Electron-lattice interaction of the Au- centre in KBr and RbCl

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Electron-lattice interaction of the Au- centre in KBr and RbCl

R. Harju, R. Laiho

To cite this version:

R. Harju, R. Laiho. Electron-lattice interaction of the Au- centre in KBr and RbCl. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-195-C6-198. �10.1051/jphyscol:1980650�. �jpa-00220088�

JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 1, Tome 41, Juillet 1980, page C6-195

Electron-lattice interaction of the Au

^_

centre in KBr and RbCI

R. Harju and R. Laiho

Wihuri Physical Laboratory, University of Turku, 20500 Turku 50, Finland

Résumé. — La dépendance de température de bande optique d'absorption et celle du dichroïsme circulaire magnétique sont mesurées pour les centres A u- dans KBr et en RbCl. Les données sont analysées par la méthode des moments à l'aide de six coefficients d'interaction de l'électron-réseau pour décrire le couplage des états excités I lTlu} et | 37\„ > aux modes de réseau Aig, Eg et T2g. Le centre Au" est remarqué à accoupler avec la force égale aux modes Eg et T2g-

Abstract. — The temperature dependence of the optical absorption bands and of the magnetic circular dichroism are measured for the Au" centre in KBr and RbCl. The data are analyzed with the method of moments by using six electron-lattice interaction coefficients to describe the coupling of the | 1rl u> and | 3Tlu > excited states with the AXg, Eg and T2g lattice modes. The centre is found to be coupled with equal strength to the Eg and the

7*23 modes.

1. Introduction.—The Tl+-like centres in alkali halides have three characteristic absorption bands, which arise from transitions ns1 -*• ns, p of the impu- rity ions at the Oh site symmetry. The absorption bands are called A, B and C in the order of the increas- ing energy. As first shown by Toyozawa and Inoue [1]

the splittings of the bands often seen in the spectra of these ions can be attributed to the Jahn-Teller interaction in the excited state. They assumed the impurity centres to be coupled only to the Alg and the T2g modes. Later on, a number of theoretical and experimental results have been published in favour of this model. On the other hand, there are data suggesting that also the Eg modes should be included into the vibronic model of these centres [2- 4]. Cho [5] has made band shape calculations by allowing the coupling to the Alg, Eg and the T2g

modes. The results show that rather similar band shapes can be obtained by using quite different sets of coupling parameters. The band shape calculations are usually made by applying the classical or semi- classical Franck-Condon approximation, although it is accepted that these approaches may not be quite correct for the Tl + -like centres.

Despite of the amount of the experimental and theoretical results available, it has not been possible to work out a consistent model for the electron-lattice interaction in the present systems. Reported values of the electron-lattice coupling coefficients vary considerably even for the same host-impurity complex.

This is partly due to difficulties of measuring faint features of incompletely resolved ultraviolet spectra but the results may also depend on the experimental method used. The KC1 : Au" centre provides an interesting example of a system with equal coupling

to the Eg and the T2g modes [6, 7]. In contrast to the other heavy metal ions, the A and C bands of Au~

have phonon structure with resolved zero-phonon lines suggesting that this ion is weakly coupled to the lattice. Obviously it resemples to the case of CaO : F+, which has been treated by a model with equal coupling to the low symmetry modes and approaching the exact solution of the Jahn-Teller Hamiltonian of a triplet state in the Oh symmetry [8, 9]. We present here results of the electron-lattice coupling of KBr : Au~

and RbCl : Au" to the Alg, Eg and T2g lattice modes.

The data were obtained by the moment analysis of the absorption and the magnetic circular dichroism spectra.

2. Electronic states of the Au- centre. — The Hamiltonian of Au~ is written as

H = H0 + Hel + Hz

where H0 is the purely electronic part, Hel is the elec- tron-lattice interaction and Hz is the Zeeman inter- action. Since Au~ is isoelectronic to Tl+ the ground state is assumed to be | 1Aig > and the excited states for the A and C bands, which are considered here, can be written as \Al > = - v | 1T{„ > + /x \ 3Plu >

and | C > = n | lT[u > + v | 3TJU >. The mixing coef- ficients of the spin singlet and the spin triplet states, v and (i can be obtained from the condition fi2 + v2 = 1 together with the measured dipole strength ratios of the C and A bands R = /J2/v2. There are in alkali halides containing Au~ centres two absorption bands at higher energies from the C band. Presumably they arise from transitions to higher excited states of the Au~ ion. The possible interaction with these states

14

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980650

C6- 196 R . HARJU AND R . LAlHO

would modify the orbital distributions of the

1

' T I , ) and the

1

^{3 ~ 1 , ) states.}

We restrict here to the linear electron-lattice inter- action He, = V j Q j (j = 1,

. . .,

6) where Q j are the interaction mode coordinates defined so that Q , corresponds to the symmetric A,, mode, Q 2 , Q 3 to the tetragonal E, modes and Q5, Q 6 , Q7 to the trigonal T2, modes. Since the orbital functions of the spin singlet and the spin triplet states may differ, six parameters are needed to describe the electron- lattice interaction in the excited state. For

1

3 ~ , , ) these are defined as

The corresponding coefficients for

1

IT,, ) are denot- ed by a', b' and c'.

3. The method of moments. - Honma [lo] has derived the expressions for the first few moments ( E n ), ( M ⁼ A , C) of the absorption bands due to singlet to triplet transitions as :

( E 2 ) M = i ( a 2 + Q b , & + 2 c & ) k T (1) and

3(( E 2 )M)' - ( E4 )M = cL(2 b& f

4

ch) kZ T 2 (2) where is a, = v2 a'

+

p2 a , bA = v2 b' -

:

^{p2 b and}

c, = v2 C'

- 9

^pZ c for the state which causes the A band absorption. The corresponding coefficients for the C band can be written by interchanging p2 and v2. Further information can be obtained from stress dichroism or from magnetic circular dichroism measu- rements. The magnetic field induced changes of the first and third moments are

( A E : ) M = + Q M P D H (3) and

where ,g is the effective g-factor of the band, H i s the magnetic field parallel to the light beam, and (+) and (-) refer to the absorption of left or right circu- larly polarized light.

The absorption and the magnetic circular dichroism spectra were measured from 4.5 K to 300 K. Typical results are shown by figure 1 for the A band of RbCl : Au-. At low temperatures the zero phonon line and another phonon line at the distance of 88 cm-

'

can be seen. The values of the coupling parameters were calculated from the equations (1) to (4) by using the linear part of the plots of the moments and of the

Fig. 1. -The A band of RbCl : Au- (a). Linear parts of the tem- perature dependences of the A band moments of RbC1 : Au-.

The upper line corresponds to ( E Z ) (b).

magnetic field induced change of the third moment when measured as the function of T. The linear behaviour was usually found between 80 and 300 K.

The values of R = 6.4 and 10.4 were used to calcu- late v and ,u for KBr : Au- and RbCl : Au-, respec- tively. The results, in units of (ev)'IZ, are compiled in table I together with those for KC1 : Au- [7]. In this type of measurements the main errors come usually from the uncertainty of the background abs6rp- tion of the host matrial and of other possible defects.

After some trial with different backgrounds it was estimated that the values quoted are accurate to

i-

15

%.

Table I. - Electron-lattice coupling parameters of Au-.

I

^{A )} I C >

0.4 bA C A a , b~ c~

- - - - - - KC1 0.37 0.22 0.22 0.42 0.33 0.31 KBr 0.39 0.19 0.19 0.69 0.28 0.28 RbCl 0.24 0.21 0.21 0.70 0.39 0.39

1

3Tlu

> ^I

l T l " )

a b c a' b' c'

- - - - - - KC1 0.37 - 0.42 - 0.41 0.42 0.34 0.33 KBr 0.34 - 0.35 - 0.35 0.72 0.30 0.30 RbCl 0.19 - 0.38 - 0.38 0.75 0.41 0.41

Evidently the coupling of the A and C band states to the symmetric mode is dominant in the present systems. However, in the case of RbCl the A band states are almost equally coupled to all the modes considered. In line with the earlier results for KC1 : Au- also in KBr : Au- and RbC1 : Au- the

ELECTRON-LATTICE INTERACTION OF THE Au- CENTRE IN KBr AND RbCl C6- 197

couplings to the E, and T2, modes are equal. The interaction parameters for the singjet and triplet states are considerably different. Presumably this is due to different mixing of these states with higher excited states of Au-.

4. Analysis in terms of the Huang-Rhys factors. -

The Jahn-Teller energies of the vibronic

1

Ai ) states can be given by the Huang-Rhys factors S ,

(r

^{= A, E,}

T ) corresponding to the modes At,, E, and Tz, as

where ur, Vr and mr are the effective frequencies, the coupling coefficients and the masses of the vibro- nic modes. The results of the moment analysis suggest that in the present systems the relations

E(A )

*

E J T ( E ) = E,r(T)

are valid. Therefore we make the following simplifi- cation :

S A + S E = S T = S and f i o A + h , = h c o T = h o . The 2nd and 3rd central moments of the absorption band can be given in the form

with ( E; )M =

2

⁽ E i ^{) M .} AS far as the absorption band due to transitions to the ( A' ) states is consider- ed the 2nd moment does not have any contribution from the spin-orbit splitting. Under the assumptions made above, the broad band mcd measurements can be used to relate the magnetic field induced changes of the 1st and 3rd moments to the 2nd mo- ments of the A band as

The separation of the band centroid from the zero- phonon line can be approximately given for the cases S

-

2 [9] in the form

Assuming that w, do not depend too strongly on temperature and by using the measured value of D = 0.0446 eV it is possible to calculate the values of Sr and or from the equations (8) to (1 1). A consis- tent solution of these equations could be found only with o, x 90 cm-l. Therefore the values of S , and o were recalculated on the basis that the observ-

ed phonon at 88 cm-' is due to the totally symmetric mode. The results for RbCl : Au- are shown in table I1 together with those for KC1 : Au- [6].

Table 11. - Vibrational parameters and the Jahn- Teller energies for the

I

A ) state of Au-.

S A S &@A ~ ~ W E , T

- - - -

KC1 3.8 0.72 65 cm-' 160 cm-'

RbCl 1.8 0.9 88

cm-'

107 cm-'

E(A )

- EJAE)

- E,r( T )

-

KC1 247 cm-' 115 cm-' 115 cm-'

RbCl 158 cm-

'

^{96 cm-}

'

96 cm-' It is interesting to note that the results of the vibrational parameters show consistently with those of table I that the interaction of the A band states with the A , , mode is stronger in KC1 : Au- than in

RbCl : Au-.

The observed line shapes resemple to those predict- ed by the numerical diagonalization of the Jahn- Teller Hamiltonian [8] but do not indicate the triple peak structures obtained by the calculation made under the classical Franck-Condon approximation [5].

The parameter B ⁼ ( E4

)/(

E' )* is related with the band shape being 3 for a Gaussian band and 1.8 for a rectangular shape [Ill. For the A band of all the complexes considered here, we got _{300 K} and 2.8 a t 4.2 K. Hence, the difference in B

-

^{2.5 at}

the coupling to the A , , was not detected between KC1 : Au- and RbC1 : Au- as may have been the case with F centres in alkali halides and in CaO [ll].

5. Conclusion. - In line with the earlier results for KC1 : Au-, also in KBr : Au- and RbCl : Au- the excited state is predominantly coupled to the' A,, mode. However, in RbCl : Au- the coupling of the A band states to this mode seems to be relatively weaker than in the other alkali halides considered. All these impurity systems provide an interesting example of a Jahn-Teller centre with equal coupling to the E, and the Tz, modes. Analysis of the A band of RbCl : Au- was made both by extracting the values of the electron-lattice coupling parameters and those of the Huang-Rhys factors and the effective mode frequencies. Both methods were found to give consis- tent results. The use of six electron-lattice interaction parameters makes it possible to consider separately the properties of the excited orbital spin singlet and spin triplet states. It is evident that their electron- lattice interactions are different, especially in the case of RbCl : Au-. At present, the reason to this situation is not clear but it can be suggested that the charge distribution of the tl, electron is modified by the combined effects of the Jahn-Teller interaction and the configuration interaction within the Au-

C6-198 R . HARJU AND R . LAlHO

ion. The observed absorption band shapes resemple approach than to those predicted by using the classi- more to those obtained by a quantum mechanicaI cal Franck-Condon approximation.

References

111 TOYOZAWA, Y. and INOUE, M., J. Phys. Soc. Japan 21 (1966) [6] LEMOYNE, D., DURAN, J., BILLARDON, M. and LE SI DANG.

1663. Phys. Rev. B 14 (1976) 747.

[2] EDGERTON, R., Phys. Rev. 138A (1965) 85. [7] LAIHO, R. and TERVOLA, A., Physica 83B (1976) 92.

[3] SHIMADA, T. and ISHIGURO, M., Phys. Rev. 187 (1969) 1089. [8] ~'BRIEN, M. C. M., J. Phys. C 4 (1971) 2524.

[4] LE SI DANG, ROMENSTAIN, R., MERLE D'AUBIGNE, Y. and [9] ESCRIBE, C. and HUGHIS, A. E., J. Phys. C 4 (1971) 2537 FUKUDA, A , , Phys. Rev. Lett. 38 (1977) 1539. [lo] HONMA, A., J. Phys. Soc. Japan 35 (1973) 1115.

[S] CHO, K., J. Phys. Soc. Japan 25 (1968) 1372. I1 1] HUGHES, A. E., J. Phys. C 3 (1 970) 627.