Acoustic evidence against BCS behavior in monocrystal YBa2Cu3O7

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PHYSICA ®

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Physica C 282-287 (1997) 1077-1078

ELSEVIER

Acoustic Evidence against BCS Behavior in Monocrystal YBa2Cu307 Ming Lei, a Albert Migliori, a and Hassel Ledbetterb aLos Alamos National Laboratory, Los Alamos, New Mexico 87545, USA bNational Institute of Standards and Technology, Boulder, Colorado 80303, USA

Using a detwinned YBa2Cu307 monocrystal and acoustic-resonance spectroscopy, we measured internal friction Q-l = fl.III, through the 91-K superconducting-transition temperature. We show measurements for the first ten macroscopic resonance frequencies If" None of the modes show classic BCS-model behavior based on simple-pairing, isotropic-s-electron, weak-coupling assumptions. Beside being non-BCS-like, essentially every mode behaves differently, suggesting a strongly anisotropic energy gap fl.(k), and practically ruling out any simple Fermi-surface gap function, especially s-wave. Some modes actually show increasing Q-l upon cooling below Tc, suggesting either strong Fermi-surface changes or lattice-relaxation mechanisms. The Bardeen-Cooper-Schrieffer theory achieved a real triumph in explaining the sound-attenuation drop that occurs in superconductors below Tc' The original microscopic theory [1] contains a relationship for the normal-superconductive ultrasonic-wave absorption change: 2 exp [fl.(T)/kBT] + 1

(1)

Here a denotes acoustic attenuation; I, Fermi function; fl., temperature-dependent energy gap (the major superconducting parameter); kB , Boltzmann's constant; and T, absolute temperature. From Eq. (1) and aiT) measurements, the energy gap was determined for many classical BCS materials, with good agreement with other-method results [2]. In the present study, we measured attenuation by acoustic-resonance spectroscopy [3]. From the width of the resonance peak fl.1, one can calculate the associated internal friction Q-I or, equivalently, the attenuation a:

Q -I = Nil, = 2valw .

(2)

Here, v denotes sound velocity and w denotes angular frequency. Thus, one can determine Q-I for each macroscopic-vibration mode. 0921-4534/97/$17.00 Elsevier Science B.V. PH S0921-4534(97)00643-6

The detwinned crystal of Y Ba2 CU3 07 -0 (0 < 0.1) was described in a previous study [4], where the nine orthorhombic-symmetry Voigt elastic coefficients were also reported. From magnetic susceptibility, Tc is 91.4 K. Figure 1 shows the principal results: for the first ten vibration modes, Q-l versus temperature in the region of the normal-superconductive transformation. Figure 1 contains several interesting features: 1. Each vibration mode shows different Q-l(T) behavior. This behavior suggests strong anisotropy in the Fermi surface and practically excludes any simple Fermi-surface gap function, especially swave. In the future, if we succeed in identifying the various macroscopic vibration modes, then a possibility would arise to comment on other proposed symmetries, such as extended s-wave and d-wave symmetry x 2 _ Y 2. 2. Unlike conventional BCS superconductors, no remarkable slope decreases occur at Tc' Thus, the BCS relationship, Eq. (1), fails to apply. 3. The first mode (which reflects mainly the shear moduli, such as C44 , C55 ' C66 , C ll -C12 ) shows a sharp Q-l maximum at Tc' Such a maximum typifies sharp phase transitions, such as a secondorder normal-superconductive transitions.

M. Lei et aU Physica C 282-287 (1997) 1077-1078

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Figure 1. Internal friction Q-I versus temperature for a detwinned YBa2Cu307 monocrystal. See Eq. (2). Numbers 1 through 10 indicate, in order of increasing frequency, various macroscopic-vibration-frequency modes. The first peak is determined mainly by shear-mode Cij' The vertical dashed line corresponds to Tc' 4. Below Tc' depending on the mode, Q-I decreases, remains level, or sometimes increases. [Presumably, a level Q-I(T) corresponds to a zero .d.] This behavior opposes the concept from the BCS model that, as electron pairs condense during cooling into the superconducting state, the attenuation decreases continuously to a minimum. 5. Below Tc we could not solve the inverse problem to estimate the Cij' a procedure that succeeded well for ambient-temperature measurements. 4 Our results oppose several previous reports. For YBa2Cu307' several studies found relaxation peaks near Tc [5,6], and some actually used the exponential a(T) behavior to estimate the energy gap .d [7,8]. Our results show a strong Q-I peak at Tc only for a nearly pure shear mode, and we see no possibility to determine .d from a(T) by using existing models. Indeed, our results suggest a.d that is strongly direction (mode) dependent.

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Elastic Constants and Their Measurement, McGraw-Hill, New York (1973), especially chapter 5. 4. M. Lei, J. Sarrao, W. Visscher, T. Bell, J. Thompson, A. Migliori, W. Welp, and B. Veal, Phys. Rev. B. 47 (1993) 6154. 5. G. Cannelli, R. Cantelli, F. Cordero, and F. Trequattrini, Supercond. Sci. Technol. 5 (1992) 247.

6. B. Berry, W. Pritchet, and T. Shaw, Defect and Diffusion Forum 75 (1991) 35. 7. G. Cannelli, R. Cantelli, F. Cordero, G. Costa, M. Ferretti, and G. Oleese, Phys. Rev. B 36 (1987) 8907.

8. K. Nagai, Y. Wang, and L. Magalas, J. Alloys Compounds, in press.