

u(/4

OBSERVED

LEVELS

NORMAL

CALCULATED

TABLES

LEVELS

-

u( /4

OBSERVED

LEVELS

NORMAL

CALCULATED

TABLES

LEVELS

Fig. 4. The observed and calculated (with normal and modified U“ tables) *H(2),,,, levels in: (a) NdAlO,; (b) LuA103:Nd3+.

(b) If configuration interaction with opposite parity excited configurations was the physical mechanism responsible for the discrepancies stated between experimental and calculated levels, this discrepancy would vanish for symmetries forbidding configuration mixing via odd k crystal field parameters, namely for the cubic point symmetry. We compared the experimental 2H(2),1,2 energy levels of NdAlO, with those of LaA103:Nd3+ at room temperature. The latter compound is closer to cubic than NdA103. In fact, the representations appear in the same order in both compounds and the overall splitting of the level is even slightly larger (5%) for 2fwh,,2 LaA103:Nd3+ which is opposite to what we would expect if configuration interaction had an appreciable influence on this particular level. We temporarily put aside the idea of finding the physical reason of the phenomenon and we tried empirical changes in the calculation. The manipulations which proved to be successful in reproducing the correct representation sequence were finally the following: -either multiplication of the reduced matrix element of U4 between 2H(1) and 2H(2) by 3112. ---or division of the reduced (H(2) IIU4 /I2H(2)) by four.

matrix

element

--or multiplication of elements by seven.

reduced

matrix

both

The first two manipulations give practically identical results and a better experimental/calculated match than the third. The result for NdAlO, is shown in Fig. 4(a). The remarkable fact is that the procedure works not only for one compound but, applied to nine other neodymium compounds, it removes from 80 to 100% of the discrepancy [17]. 5.2. LuAlO,: Nd3+ Figure 4(b) represents the experimental levels and the calculated scheme with “normal” U4 tables. The observed and calculated splittings AE, and BE, amount to 230 and 153 cm-‘, respectively. If the reduced matrix element U4 between ‘H(2) and ‘H(2) is divided by four, the overall calculated splitting of the 2H(2),,,2 levels climbs to 240 cm-’ and the match between experimental and calculated energy levels becomes rather good. The ratio B”/(B’ + B6) is equal to 0.69. This ratio when plotted against AE,,/AE (= 1.38) fits nicely close to NdOCl and NdF3 on the curve plotted in Fig. 6 of Ref. 16.

6. SPIN CORRELATED AND ORRITALLY CORRELATED CRYSTAL FIELD MODELS

The spin-correlated crystal field model [19] provides a practical approach to account for spin dependent radial eigenfunctions and hence deals with

M. FAUCHER et al.

1234

discrepancies experimental/calculated affecting low spin energy levels. A similar idea led to the orbitally correlated crystal field model [20] which was applied with success to the deviant ‘D, level of LaCl,:PP+. Both models were applied to the NdAlO, case. We use a Slater determinants-based routine which is extremely convenient for testing one- or twoelectron models without the constraint of using tables for coupled states [33]. The expressions for the matrix elements in the SCCF and the LCCF are the following: 6.1. SCCF The bi are the spin correlated crystal field parameters and obey the same symmetry selection rules as the conventional cfp.

-l
=

C

(-l)PS,(i).S_p(j).C:(i).b~.

k>y

The interaction matrix element for f spin orbital functions (msi, mli) is therefore equal to:

<(ms,m,,L(m,,m,,)lHscc~l(m,,m,,), hmd) =C(_l)(p-msl-msZ-m/l)

x C--21/2). w%2,44). X

(

112 1

--m,,

P

l/2

l/2

ms3>-( - ms2

1 -P

B: (new value) = Refined(Bi)/2 bi = Refined(Bl)

x 2 (spin ccf).

(2)

For these values, the overall splitting of the 2H(2),,,2 level is equal to 169 cm-’ (experimental splitting = 190 cm-‘) and the representations appear in the correct order. The high spin (S = 3/2) levels are not affected. The energy shift of the low spin levels (S = l/2) ranges from 5 to 30 cm-‘, but no refinement was attempted, our present aim being to find a specific operator for the discrepancy of the 2H(2),,,2 levels. Since we empirically deduced that the discrepancy is all the more pronounced when the k = 4 parameters are strong, we are searching for an operator enhancing the effect of fourth order cfp and likely to be transposed to any compound. Therefore, the same procedure was applied to Nd,O,, with parameters obeying conditions (2). The final splitting of the 2H(2),r,z level was equal to 116 cm--’ which represents a 20% increase. What we need is a 200% increase. Of course we could try to fit simultaneously both sets of cfp and ccfp but then, it seems as if we were perverting our primary goal. 6.2. LCCF The two-electron expression for the orbitally correlated crystal field is the following:

l/2 ms4>

H LccF = c I(i) . I(j) . Ci (i) . dt k.4

X _‘,,,

A good result is obtained for A = Refined(Bl)/2, and therefore:

:

:,J-(i

“0

p:.

(l)

(

The p value is assigned by the non-vanishing conditions for the 3 -j symbols. For spectroscopic terms with maximum multiplicity, expression (1) reduces to:

= f (- l)pl,(i) . l_,(j).

C:(i).

dl;.

k, 4

The dt are the orbitally correlated crystal field parameters. As the b:, they obey the same symmetry selection rules as the conventional cfp.

( - 1Y” . (7/4) .6 b2, m ) =C(_l)(P-ml-m2-ml which is just four times less than the matrix element of the conventional one-electron crystal field. Since our previous observations show that mainly the fourth order parameters need some corrections, we restricted our investigations to combinations of fourth order crystal field and correlated crystal field parameters (ccfp) which do not affect the good agreement of the experimental/calculated high spin level values. Following the former statement, these combinations are just: B4,+ Refined(B:) b; + 4.A.

- A

a@,,.m,,)

x 588~6(m,,,4. I X -

X

ml2

(‘,

1 -P

1 >( 94

1 -ml1

1

1

P

m>

E J.(:, “0+J:.(3)

The energies of the 4I levels are unchanged the following combinations are used: Bi -+ Refined(B:) -t A d;+

A/12.

when

The spectrum of Nd ‘+ in rare earth orthoaluminates For NdAlO,, a correct order of the representations is obtained for A = Refined(B:) and therefore: B:

(new value) = Refined(Bi)

x 2

di = Refined(B:)/12

(orbitally ccf). (4)

The overall *H(2),,,, splitting is equal to 171 cm-‘. Again, the same procedure is applied to Nd203, yielding a splitting equal to 111 cm-‘, which is also unsatisfactory since the experimental value is equal to 280 cm-‘.

7. CONCLUSION

The trigonal+orthorhombic transition in orthoaluminates was studied in a series of Nd,Sm, _, AlO, compounds. At room temperature, the phase transition occurs for x ranging between 0.65 and 0.8. The evolution of the X-ray patterns and a projection of both structures suggests a possible epitaxial growth of the two phases along the trigonal [OOl] direction. The ab initio electrostatic values are used as a starting set for the refinement of the crystal field parameters of LuAlO, :Nd3 + . We also focused on the anomalous calculated splitting of the *H(2),,,, levels. The defect is weak, but well characterized in NdA103 whose spectra retain the features of a distorted cubic compound. We tried unsuccessfully to correct the anomaly by employing direct configuration interaction. The spin correlated crystal field and orbitally correlated crystal field models succeeded in correcting the anomaly in NdAIO, but were unsatisfactory when applied to Nd,O,. We simply transposed the procedures which were effective for NdA103 to the case of Nd203 where the discrepancy amounts to 200%. Some more work could be done on the matter, since we have not tried to adjust the correlated crystal field parameters in the Nd203 case in order to improve the experimental/calculated agreement. Acknowledgements-The

authors are grateful to Dr J. P. Coutures who provided the LuAlO,:Nd’+ sample and to Dr P. Percher who gave access to his refinement program IMAGE. The numerical calculations were performed on the Norsk-Data 56OCX computer of Laboratoires de BellevueCNRS.

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REFERENCES 1. Anan’eva G. V., Ivanov A. O., Merkulyaeva T. I. and Mochalov I. V., Soviet Phys. Crysrallogr. 23,101 (1978). 2. De Rango C., Tsoucaris G. and Zelwer C., Cr. Acad. Sci. Paris 259, 1537 (1964). 3. De Raneo C.. Tsoucaris G. and Zelwer C.. Acfa crystallog;. 20;590 (1966). 4. Geller S. and Bala V. B., Acfa crystallogr. 9, 1019 (1956). 5. Marezio M., Dernier P. D. and Remeika J. P., J. solid St. Chem. 4, 11 (1972). 6. Diehl R. and Brandt G., Muter. Res. BUN. lo,85 (1975). 7. Martin-Brunetiere F., C.r. Acad. Sci. Paris B279, 719 (1969). 8. Bagdasarov Kh. S., Bogomolova G. A., Gritsenko M. M., Kaminski A. A. and Kevorkov A. M., Sovier Phys. Crystallogr. 17, 357 (1972). 9. Finkman E. and Cohen E., Phys. Rev. B7,2899 (1973). 10. Antic-Fidancev E., Lemaitre-Blaise M., Beaury L., Teste de Sagey G. and Caro P., J. them. Phys. 73,4613 (1980).

11. Arsenev P. A. and Bienert K. E., Phys. Status Solidi (a) 9, K53 (1972). 12. Weber M. J. and Varitimos T. E., J. appl. Phys. 42, 4996 (1971). 13. Kaminskii A. A., Laser Crystals, p. 128. Springer, New York (1981). 14. Ivanov A. O., Morozova L. G., Mochalov I. V. and Feofilov P. P., Opt. Specrrosc. 38, 230 (1975). 15. Kaminskii A. A., Ivanov A. O., Sarkisov S. E., Mochalov I. V., Fedorov V. A. and Li L., Soviet Phys. JETP 44, 516 (1976). 16. Faucher M., Garcia D., Caro P., Derouet J. and Caro P., J. Phys. France 50, 219 (1989). 17. Faucher M., Garcia D. and Percher P., C.r. Acad. Sci. Paris 11-308, 603 (1989). 18. Judd B. R.. Phvs. Lett. 39. 242 (1977). 19. Crosswhite’H. and Newman D. J., J.‘chem. Phys 81, 4959 (1984). 20. Yeung Y. Y. and Newman D. J., J. them. Phys. 86, 6717 (1987). 21. Glazer A. M., Acta crystallogr. A31, 756 (1975). 22. Piriou B., Halwani J. and Dexpert-Ghys J., Sci. Cerum. 14, 473 (1988). 23. Faucher M., Dembinsky K. and Anthony A. M., Am. Ceram. Sot. Bull. 49. 707 (1970). 24. Shannon R. D., Acta crystallogr. A32, 751 (1976). 25. Brown I. D. and Shannon R. D., Acta crystallogr. A29, 266 (1973). 26. Coutures J. P., Rifflet J. C., Billard D. and Coutures P., E.S.A. SP256, 427 (1987). 27. Percher P., Program IMAGE (unpublished). 28. Faucher M. and Garcia D., Phys. Rev. B26,5451 (1982). 29. Aminov L. K., Kaminskii A. A. and Chertanov M. I., Phys. Status Solidi (b) 130, 757 (1985). 30. Karayanis N., Workman D. E. and Morrison C. A., Solid St. Commun. 18. 1299(1976I

31. Deb K. K., J. them. Solids 43, 819 (1982). 32. Caro P., Derouet J. and Beaury L., J. them. Phys. 70, 2542 (1979). 33. Garcia D. and Faucher M., J. them. Phys. 90, 5280 (1989).