NMR-investigation of the dynamic properties of off-center Ag+ defects in RbCl

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NMR-investigation of the dynamic properties of

off-center Ag+ defects in RbCl

O. Kanert, R. Küchler, M. Mali

To cite this version:

O. Kanert, R. Küchler, M. Mali. NMR-investigation of the dynamic properties of off-center

Ag+ defects in RbCl. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-404-C6-407.

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JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 7, Tome 41, Juillet 1980, page C6-404

NMR-investigation of the dynamic properties of off-center

Ag+ defects in RbCl

0. Kanert, R. Kiichler and M. Mali (*)

Institut fur Physik, Universitat Dortmund, 4600 Dortmund 50, West-Germany

RBsumB. - Les propri6ti.s des centres de dipble Ag' dans les monocristaux de RbCl ont Btk CtudiCes entre 4 et 50 K au moyen de la mkthode de resonance magnitique nucltaire. Les donnees de relaxation de spin-rkseau des noyaux 85Rb, "Rb et 35C1 fournissent les temps de correlation uniforme du mouvement localis6 des centres Ag+ de direction ( 110

>.

Les donnCes experimentales ont ete expliqukes par un modele de reorientation par effet tunnel assisti! par des phonons, rtcemment propose par Tonks et Dick.

Abstract. - The dynamic properties of Agf dipole centers in RbCl single crystals were studied between 4 K and 50 K with the nuclear magnetic resonance method. The spin-lattice relaxation data of the nuclei 85Rb, 87Rb and 35C1 provide uniform correlation times of the localized motion of the

<

110 ) oriented Ag+ centers. The experimental data can be explained by a phonon-assisted orientational tunneling model recently proposed by Tonks and Dick.

1. Introduction.

-

The dynamic orientational behaviour of off-center defects in alkali halide crystals has been studied very extensively in the last decades with different techniques. In basically all of these experiments, electric fields [I, 21 or stress [3] have been applied to the crystals. At low temperatures, this leads to a paraelectric or paraelastic dipole alignment, which can be monitored by dynamic optical or di- electric techniques in order to detect the dynamic behaviour of the dipoles. The NMR technique, however, allows the determination of the dynamic orientational properties without application of field or stress over a wide temperature range. The nuclear spin-lattice relaxation rate of all the nuclei in the crystal is strongly influenced by the localized motion of the dilute off-center defects [4]. An evaluation of the relaxation data leads to the correlation time of the hindered rotation of the defects.

In this paper, a first comprehensive NMR investigation of the dynamic properties of Agf defects in RbCl is presented using the 35C1, 85Rb and 87Rb nuclei as probes.

2. Experimental. - The relaxation~neasurements were performed with a Bruker pulse spectrometer SXP 4-100 at magnetic fields in the range between 0.46 T and 6.3 T using the saturation pulse technique. The NMR signal was stdred in a transient recorder (Data Lab DL 905) connected to a Varian 620 L computer in order to calculate the relaxation rates. Ultrapure and Agf-doped RbCl single crystals

(*) Physik-Institut, Universitat Zurich, Switzerland.

were grown from ultrapure material by the Czochralski method in an inert argon atmosphere.

The Ag' concentration in the doped crystals ana- lyzed by optical methods was about 350 ppm. It is well known, that Ag+ ions tend to form aggregates at higher temperatures [3]. Therefore, after a quenching procedure the crystals were kept below 77 K during the whole period of investigation. During the NMR measurements, the crystal under investigation was mounted inside a He-evaporation cryostat which could be temperature controlled within an accuracy of about 0.2 K.

3. Experimental results and discussion. - In ultra-

pure RbCl single crystals, the nuclear spin-lattice relaxation rate l / T t of 5Rb, "Rb and 35C1 is caused by the interaction of the nuclear quadrupole moment with the phonon-induced fluctuations in the local electric field gradient [5]. According to Mieher [6], the quadrupolar relaxation rate can be written as :

Here I and Q are the spin and quadrupole moment of the nucleus, respectively, y is the Sternheimer factor [7], p is the density of the crystal, c is the sound velocity, r is the next-neighbor distance, and 9 is the Debye temperature. The function E(T/B) is equal to one for T/B

2

0.5 and is proportional to T5 for T/B 4 1. It is seen, that the experimental data of the relaxation rates of ultrapure crystals shown in figure 1

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NMR-INVESTIGATION OF THE DYNAMIC PROPERTIES C6-405

Fig. 1. - 87Rb spin-lattice relaxation rate l/Tl vs. temperature in ultrapure and Agf -doped (350 ppm) RbCl single crystals for different external magnetic fields.

and figure 2 confirm the temperature dependence described by Eq. (1) (B(RbC1) = 179 K). Further- more, the relaxation rates are independent of the strength of the magnetic field and obey the (ye)'-law given by Eq. (1).

t

A Ultrapure 8 5 ~ b ~ l s-1 85RbCl: Ag+

Ultrapure Rb 3 5 ~ ~

Rb3'Cl : Ag+

Fig. 2. - Temperature dependence of the spin-lattice relaxation rate l / T l of 85Rb and 35C1 in ultrapure and Ag+-doped (350 ppm) RbCl single crystals. Magnetic field H , = 4.25 T.

As shown in figures 1 and 2, the corresponding relaxation rates of the Ag+-doped RbCl crystals are drastically larger than the rates of the undoped crystals in the low temperature region. The additional rates AR = T;'

I,,,:,,+

- T;'

,,

I,

plotted in figure 3 as a function of the inverse temperature are

due to the localized motion of the Agf centers, which produce additional fluctuations in the local electric field gradients.

Flg. 3. - Ag+-induced part of the relaxation rate AR of sSRb, s7Rb and 35C1 in RbCl vs. inverse temperature as obtained from figures 1 and 2.

Theoretically, the Ag+-induced part of the relaxation rate AR can be expressed by the relation [8, 91

Here c. ( w6(Agf) ) is the mean quadrupole distor- tion of all resonant nuclei in the crystal due to the Ag' defects, where c is the concentration of the

defects and w0 is the Larmor frequency.

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C6-406 0. KANERT, R. KUCHLER AND M. MALI

hood of the defects. For g(z) = 6(z - z,), Eq. (2) Below 9 K, deviation of the Arrhenius behaviour

leads to the BPP-relation indicates that the motion is influenced by phonon- assisted tunneling.

AR = c.(06(Ag+)) x The experimental results are in reasonable agreement with a tunneling model for the off-center system

)

.

(3) RbCl : Ag+ recently presented by Tonks and Dick [lo].

+ 4 ~ 0 : 4

The model, which includes both linear and quadratic Since the experimental data follows some of the

general aspects of this relation, in a first approximation we have calculated the correlation time 7, by

means of Eq. (3) using c . ( o$(Agf) )

as

a fit parameter. The average value of the best fit parameter

[ c . ( w$(Ag +) was found to be of the order of 5.0 x lo3 s-' for 85987Rb and 1.3 x lo3 s-' for 35C1, respectively.

As discussed in an earlier paper [4], this is in reasonable agreement with theoretical considerations.

Figure 4 summarizes in an Arrhenius representation the temperature dependence of the correlation time

7, of the Ag' defects obtained from the data of

figure 3. By comparing the correlation time 7, of

figure 4 with optical measurements performed by Kapphan and Liity [2] we identify our data as correlation times for the 90° reorientation process of the Agf dipoles. For T > 9 K, the experimental data show a quasi-Arrhenius behaviour with a rate

defect-lattice interactions as well as lo&l lattice softening, leads to a quasi-Arrhenius behaviour of the 900 reorientation rates in the temperature range between 16 K and 50 K. According to Tonks and Dick, the eflective activation energy for 20

%

local lattice softening lies between 46 K and 55 K depending on the strength of the phonon perturbation, which agrees quite well with our measurements. Although a detailed calculation of the transition rates fails below 16 K, the authors [lo] have determined a single value for the rate a t T = 2 K using a first order approximation. This value together with their theoretical data above 16 K indicate a similar deviation of the quasi-Arrhenius behaviour below 16 K as it is shown by the experimental data in figure 4. By comparing the value of the theoretical (normalized) rate for T = 2 K of 4 x l o p 5 K-' with the (extra- polated) data given in figure 4 one yields as a rough estimation for the bare-tunneling matrix element

As,* /

-

a value of about 1 K.

Assuming a dressing exponent 2 R , 5 as dis-

l/z, = 3 x 101Os-'

*

exp

[

-

5y]

_{(4) cussed by Tonks and Dick, the dressed tunneling}

matrix element A,, is found to be about 0.08 K. It should be noted, however, that our data deviates in some ways from the BPP-relation given by Eq. (3).

10-7K50 2 G .

5

4

For instance, the field dependence of the motion-

f '

. '

- - , .

I

induced rates on the cold side of the maxima (see Fig. 3) is substantially less than the BPP-type field- squared dependence. Generally, such a deviation indicates the influence of internal broadening mecha- nisms on a reorientation process [9]. On the other hand, it is well known that internal broadening effects may play an important role on the dynamic behaviour of the system RbCl :Agf [Ill. Using an appropriate distribution function g(z) in Eq. (2), we suppose to be able to interprets our experimental data in terms of random internal fields.

Furthermore, experiments are planned to probe the effects of electric fields and hydrostatic pressure on the nuclear spin relaxation rate. For instance, a strong

( p E $ k T ) electric field parallel to the ( 111 )-

direction of the crystal will suppress the 90°-jumps but will leave the 600-jumps uneffected. This would offer the possibility of measuring the correlation time of 600-jumps by nuclear magnetic relaxation experiments. S I

'GI

1

lo+: 10-9:;

IcrlQ..

1 2---+- T

Acknowledgments. - We are gratefully to Prof.

Fig. 4. - Arrhenius plot of the correlation tlme .r, of the 90° A. W. Sleeswyk of the University of Groningen for

reorientation process of Ag' centers in RbCl determined from performing the of the samples. The work was NMR data of figure 3. supported by the Herbert-Quandt-Stiftung.

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NMR-INVESTIGATION OF THE DYNAMIC PROPERTIES C6-407

DISCUSSION

Question.

-

S . E. KAPPHAN. types of jumps by applying an electric field in ( 100 )-

The extrapolation of the temperature dependence direction and ( 111 ) direction respectively (see next of the 600 and 900 relaxation times for RbC1 :Ag+ question).

could also lead to the conclusion that these values

are becoming equal at higher temperatures and the Question. - J . M . SPAETH.

NMR experiment should see the contributions from 1s it possible to align the Ag+ centres by stress or both processes (600 and 900). electric field and then distinguish between 600 and

Reply.

-

0 . KANERT. 90° jumps with your method ?

In principle, that is right. But in this case, one - O. K4NERT-

would observe a decay of the NMR magnetization, Of course, we have planned to probe the effect of which is the sum of two exponential functions with z an electric field on 1/T,. A strong electric field (900) and 7 (600) as time constants, respectively. We parallel to the ( 11 1 ) direction will suppress 900 never observed such a behaviour. On the other hand, jumps, whereas a strong electric field in the ( 100 )

it may be possible to distinguish between the two direction will suppress the 600 jumps.

References

[I] KAPPHAN, S., J. Phys. Chem. Solids 35 (1974) 621. [7] STERNHEIMER, T., P h y ~ . Rev. 146 (1966) 140.

121 KAPPHAN, S. and LWTY, F., Phys. Rev. B 6 (1972) 1537. (81 FEDDERS, P. A., Phys. Rev. B 14 (1976) 1842.

[3] JIMENEZ, R. V. and LOR, F., Phys. Rev. B 12 (1975) 1531. [9] WALSTEDT, R. E., DUPREE, R., REMEIKA, J. P. and RODRI- [4] KANERT, 0. and MALI, M., Phys. Lett. A 69 (1979) 344. GUEZ, A,, Phys. Rev. B 15 (1977) 3442.