Soft mode behavior in RbH2AsO4

Volume 44A, number 6

PHYSICS LETTERS

16 July 1973

SOFT MODE BEHAVIOR IN RbH2AsO4

*

R.C. LEUNG, R.P. LOWNDES and N.E. TORNBERG High Pressure Physics Laboratory, Northeastern University, Boston, Mass. 02115, USA Received 28 May 1973 The low frequency xy Raman spectra of RbH2AsO4 are reported as a function of temperature in the paraelectric phase and are fitted to a coupled damped harmonic oscillator model to yield the soft mode behavior of the ferroelectric model.

The phase transitions in hydrogen bonded ferroelectrics have traditionally been described in terms of a cooperative ordering of protons in a double well potential, but more recently a number of authors [l—3] have proposed descriptions of the transition in hydrogen bonded ferroelectrics invoking anharmonic phonons. In this paper we present the first evidence of

softthe mode behavior inand via Raman spectroscopic consistent measurements with anharmonic showis RbH2AsO4 that phonon these descriptions results are of temperature ferroelectric of the 110.1 transition. KRbH2AsO4 and isomorphous has with a Curie KH2PO4. The Raman measurements were performed using excitation from a coherent radiation 52G argon ion laser. Using a right angle scattering geometry, the scattered radiation was analyzed by a Spex 1401 dual spectrometer used in conjunction with a cooled photomultiplier and pulse counting electronics. We observe a distinct broadening or shoulder close to the exciting line in the xy spectra for RbH2AsO4 which is not observed in other orientations. As fig. I shows, this feature is markedly temperature dependent apparently moving to lower frequencies with decreasing temperature. We believe this feature is associated with the ferroelectric mode. In addition, the spectra exhibit an anti-resonant interference between the ferroelectric mode and a low frequency B2 phonon. Such phenomena have recently been observed in a few other hydrogen bonded ferroelectrics [4—6]. Following Katiyar achieved computer least squares fit et to al. the[4], xy we spectra in thea range 10—250 cm~using a model of two coupled damped *

Work supported by the Army Research Office at Durham, North Carolina.

RbDA Y(xy)X

L~282

U z

K 241 162 K 148 K 118 K

__________________________________ 0

50

00 50 WAVENUMBER SHIFT

200

250

(cm-’) Fig. 1. The low frequency xy Raman spectra for RbH2AsO4.

harmonic oscillators. For the coupled system, the experimentally determined susceptibility is given by ~“

~

=

Im

PP.G~1(w),

(1)

where F, is the strength of the mode i and G,, the solutions to the coupled equations

r(~~iwra) —

L@2

~2 +

(42 + 2

+ iw~b)

—

(w)

are

lWrb)1

w2

(w

rG

11 G12

X

1

LG12 G22j

=

L0

~i

(2)

383

Volume 44A, number 6

PHYSICS LETTERS -~

I

~..-‘

RbDA

,20

20~-~

~

16 July 1973

and —* 0 not at the Curie temperature, 1~, as our simple model would suggest. but at a lower temperature. This behavior is consistent with the recent fiiidings of Cowley et al. [1J and Coombs and Cowly 12J who have pointed out that the self-energy for the ferroelectric mode in piezoelectric crystals contains an additional contribution, arising from the coupling of the

~

-~

<

200

TEMPERATURE

~

Fig. 2. The temperature dependence of the ferroelectric mode.

and

Tw~

/I~for

where the w and F are, respectively, the characteristic frequency and damping of a mode. Using this model. fits to the observed spectra were obtained with weighted variances of 10-~---l0~~. The central feature of the results is that the mode a is a soft mode which is overdamped, and which we therefore interpret as the ferroelectric mode, whilst the mode b is a conventional phonon. Although the standard errors for the mdividual parameters in these fits were of the order of a few percent, it should be noted that fits with almost equivalent variances could often be obtained with other values for the parameters. As far as the ferroelectric mode is concerned, however, we find that the quantity hr = w~/ç. where r is the relaxation time of the ferroelectric mode, to be reasonably invariant to the individual parameter changes. Fig. 2 shows the observed linear dependence on temperature of Tw2/F and w2 It is apparent, however, that both Tw2/F a a

384

a

a

niode with fluctuations in the phonon distribution, which decreases the real part of the self-energy and increases the damping. The presence of such an anomalous contribution to the self-energy leads to the conclusion that, in the high temperature limit, w~x (T---TA) where TA< T~,which is in agreement with our experimental findings. It can be shown that the ratio (1 —TA/TC) determines the ratio of the anomalous selfenergy contribution to that of the conventional selfenergy term (in the high temperature limit). The intercepts arising from the curves shown in fig. 2 suggest that the anomalous self-energy term is either somewhat larger than the conventional contribution or at a considerable fraction of this quantity.

References

1J

R.A. (owley et aL, J. of Phys. C: Solid State Phys. 4 (1971) L203. f21 G.J. Coombs and RA. Cowley, J. Phys. C: Solid State 6 (1973) 121. 131 Phys. R.A. cowley and G.J. Coombs, J. Phys. C: Solid State Phys. 6(1973)143. 41 R.S. Katiyar, J.F. Ryan and iF. Scott, Phys. Rev. B4 (1971) 2635. 15] J.F. Ryan, R.S. Katiyar and W. Taylor, J. Phys. (Paris) Suppi. C2 (1972) 49. 16] T.W. Broberg et al., Phys. Rev. B6 (1972) 3332