OFF-CENTRE IMPURITY CENTRES.Temperature dependence of the reorientation behavior of < 110 > off-center Ag+ defects in RbBr

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OFF-CENTRE IMPURITY CENTRES.Temperature dependence of the reorientation behavior of < 110 >

off-center Ag+ defects in RbBr

S. Kapphan, J. Koppitz

To cite this version:

S. Kapphan, J. Koppitz. OFF-CENTRE IMPURITY CENTRES.Temperature dependence of the reorientation behavior of < 110 > off-center Ag+ defects in RbBr. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-401-C6-403. �10.1051/jphyscol:19806102�. �jpa-00220008�

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JOURNAL DE PHYSIQUE Colfoque C6, suppkment au no 7 , Tome 41, Juillet 1980, page C6-401

OFF-CENTRE IMPURITY CENTRES.

Temperature dependence of the reorientation behavior of < 110 > off-center Ag+ defects in RbBr

S. Kapphan and J. Koppitz

FB 4, University of Osnabruck, 4500 Osnabruck, W-Germany

Rbsumb,

-

Des mesures Clectro-optiques effectuees dans RbBr : Ag+ au-dessous de 4 K mettent en Cvidence la reorientation des defauts Ag+ ( ( 110 ) off-center). Celle-ci s'effectue uniquement par des sauts de 90"

dans un plan (100). Au-dessous de 2 K le temps de relaxation ^T,, est proportionnel a T - ' et caractkristique d'un processus tunnel assist6 par un phonon. La reorientation par saut de 600 est totalement congelbe. Au-dessus de 4 K les rkorientations par sauts de 600 et 900 sont dtcrites par m e loi d'Arrhenius avec une 6nergie d'activation de (kB. 161 K) et (kB.87 K) respectivement.

Abstract.

-

Electro-optical measurements in RbBr : Agf reveal below 4 K the reorientation of < 110 > off- center Ag+ defects by 90" transitions only in a (100) plane. Below ²K a clear T-1 dependence of the relaxation time ^T~,,is found, characteristic for. a one-phonon-assisted tunneling process while the 60" reorientation process is completely frozen in. Above 4 K, both, the 60" and the 90" reorientation process become Arrhenius-like with an activation energy of (k,. 161 K) and of (k,. 87 K) respectively.

The dynamics of paraelectric impurities in alkali halides has been found to depend strongly on their interaction with the lattice [ I , 21. Low symmetry dipolar defects, of both the molecular ( O H - , C N - , etc.) and the off-center type (Li+, F - , etc.), replac- ing host ions of larger ionic radius may influence their local neighborhood in a number of ways. The size difference can produce a relaxation of the lattice around the defect [3]. The mass difference along with changes of the nearest neighbor forces can give rise t o local (or resonant) modes [4] and may produce a perturbed phonon frequency spec- trum [5]. The lower than cubic symmetry of the defect leads t o anisotropic distortions of the lattice in the vicinity as measured by the components of the elastic dipole tensor. This lattice distortion follows a reorientation of the defect, thereby increas- ing the effective moment of inertia. The phonon- assisted tunneling model describing the low temperature defect reorientation has t o be adjusted t o take this polaron-like effect of the lattice distortion into account by renormalizing the rigid lattice tunneling matrix element A , giving a smaller dressed tunneling parameter A' = A exp(- R), with R depending on the lattice coupling [6].

A model system for the influence,of most of the above mentioned effects seems to be Ag+ in RbCl and RbBr. Electro-optical studies 171 of this system gave rather surprising results. The measurements established not only clearly a ( 110 ) orientation of the defect under applied fields but revealed that

these centers reorient with high preference by next nearest neighbor 90"

-

tunneling compared t o the 60" - nearest neighbor reorientation process. This latter result can not at all be understood in a rigid potential of octahedral symmetry where the 60"

transition should dominate and the 90" transition at best could be equal. However the experimental results can be explained on the basis of an elastic distortion around the ( 110 ) defect with strong Eg and a much weaker Tz, part. The 90" transitions in the (100) plane of the dipole would leave the E,-distortion unchanged, making the 90" rotation relatively easy. The 60" transition however would require a rotation of the large E,-distortion, thereby reducing the transition probability by a large renor- malization factor. These particular elastic properties predicted for Ag+ defects in RbBr and RbCl have been recently verified quantitatively in stress dichroism measurements by Jiminez and Liity [8].

The optical relaxation times [7, 81 measured in the ultraviolet show for the 90" reorientation at low temperature (2-5 K) a T-2 to T-6 dependence becoming at higher temperature an exponential Arrhenius-like behavior (activation energy k B . 87 K), which may be interpreted as the result of higher order phonon processes. The 60" transition relaxation time below 4 K is too slow to be measured ( > 105 s), but follows above 5 K an exponential dependence with an activation energy of kB. 161 K.

The optical methods so far seem to be best suited to distinguish the 60" and 90" transitions and to fol-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19806102

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C6-402 S . KAPPHAN AND J. KOPPITZ

low their temperature dependence individually. Mis- sing so far in the low temperature measurements on RbBr : Ag+ was an indication for the T-1 dependence of rgO expected for a one-phonon-assisted tunneling reorientation and any kind of lower than

T-25 dependence in the 60" process. In RbCl : Ag+

the measurements seem to indicate such a T-1 beha- vior between 1 and 2 K with some rather large scat- tering of the data below 1 K [I]. We have extended therefore the electro-optical measurements in RbBr : Ag+ t o temperatures below 2 K , with the crystals being immersed in superfluid helium to provide an unambiguous coupling to the temperature bath.

The experimental techniques used are similar to earlier measurements [7, 81 with only minor adjust-, ments. The crystals, grown in our laboratory from.

ultrapure material under an argon atmosphere were, cut into properly oriented samples, immediately after cooling the crystal (in 48 h) from the melt to room temperature. This way no further heat treat-' ment and quenching procedure [7, 81 was found to be necessary by the complete absence of interaction effects in the optical spectra. The crystal holder used allows both, electric field and stress to be applied perpendicular to each other, with the light either propagating perpendicular to E, or through metal nets parallel to E,.

Thus the time dependence of the A-bahd absorption (absorption parallel t o the dipole axis) after a rapid step function of the applied field could be fol- lowed up to a maximum time constant of about 105 s (by extrapolating the initial rise or decay of the signal). For the interpretation of the optical decay time the rate equation analysis described in reference [7] is used.

Figure 1 shows the low temperature values of T ~ ,

clearly indicating a T-1 dependence below about 2 K. Only the field-independent switch-off values ( E

-

0) are shown to avoid additional factors

Inverse ~ e m ~ e r a t u r e x l ~ - ~ [ e l

-

Temperature (log scale)

-

[KI

Fig. 1. - Temperature dependence of the optical relaxation time r 9 ~ after a rapid switch-off (E

-

⁰⁾of the electric field applied in a (. 111

>

direction. Solid points indicate values taken from reference [7].

"

^lo2

9 8 _w

varying with the applied field strength for the switch- on case (0

-

E). Values taken from reference [7]

are also indicated to show the quantitative agreement in the temperature range common to both sets of experiments. This temperature dependence is fully consistent with the interpretation of a low temperature one-phonon-assisted tunneling process being dominated above 2 K by higher order phonon processes [6, 91. In the temperature range below 4 K only the 90" transitions are observed experimentally, the relaxation time for the 60" reorientation being so long ⁽ ^T

>

^~ ^~105 s below 4 K) that this process .can be considered to be frozen out. Therefore the dipoles are trapped in a (100) plane dipole state which is unique among the paraelectric dipole systems. Electro-optical experiments with E applied in ( 110 ) direction can be analyzed with similar rate equations given in reference [7] for Elll, but with an bias energy AU = pE, with p the electric dipole moment. The optical relaxation times rgO determined this way (for Ello) give quantitative agreement with the values of figure 1 for the E

-

0 reorientation process. Measurements with electric field and uniaxial stress applied perpendicular to each other to test the stress dependence of rgO and to look for possible anisotropic interaction effects among the Ag' defect centers are under way.

-

Rb Br:

Ag+ for €111-0 a n d

Ell, = 8 x 1 0 ~ ~ / c m ; A-Bond ^{~ 9 0 '}

[

L ~ g h t p o l a r ~ z e d 111111

At temperatures above 4 K (Fig. 2) the 90" and the 60" relaxation times show the known exponential temperature dependence. The new values for

7 6 0 (Elm

-

0) extend the exponential behavior t o time constants uf about 1 6 s, but indicate only a slight change in the dependence at these temperatures.

rn 0

-

z

^O-a- - o o -

Iz

C 9 lo1

- - _ - _

4-

(3

.

^\

X

- 0 - ^T-T-'

0 thls work

.

^--T % T - ~

-

_o_I_! .Kapphonand Luty

.

4- a - - G I 7 38seclxexpR 52KIT)

O i n o Î Î ¹ Î Î Î Î

In recent theoretical calculations [lo, 111 the usual polaron-like treatment of phonon-assisted tunneling with linear coupling of the defect-lattice interaction has been extended to include quadratic terms in lattice displacement and moments. This is designed to take care of the in-band resonant modes of the heavy Ag+ ions seen in the far-IR absorption bands and the perturbed phonons resulting from force constant changes. The temperature dependence of the transition rates predicted this way shows indeed an Arrhenius type behavior extending to relatively low temperatures (0.2 B,,,,, < 7) [lo, 111. This temperature region is however well above the one found experimentally for the exponential temperature dependence (Fig. 2).

For Agt in RbBr the far-IR resonant modes and therefore the perturbed phonons are not known experimentally yet. A fit of the calculations to the measurements therefore is presently possible for the high and low temperature transition rates in the linear coupling limit only. The activation energy [lo] A = R.8/3 yields with a RbBr Debjre tempe- rature 0 = 120 K for the reorientation process a dressing exponent R (90") = 2.2 and R (60") = 4

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TEMPERATURE DEPENDENCE OF THE REORIENTATION BEHAVIOR OF < 110 > ^C6-403

-

_{l o 6}

111 1 1 1,1 1 11 111 1 1 1 3 1 , 1 1 1 1 1 1 ,106

(0

-

10

5

I

_\

-

^loL ⁰

i ^--

^P

0

U) - ^exp^1161K/TI _Z _%_10'

g

Cn ^lo2

-

_.-^V)

E

+

,

lo3

+ 0 C

*. = - -

0_ -

::

- _-

^-0

22

"- lo2

0

a, - ₀

K

-

0

-

₀^lo<- ^K

5

' - ^10'

-

a 20 16 12 8

0 , , , , , , , , , , , , , , , , , , , , , , , , , ^I~ ~ ~ - 6 Inverse Temperature x [K-']

80 70 60 50 LO 30 20 10 0 2 4 6 810 20 Inverse Temperature ~ 1 0 . ~ IK-'1 Temperature (log scalel[Kl

Fig. 3 . - Temperature dependence of the ratio ^T ^~ ^~of the ^/ ^T ^~ ^~ Fig. 2. - Temperature dependence of the optical relaxation Optical times'

times for the 60' (El,

-

0) and the 90' (Ell,

-

0) reorienta-

tion process measured in the ultraviolet A-band absorption of WA = A ' / A k ( ~ / 4 AT)'/' exp[- A(1 - Tb/4 A)'/T]

RbBr : Ag+. Solid points indicated are values taken from refe-

rence [7]. ( 2 )

with the bias Tb usually being small compared to A , the pre-exponential factor multiplied by a factor which together with the experimental one-phonon 3/2 from the rate equation analysis [7] should be relaxation rate W ⁼(4 T ~ ~ ) - ' = s K 1 at 1.3 K given by

and equation (30) of reference [lo]

2 AiO/3 A& . ( A , ~ ~ A , , ) ' / ~ = lo-'

W = ( A 2 / & ) exp(- 2 R ) [8 KR/O'] T (1)

.

⁽³⁾

which together with the experimental values of the gives a rather small rigid lattice tunneling parameter. activation energies yields a reasonable ration of A, (90") ⁼kB .4.5 x l o K 5 K . Plausible values are

A,o ²ⁱ 10 Ago with Ago = 0.25 cm-I for the rigid expected to be several orders of magnitude higher lattice tunneling matrix

[ I l l . This underlines the need for a strong enhance- Thus, if we interpret the Arrhenius behavior as ment of the dressing factor by the in-band resonant the high case and the Tl-behavior of mode coupling. Calculations of Dick [lo1 for Agf the relaxation times as the one-phonon-assiste~

in RbCl yield a resonant-mode-induced enhance- case, the experiments are in a qualitative agreement ment of the dressing factor for the low temperature with recent theoretical models. For a quantitative region of about one order of magnitude. agreement further modifications of the model para- The high temperature limit should be less affected meters are necessary and the local lattice softening by higher order coupling terms [I I] and should [6, 111 proposed may provide such a mechanism.

therefore yield more realistic estimates. We have Another possible mechanism not yet included could plotted in figure the the be a temperature dependence of the off-center relaxation times with a best fit to these values giving potential, suggested by Fussgaenger as an explana-

r60'r90 = lo-' exp(74

K/n.

The temperature tion for the temperature dependence of the uv-

of the ratio '60"90 = ^W90'6 ^W60 is oscillator strength of Ag+ in RbCl and RbBr [12].

given mainly by the difference in the activation

energies in agreement with the high temperature, Acknowledgment. - The authors are very grateful low bias field limit of the theoretical calculations. to Dr. H. Hesse of our crystal growth laboratory Following equation (31) of reference [lo] for supplying the crystals used.

References

[I] BRIDGES, F., Crit. Rev. Solid State Sci. 5 (1975) 1. [7] KAPPHAN, S. E. and L U n , F., Phys. Rev. B 6 (1972) 1537.

[2] KAPPHAN, S. E., J. Phys. Chem. Solids 35 (1974) 621. [8] JIMENEZ, R. V. and LUW, F., Phys. Rev. B 12 (1975) 1531.

[3] PAUS, H. and LUn, F., Phys. Status Solidi 12 (1965) 341. [9] DICK, B. G. and STRAUCH, D., Phys. Rev. B 2 (1970) 2200.

[4] KIRBY, R. D., HUGHES, A. E. and SIEVERS, A. J., Phys. Rev. B [lo] DICK, B. G., Phys. Rev. B 16 (1977) 3359.

2 (1970) 481. [Ill TONKS, D. L. and DICK, B. G., Phys. Rev. B 19 (1979) [5] MOKROSS, B. J. and DICK, B. G., Phys. Rev. B 15 (1977) 5938. 1136

+

^1149.

[6] SHORE, H. B. and SANDER, L. M., Phys. Rev. B 12 (1975) 1546. [12] FUSSGAENGER, K., Phys. Status Solidi 36 (1969) 645.

27

~ b ~ r : ~ g +

O * E 1 l ~ -0 DE,20+005

A-Band mmE1oo-O kT

Temperature (K1

-

5 6 7 8 125