Theory of the 4d → 2p and 4f → 4d X-ray emission spectroscopies in rare-earth compounds

Journal of Electron Spectroscopy and Related Phenomena 79 (1996) 199-202

Theory of the 4d 2p and 4f --, 4d x-ray emission spectroscopies in rare-earth compounds Satoshi Tanaka, ttaruhiko Ogasawaraa, Kozo Okada b and Akio Kotani a College of Engineering, University of Osaka Prefecture, Gakuen-cho, Sakai 593, Japan aInstitute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan bFaculty of Education, Yamaguchi University, 1677-1, Yoshida, Yamaguchi 753, Japan The 4d --* 2p x-ray emission spectra (XES) of rare-earth compounds are calculated with an impurity Anderson model with the full multiplet couplings, following the formula of a coherent second order optical process. Recent experiments are well reproduced with this model by using a constant value for the 4d core hole lifetime damping F(4d) in light rare-earth compounds. On the other hand, in heavy rare-earth compounds it is necessary to take into account the term dependence of F(4d). The 4 f ~ 4d XES of Dy203 is also investigated theoretically. The multiplet term dependence of the 4d core hole lifetime affects more drastically the spectral shape in the 4f ~ 4d XES than in the 4d ---* 2p XES. Some theoretical predictions are also given on the coincidence spectra between the 4d-XPS and 4 f -* 4d XES.

1. I N T R O D U C T I O N The electrostatic interaction between the 4d core hole and the 4f electrons is so large in the rare-earth compounds that the X-ray emission spectra (XES) due to the 4d --* 2p dipole transition ( 4d ~ 2p XES ) of these compounds have characteristic multiplet splittings [1]. In the 4d --* 2p XES, the final state is just the same as that of the 4d-XPS. Recent theoretical analysis of the 4d-XPS of rare-earth compounds has shown that a 4d core hole lifetime damping r(4d) in heavy rare-earth compounds strongly depends upon the multiplet terms in the final state, while in light rare-earth compounds this multiplet term dependence is not so strong[2]. This is because in heavy rare-earth compounds the 4d core hole decay is mainly attributed to the 4d-4f4f super CosterKronig (4d-4f4f s-CK) decay, the transition of which has the strong multiplet term dependence, while in light rare-earth compounds the 4d core hole decay is mainly governed by several Auger decay channels independent of the 4 f electrons, 0368-2048/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved PII S0368 - 2048 (96) 02836-8

such as 4d-5s5s, 4d-5s5p Auger decays and so on. Therefore, the multiplet term dependence of r(4d) in heavy rare-earth compounds is expected to make a large effect on the spectral width of the 4d ~ 2p XES. On the other hand, in the 4 f --* 4d XES, a 4d core hole exists in the intermediate state. The 4f ~ 4d XES is a competitive decay process of a 4d core hole state with the above mentioned 4d - 4 f 4 ] s - CK decay process. Therefore, the multiplet term dependence of F(4d) is expected to affect more drastically the spectral shape. It is to be noted that the intermediate state with a 4d core hole in 4f --~ 4d XES coincides with the final state of the 4d-XPS. If we measure the emitted photon energy in coincidence with the measurement of the 4d photoelectron kinetic energy, we can select a certain intermediate state. Then it is possible to extract the contribution to the emission process involved in the restricted intermediate state. Such a coincidence measurement between the 4f ---* 4d XES and the 4d-XPS (called 4f ~ 4d XEPECS hereafter) can be very useful

200 (a) Ce203 I

•

i

.

i

'

I

'

i

'

i

'

i

'

i

.

I

'

i

.

i

'

I

'

i

'

i

,

i

il

,

I

,

-180

I

.

i

.

i

.

}

I

.

i

.

~

I

.

i

,

-160 -140 280 300 RELATIVE PHOTON ENERGY (eV)

,

i

,

i

i

'

~

'

i

'

I

,

F

'

i

Ly

LB

I

320

-300

-280 -260 520 540 560 RELATIVE PHOTON ENERGY(eV)

(b) Pr203

Figure 2: The calculated results of the Lp and L~ lines of Dy203, with the constant F(4d) = 0.7eV.

-190

-170 -150 300 320 RELATIVE PHOTON ENERGY (eV}

340

(C) Dy203 •

t

'

L~

-300

i

•

i

'

i

.

i

.

i

I

'

=

.

i

'

J

.

i

'

Ly

-280 -260 520 540 560 RELATIVE PHOTON ENERGY (eV)

Figure 1: The calculated results of the L~ and L~ lines of Ce203, Pr203 and Dy203 in (a), (b) and (c), respectively, where r(4d) is a constant (0.7eV) in Ce~O3 and Pr203, while in Dy203 the term dependence of F(4d) is taken into account. Experimental results are also shown by broken lines [1]. in investigating the decay process of the 4d core hole state in rare-earth compounds. In this paper, we calculate the 4d --~ 2p XES of Ce203, Pr203 and Dy203, and 4f --* 4d XES and 4 f ---* 4d XEPECS of Dy203 with an impurity Anderson model including full multiplet couplings by following the formula of a coherent second order optical process. We consider here the situation where a core electron of the rareearth is excited to a high energy continuum by a monochromatic x-ray with a large photon energy. For the multiplet term dependence of r(4d)

in Dy203 we use the same F(4d) as determined by the theoretical analysis of the 4d-XPS[2], while a constant value is used for F(4d) in Ce203 and Pr203. As found from the theoretical analysis of 3d and 4d-XPS[3-5], the hybridization effects are important in Ce203 and Pr203, while they are not important in Dy203. Thus, for the parameter values in Ce203 and Pr203, such as the hybridization strength, the charge transfer energy and so on, we use the same values as those used in the previous analysis of 4d-XPS. We regard Dy203 as a Dy 3+ ion system, neglecting any hybridization effects, for simplicity. The Salter integrals which represent the multiplet couplings are calculated by the Cowan's program[6]. 2. 4d --* 2p XES The calculated results of the 4d --. 2p3/~ (Lz line) and 4d --* 2pl/~ (L.~ line) XES are shown in Fig.1. Experimental results [1] are also shown by broken lines. There is good agreement between the experimental and calculated spectra. In all the calculated spectra weak satellite structures appear about 20eV below the main peaks. The intensity ratio of the satellite to the main peak is larger in L.~ lines than in L~ lines, which is quite conspicuous in Dy203. Both the spin-orbit couplings of the 4d core level in the final state and the 4 f level in the initial state are key factors to make the intensity ratio of satellite to main peaks in the L.r line larger than that in the L~ line [7]. The calculated 4d ---* 2p XES of Dy203 calculated with a constant r(4d) (0.7eV) is shown in

201

'

,

I I

•

1 I

,

I I

•

I I

,

" t

'''1

(c) XPS

(b) XEPECS

I

(c) XPS

(b) XEPECS

>-

>-

i°

v

v

p

W Z oU.J

.

IH

Z oW

Z

N _ _

-20

t

I

t

..

0 20 PHOTON ENERGY(eV)

Z

z__ m

o

o I

Figure 3: The calculated results of the 4f ---, 4d XES (a), 4 f ~ 4d XEPECS (b), where the 4 f --* 4d XEPECS are calculated at several peak positions in the 4d-XPS, as shown in (c). In this figure, term dependence of F(4d) is taken into account. Fig.2. As clearly seen in the L.r line, the spectral width of the satellite is too narrow and the satellite peak is too high to reproduce the experiments. Since the low-spin final states have higher binding energies than the high-spin final states, the satellite corresponds to the low-spin final states, which have the large transition probabilities in the 4d4f4f s-CK decay [2]. Consequently the larger values of F(4d) for the low-spin than the highspin final states make the satellite more broadened than the main peak. 3. 4f --* 4d XES A N D X E P E C S In the 4 f -~ 4d XES, a 4d core hole exists in the intermediate state, which is just the same as the final state in the 4d --~ 2p XES and the 4dXPS. The calculated result of the 4 f ---* 4d XES

-20

l

I

0

t

....

2'o

I . . . . . . . . .

,{'~1

T

PHOTON ENERGY (eV)

Figure 4: The calculated results of the 4f --~ 4d XES (a), 4 f ~ 4d XEPECS (b), where the 4f --~ 4d XEPECS are calculated at several peak positions in the 4d-XPS, as shown in (c). In this figure, I'(4d) is a constant (0.7eV). of Dy203 taken into account the multiplet dependence of r(4d) is shown in Fig. 3(a), and that with use of a constant r(4d) is shown in Pig.4(a). The effect of the multiplet term dependence of F(4d) is outstanding: the spectral intensity of the highest energy peak in Fig.3(a) at 15eV photon energy is strongly suppressed compared with Fig.4(a). Thus in the 4 f ---* 4d XES the multiplet term dependence of F(4d) changes drastically overall spectral shapes, while in the 4d --* 2p XES it affects mainly the spectral broadening. The origin of each peak of the 4 f ~ 4d XES can be well specified with the 4f --~ 4d XEPECS. The calculated results of the 4 f ---* 4d XEPECS are shown in Fig.3(b) ( with the term dependent F(4d)) and Fig.4(b) ( with a constant r(4d)). The 4f --~ 4d XEPECS are calculated at several binding energies corresponding to 4d-XPS peaks, as shown in Fig.3(c) and Fig.4(c). It is found that

202 the highest energy peak of the 4 f --* 4d XES comes from the intermediate state with high binding energy about 18eV. Since the low spin intermediate state with higher binding energy have a large decay probability of the 4d-4f4f s-CK process, the 4 f ---* 4d radiative decay is overwhelmed by the 4d-4f4f s-CK decay. Therefore, the 4 f ~ 4d XES intensity from the high binding energy state is greatly suppressed. 4. S U M M A R Y We have shown that the calculated results of the 4d ~ 2p XES of Ce203, Pr203 and Dy203, and the 4 f --* 4d XES and the 4 f --~ 4d XEPECS of Dy203. The strong multiplet term dependence of F(4d) in heavy rare-earth compounds revealed by the theoretical analysis of the 4d-XPS is also important in these spectrosopies. It makes the spectral width of the satellite of the 4d --* 2p XES broadened, because the satellite corresponds to the low spin final state with a large 4d-4f4f s-CK decay probability. On the other hand, in the 4 f --~ 4d XES the multiplet term dependence of r(4d) strongly suppresses the intensity of the highest energy peak and causes the change of overall spectral shape. It is clear from the 4 f --* 4d XEPECS that the highest energy peak in the 4 f --4 4d XES is attributed to the low spin intermediate state, and that the 4 f ---* 4d x-ray emission decay is overwhelmed by the 4d-4f4f s-CK decay. The calculated results of the 4d --~ 2p XES of Ce203, Pr203 and Dy203 are in good agreement with experiments by Demekhin et al [1]. Recently, Jouda et al. have obtained experimentally the 4d --* 2p XES of rare-earth trifluorides with high resolution by using a monochromatic x-ray as an incident excitation source[8]. These experiments can be also well reproduced by the theory presented in this paper. On the other hand, 4 f --* 4d XES with the x-ray excitation has not been made as yet, because the spectral intensity is very small. Experiments of the 4 f --* 4d XEPECS may require an extremely high technique, but it can be very powerful tool in the investigation of the 4d core hole decay mechanism.

REFERENCES

1. V. F. Demekhin, A. I. Platkov and M. V. Lyubivaya, Soviet Physics J E T P 35 (1972) 28. 2. H. Ogasawara, A Kotani and B. T. Thole, Phys. Rev. B 50 (1994) 12332. 3. A. Kotani and H. Ogasawara, J. Electron Spectrosc. Relat. Phenom. 60 (1992) 257, and references therein. 4. H. Ogasawara, A. Kotani, R. Potze, G. A. Sawatyky and B. T. Thole, Phys. Rev. B 44 (1991) 5465. 5. S. Imada and T. Jo, J. Phys. Soc. Jpn. 58 (1989) 402. 6. R. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, 1981). 7. S. Tanaka, H. Ogasawara, K. Okada and A. Kotani, J. Phys. Soc. Jpn. 64 (1995) 2225. 8. K. Jouda, S. Tanaka and O. Aita, contribution to this proceedings.