Evidence for coexistence of ferroelectricity and high-Tc superconductivity in YBa2Cu3O7-δ (δ < 0.15) from ultrasonic experiments

Physica B 165&166 (1990) 1271-1272 North- Holland

Evidence for coexistence of ferro electricity and high-Tc superconductivity YBa2CUa07_6 (6 < 0.15) from ultrasonic experiments

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V. Milller, C. Hucho, D. Maurer, K. de Groot and K.H. Rieder Freie Universitiit Berlin, Fachbereich Physik, Arnimallee 14, D-lOOO Berlin 33, FRG In order to determine the dielectric properties of the bound charges (soft dipoles) in superconducting YBa2CUa07-6 (6 < 0.15) we have extended conventional ultrasound experiments to the determination of the dispersion and absorption of the sound-induced rf magnetic field. In contrast to the ultrasonic behaviour, the temperature dependence of the dispersion and absorption of the sound-induced rf magnetic field shows pronounced anomalies. It is shown that these experimental findings are highly indicative for displacive ferroelectric phase transitions appearing in the temperature range of 150 K < T < 180 K and in the vicinity of the superconducting transition temperature. The possible connection between ferroelectricity and high temperature superconductivity is also discussed. The actually known high-T c superconductors as well as more than 90% of the known ferroelectrics and antiferroelectrics are oxides. Therefore, and because superconductivity and ferroelectricity are of the same origin (namely the presence of soft dipoles), the question is of basic physical interest, whether or not a possible relation exists in these materials between highT c superconductivity and ferroelectricity. Within the frame of the present understanding of superconductivity, the formation of superconducting electron-pairs requires (1) a negative permittivity €(O,q) at q ~ k F (i.e. an attractive effective electron-electron interaction) and therefore the presence of soft dipoles, since the latter provide a possibility to overscreen the repulsive electron-electron Coulomb interaction. The permittivity 10(0, q), however, cannot be negative at q = 0, because in that case the system would become unstable (2). In conventional superconductors (metals), where the soft dipoles (with polarization P = 100(10 - 1)E) are formed by the conduction-electrons plus the positive background (and may be induced by both the electron-phonon interaction and an external field), we have 10(0, q) = 00 for q = 0, because in the presence of an external electric field E e., the mean macrospic internal field E = E e., - P / 100 must be zero in a stationary state (j = 8P/ &t = O"oE = 0). The same situation (i.e. 10(0,0) = 00) also exists in ferroelectrics where, in contrast to the effective field EelI = E + fP / 100 acting on the soft dipoles in the absence of an external electric field, the mean macroscopic internal field E is cancelled by the formation of a spontaneous electric polarization (i.e. fan = 1, where f is the Lorentz factor, a the polarizability of the soft dipoles, n their number density and 10 - 1 = an/(l - fan)). Whether in ferroelectrics 10(0, q) may become negative at q ~ kF , however, is an open question. From an experimental point of view a rigorous answer whether ferroelectricity and superconductivity coexist in (1-2-3) compounds, is still a very difficult but, nevertheless, a challenging task. The difficulties arise,

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because in highly conducting systems the total permittivity is dominated by the conduction-electrons (holes) whose electric polarizability is extremely high (i.e. of the order of 1010 in the MHz range) and therefore is orders of magnitude larger than that of the soft dipoles. Although ultrasound is a sensitive probe of ferroelectric phase transitions in insulators, practice teaches us that in high-T c compounds, both the large dielectric permittivity of the conduction-electrons and the large ultrasonic background terms prevent a reliable determination of these phase transitions. However, the situation changes markedly if a strong dc magnetic field is applied (which reduces the screening and shielding of the conduction-electrons) and, in addition to the sound field quantities, the absorption and dispersion of the sound-induced electromagnetic fields are investigated. Noting that the energy dissipated by the conduction-electrons via their interaction with the sound-induced electric field (originating from the sound-induced polarization PP of the soft dipoles) is given by (3)

where jce is the electronic current density, f = 1/3 for a sphere and f = 1 for a layer, it can be shown (4) that, with reference to the sound field quantities, the leading term in the expressions for the change in the dispersion and absorption of the sound-induced rf magnetic field may be written in terms of the dielectric function lOb = €~ - i€~ of the soft dipoles as (3)

Here, l/rm ,l/r. and Wm,W. are the decay rates and frequencies of the sound-induced rf magnetic field and ultrasonic wave, respectively. According to these expressions the frequency shift of the sound-induced rf magnetic field should therefore reflect, above all, the

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Fig. 1: Temperature dependence of the absorption (upper part) and dispersion (lower part) at about 6 MHz of the sound-induced rf magnetic field upon heating (20 K/h) in coarse grained (grain size > 20pm) YBa2Cu307_5 (0 < 0.15) at B o = 6 T.

temperature dependence of -( e~ - 1) and the absorption the temperature dependence of Wae~ (plus additive background terms). For a dc magnetic field of 6 T and for a heating rate of 20 K/h, the upper part of Fig.1 shows the temperature dependence of the absorption and the lower part the difference between the dispersion of the sound-induced rf magnetic field and of the sound wave. The most striking feature of Fig.1 is the finding that, in contrast to the sound velocity and ultrasonic absorption, the sound-induced rf magnetic field shows a marked change in frequency and a huge absorption peak at 90 K (which does not coincide with the superconducting transition temperature). Furthermore, a less pronounced peak in the electromagnetic decay rate, but a marked change in frequency, appears at about 170 K which, like the anomalies at 90 K, are highly indicative for a dielectric phase transition.. Evaluating the temperature dependence of the frequency shift quantitatively (3), it follows that in the vicinity of To '::::: 90 K and T 1 '::::: 170 K the dielectric permittivityat 6 MHz is of the order of I(eb -1)1,::::: 103 -10 4 which may be considered as evidence that close to To and T I YBa2Cu307_5 transforms into a ferroelectric or antiferroelectric "tate. The structure of (wm -wa)/wa at

To and T I further indicates that the phase transformations should be achieved by a re"onant proce"" with a temperature dependent resonance frequency. Therefore, nonresonant ordering of preexisting permanent electric dipoles may be excluded, because this should result in a relaxator-type behaviour. Hence, the reasons for the phase transitions should be searched for in the atomic and displacement polarizabilities, where the former may be excluded, because the atomic eigenfrequencies are by far too large and should (if at all) depend only weakly on temperature. Thus, we are led to conclude that the phase transitions near To and T 1 are achieved by atomic displacements, where the formation of a ferroelectric state is closely tied with a softening of a polar optical phonon mode (Le. Wto -> 0, where wto(T) = wo(e(oo,T) - 2)/(e(0,T) - 1) and W o is the unscreened oscillator frequency). As our experiments were performed at very low frequencies (w/27r = 6 MHz, q'::::: 0) we are led to conclude that the anomalies in the acoustic dispersion (and absorption) of the sound-induced rf magnetic field reflect ferroelectric phase transitions, because at a ferroelectric transition a polar optical phonon softens at q = 0, whereas at an antiferroelectric transition a polar optical phonon softens at (q = ±G), Le. at the edge of the Brillouin zone. Summarizing our results, there is much evidence that both superconductivity and ferroelectricity coexist in YBa2Cu307_6 . References (1) N.W. Ashcroft, N.D. Mermin, Solid State Physics, Holt, Rinehart and Winston, New York (1976) (2) V.L. Ginzburg, Ferroelectrics 76, 3 (1987) and references therein (3) V. Miiller, C. Hucho, K. de Groot, D. Winau, D. Maurer and K.H. Rieder, Solid State Comm. 72, 997 (1989) (4) V. Miiller, to be published