VIBRONIC MODEL FOR AN ns2 SYSTEM : KCl : Au-

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VIBRONIC MODEL FOR AN ns2 SYSTEM : KCl :

Au-D. Lemoyne, J. Duran, J. Badoz

To cite this version:

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VIBRONIC MODEL FOR AN ns

2

SYSTEM : KCI : Au

D. LEMOYNE, J. DURAN and J. BADOZ Laboratoire d'Optique Physique de l'ESPCI (*), 10, rue Vauquelin, 75231 Paris Cedex 05, France

Résumé. — Le centre Au- dans KC1 est isoélectronique des ions de la série de Tl4'. Nous avons

effectué des expériences d'absorption optique dans la raie sans phonon et dans le continuum vibro-nique de la bande A. Les deux jeux de paramètres Jahn-Teller ainsi obtenus sont en complet accord. La comparaison avec les théories existantes montre que ce centre présente un cas très particulier d'effet Jahn-Teller où le système est également couplé aux modes Eg et T2g. Il en résulte la

formula-tion exacte de la foncformula-tion d'onde de l'état vibronique le plus bas. Cette foncformula-tion d'onde est utilisée pour le calcul des règles de sélection qui gouvernent les propriétés de polarisation de la lumière émise en présence de différentes perturbations. La comparaison entre les valeurs calculées et mesurées des taux de polarisation circulaire (ou linéaire) de fluorescence sous champ magnétique (ou contrainte uniaxiale) montre la grande cohérence du modèle et nous a conduit à identifier un processus tunnel à un phonon comme étant responsable de la relaxation entre les sous-niveaux Jahn-Teller de l'état excité relaxé.

Abstract. — The Au_ centre in KC1 is isoelectronic to the Tl+-like ions. We have performed

perturbative optical experiments both in the zero-phonon line and in the vibronic continuum of the A band, leading to two independent sets of Jahn-Teller parameters which are found in complete agreement. Comparison of the results with existing theories clearly shows that this centre exhibits a very interesting kind of Jahn-Teller effect where the system is equally coupled to the Eg and T2g

modes. It follows that the exact wavefunction of the lowest vibronic eigenstate has been obtained. In turn, this wavefunction is used for the calculation of the selection rules governing the polarization properties of the fluorescence light under various perturbations. The comparison between the pre-dicted and the measured values of the circular (or linear) fluorescence polarization degrees under a magnetic field (or a uniaxial stress) displays the high consistency of the model and leads us to identify a one-phonon tunneling process as being responsible for the relaxation between the split Jahn-Teller sublevels.

1. Introduction. — The existence of the Jahn-Teller

effect in the widely studied alkali-halide phosphors serie (ns2 ions) has been fully demonstrated since the

pioneer work of Seitz [1], Actually most of the pro-perties of these systems such as radiative or non radia-tive decay processes, absorption band shape and beha-viour under pertubation (stress or magnetic field) in absorption and fluorescence are directly connected to the vibronic wave functions of the involved electro-nic states. Therefore a precise knowledge of the Jahn-Teller effect is highly desirable for the detailed investigation of these systems.

In order to solve this problem, two ways of approach could be used. The first, which has been mostly employed, takes profit of the Born-Oppenheimer approximation and describes the Jahn-Teller problem in terms of Adiabatic Potential Energy Surfaces conveying the limits of the adiabatic approximation. The other way of tackling with this problem was to try and find among the ns2 serie a system where the

Jahn-Teller problem could be exactly and completely

(*) Equipe de Recherche n° 5 du C.N.R.S.

solved. This lead us to the choice of the KC1: Au~ system which exhibits two interesting features : (i) The spin-orbit coupling energy is large enough so as to separate clearly the 3Pt and 3P2 states, (ii) The

electron-lat-tice coupling is sufficiently weak so that a zero-pho-non line may emerge from the vibronic continuum. In fact, the existence of this zero-phonon line is essential for the purpose of elaborating an exact vibronic model since it reflects the properties of the relaxed excited state which may be thus studied through both

absorp-tion and emission experiments.

This paper gives a summarized report of the various experiments which we performed on the 3P1 state of the KC1 : Au~ system [2, 3]. Three different ways for ascertaining a vibronic model have been used which involve polarization measurements under various perturbations in absorption and emission in the zero-phonon line and in the broad band. The striking result of this study is the equality of the three different sets of parameters thus obtained by using a single vibro-nic model.

At liquid helium temperature some quenching effects due to relaxation processes occur in the

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C7-146 D. LEMOYNE, J. DURAN AND J. BADOZ

sion measurements. We also report a brief resume of the essential features concerning the relaxation process which can be derive from our experiments.

2. Experimental. - 2.1 SAMPLES PREPARATION. -

KC1 crystals containing about 1 % by weight of

- -

I

P Y1 U - _P 3

g

- . 0- 0

,

_- Illt width 51,t width -0.2

-1 k - 0.1

"

0

4

FIG. 1.

-

Absorbance and corresponding MCD signal in the broad band and in the zero-phonon line region.

AuHCI, were grown by a Kyropoulos method. The reduction into Au- was made by a solid-state elec- trolysis at a temperature of 610 OC. The crystals were kept at 650 OC in order to bleach them from F centres and then slowly cooled down to room temperature so as to minimize the effects of the internal strains.

2 . 2 OPTICAL MEASUREMENTS. - Magnetic circular dichroism (MCD) and stress induced linear dichroism (SLD) experiments at various temperatures were performed on the broad band and on the zero-phonon line with a classical technique using a photoelas- tic modulator and a gas-flow cryostat [4]. The spectra obtained for absorption and MCD experiments are shown on figure 1.

The magnetic circular (or stress induced linear) fluorescence polarization degree PC (or P 3 were measured with the use of a differential technique described in reference [5]. The crystals were placed in a helium dewar where temperature could be ranged between 4.2 and 1.1 K. Figure 2 gives a sketch of the results of the three essential experiments.

3. Vibronic model. - The excited electronic state corresponding to the so-caIled A band possesses the TI, symmetry. It may be thus linearly coupled to the A,,, E, and T,, vibrational modes. The extent of the coupling to these modes may be described by various parameters : (i) Thz coupling coefficients Vr

(r

= Al,

E, T,) which are directly involved in the vibronic hamiltonian. (ii) The Huang and Rhys factors Sr which are dimensionless numbers related to the VrYs. (iii) The quenching factors K(T,), K(E) and K(T,) which appear in the reduction in the lowest vibronic level of perturbations transforming like TI,, E, and T,,.

FIG. 3. - Quenching factors plotted against the Huang and Rhys factors (after O'Brien [6]).

The Huang and Rhys factors and the quenching factors are not independent but are connected through the vibronic model of the system. However the deri- vation of one set of parameters from the other one is made possible only in the case of particular models, e. g. when coupling to one Jahn-Teller mode is pre-

FIG. 2. -Experimental polarization degrees versus 1/T corres- _dominant_or_{when the} _{to both}_E, _{and T2,} ponding to the three perturbative measurements. The dashed

lines are the theoratical curves calculated from eq. (1) with is This latter case has been

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d'Aubignt [7]. According to the performed measurements one may experimentaly obtained either the Huang and Rhys factors or the quenching factors as sketched on table I. The analysis of the higher order moments of absorption, MCD and SLD spectra run in the vibronic continuum directly leads to the Huang and Rhys factors. The quenching factors are obtained through the comparison of the first moment changes of MCD and SLD spectra in the broad band and in the zero-phonon line. Besides, the knowledge of the vibronic model allows one to derive the quenching factors from the measurements of the fluorescence polarization degrees. Therefore, the aim of this para- graph is to elaborate a vibronic model and to prove its consistency by comparing the three sets of quenching factors thus obtained.

Synopsis of experiments and of extraction of parameters processes.

"

ul

m 0-phonon a line <AM,>

3.1 BROAD BAND EXPERIMENTS. - Following a classical procedure [8] involving the second order moment of absorption spectra and the third order moment of MCD and SLD spectra, one may extract the Huang and Rhys factors ST and the corresponding mean phonon frequencies Bw, from the perturbative mea-

surements performed on the broad band. Experimen- tally, we found :

The emerging feature of this result consists in the equality of the coupling to the E, and T,, modes. This particular case of a triplet electronic state equally coupled to the trigonal and tetragonal modes has been already observed in the case of the F+ centre in CaO 191. The corresponding theoretical problem (the so- called D-mode model) has received much attention these last years and exact solutions have been derived for the diagonalization of the total hamiltonian at least for the lowest vibronic eigenstate. In particular, O'Brien [6] calculated the curves of figure 2 which connect the Huang and Rhys factors of the noncu- bic modes to the reduction factors. According to this figure, the expected values for K(Tl) and K(E) = K(T,) are 0.26 and 0.56 respectively.

3 . 2 COMBINED ZERO-PHONON LINE AND BROAD BAND

EXPERIMENTS.

-

The quenching factors may be directly measured from the comparison of the first-moment change in the zero-phonon line and in the broad band when an external perturbation is applied. K(T1), K(E) and K(T,) are associated respectively to the magnetic, stress along

<

001

>

and stress along

<

110

>.

Experimentally, we obtained : K(T,) = 0.24 f 0.04 K(E) = 0.58

+

0.08 K(T,) = 0.53 & 0.08.

The remarkable agreement of the two sets of quenching factors values obtained by two independent methods shows the high consistency of the D-mode model applied to the KC1 : Au- system. In turn, this model may be used in the interpretation of our fluorescence experiments.

3.3 FLUORESCENCE EXPERIMENTS.

-

In the case of the D-mode model, Romestain and Merle d'Aubi- gn6 [7] have calculated the exact vibronic wave- functions of the relaxed excited state. The knowledge of these wave functions makes possible the calculation of the selection rules for polarized light emitted from the relaxed excited state sublevels split by an external perturbation. These selection rules are simple functions of the K1 = K(T,) and K, = K(E) = K(T2) factors. The knowledge of the selection rules is gene- rally not sufficient to predict the properties of the fluorescence light since both internal stresses and ther- mal relaxation may perturb the selection rules and the population of the split sublevels. However, it can be seen that these two processes are less efficient when temperature is raised. Thus, by considering the high temperature limit of our experiments, we may use the Bolt- zman partition function of the sublevels and we find :

PC= K, sh x[(2 K,

-

K,) ch x

+

(K,

-

~ , ) / 2 ] - l x = K, gp, HJkT P<ool > =

-

K, th x[l

+

*(K,

-

K,) th

XI-'

x = K2(3 B) a/2kT (1) P < l l o > = -K, th x[(2 K,-K,) c h x + + ( ~ , - ~ , ) e ~ ] - ~ x = K, ColkT X = K2(3 B) o/2kT

g, 3 B and C are the Land6 factor and the piezospec- troscopic coefficients defined by Kaplianskii [lo]. It can be seen from figure 2 that actually the theoretical lines obtained from eq. (1) and the experimental curves are found to coalesce in the high temperature region, in consistency with the fact that they are expected to be tangent at the origin. In turn, the experimental curves may be used to recalculate the Ki and K, factors. For this purpose one needs an analy-

tical expression for the various polarization degrees. Since, as quoted below, the low temperature quenching of polarization is due to a one-phonon process we have inserted a T - I law for the relaxation time in

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C7-148 D. LEMOYNE, J. DURAN AND J. BADOZ

the relaxation processes. A fit with the experimental can be shown that under these circumstances the

curves gives : circular polarization degree is given by :

K , = 0.25 f 0.03 PC = K, th x(1

+

z,/z,)-' -- -.

K, = 0.56 f 0.06

where z, and z, stand respectively for the relaxation values which are in complete agreement with those _{time and the lifetime. We have been able to show that} previously obtained- This agreement between the Pre- _zR_{deduced from our experimental results follows a} dicted and calculated values for the three experiments _{T - 1} _{law in the temperature range 1.1-4.2}_K._This strongly supports our proposed model from the _{result indicates that a classicaI one-phonon process is} absorption experiments. _{active. This was to be expected for in this temperature}

4. Relaxation process. - As can be seen on figure 2 some quenching occurs in the measured polarization degrees as soon as temperature is decreased below 4.2 K. At first, this fact may be related to two essential features : (i) The random internal strains which mix the vibronic eigenstates of the applied perturbation leading to a decrease of the theoretical polarization degrees calculated from the selection rules. Taking into account the bandwidth of the zero-phonon line, which reflects the extent of the random internal stresses, one can get an estimate of the quenching effect which reduces the polarizations measured at low temperature. Doing this, we have been able to show that the existing internal stresses could not explain the relatively large observed reductions. Roughly stated, we have calculated that the internal stresses could only account for 20

%

of the observed quenching effect. Thus we were left with the second mechanism. (ii) The relaxation processes which may be too slow to feed the split sublevels according to the Boltzman law ; such an instance has been rather frequently observed through the optical detection of the para- magnetic resonance (e. g. in self trapped excitons [I 11 or for the F centre in CaO [12]). As an example, it

range. The dependence of z, with the magnetic or stress splitting 6 follows a 6 - I law. This is compatible

with a tunneling process. One might rise the question to know wether the direct relaxation process should not be more efficient. A careful analysis of the various transition probalities indicates that a tunneling matrix element of 0.2 cm-l is sufficient to make the tunneling process predominant.

5. Conclusion. -As demonstrated in the present work, the use of the D-mole model for the relaxed excited state of the KC1 : Au- system has allowed us to explain fully the essential features of our perturbative absorption and emission experiments. More- over, it should be noticed that the agreement between the various sets of measured quenching factors implies that the same electronic TI, state is involved in the absorption and fluorescence processes. This shows that no level crossing effects occur during the relaxation process in contrast to those which occur in F centres in alkali halides. This conclusion is in accor- dance with recent results [I31 about the fluorescence lifetime of Au- in KC1 which has been found to be equal to the theoretical one calculated from the oscil- lator strength of the A band.

References

SEITZ, F., J. Chem. Phys. 6 (1938) 150.

LEMOYNE, D., DURAN, J., BILLARDON, M. and LE SI DANG,

Phys. Rev. B 14 (1976) 747.

LEMOYNE, D., DURAN, J. and BADOZ, I., J. Phys. C :

Solid State Physics (1976) to be published.

BADOZ, J., BILLARDON, M., BRIAT, B. and BOCCARA, A. C.,

Symposium of the Faraday Society 3 (1970) 27.

MOREAU, N., BOCCARA, A. C. and BADOZ, J., Phys. Rev. 10 (1974) 64.

O'BRIEN, M. C. M., J. Phys. C : Solid State Physics 4

(1971) 2524.

ROMESTAIN, R. and MERLE ~ ' A U B I G N ~ , Y., Phys. Rev. B 4 (1971) 461 1.

HENRY, C. H. and SLICHTER, C. P., in Physics of Color

DISCUSSION

Centers edited by W . B. Fowler (New York : Academic Press) 1968.

DURAN, J., MERLE ~'AUBIGNE, Y. and ROMESTAIN, R.,

J. Phys. C : Solid State Physics 5 (1972) 2225.

KAPLIANSKII, A. A., Opt. Spectres. (USSR) English Trans- lation, 16 (1964) 557.

WASIELA, A., Second Conference on Lattice Defects in Ionic Crystals Berlin (1976). J. Physique CoZfoq. 37

(1976) C 7, this issue.

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R. and TWAROWSKI, Y., Phys. Rev. Lett. 28 (1972) 1268.

KRAUSE, M., J. Lumin. 10 (1975) 391.

C. JACCARD. - The experiment yields 3 parame- wave function. Actually this wave function depends

ters K. How many free adjustable parameters are on three parameters (KT,, KE, KT,) which are related included in the vibronic model ? by two relations. Therefore we might say that as