Phonon softening in tantalum below 4.2 K

Solid State Communications, Vol. 81, No. 2, pp. 195-198, 1992. Printed in Great Britain.

0038-1098/92 $5.00 + .00 Pergamon Press plc

P H O N O N SOFTENING IN TANTALUM BELOW 4.2 K F. Sacchetti Dipartimento di Fisica, Universita' di Perugia, Perugia, Italy Istituto di Struttura della Materia del Consiglio Nazionale delle Ricerche, Via E. Fermi 38, 00044 Frascati, Italy and O. Moze and C. Petrillo Istituto di Struttura della Materia del Consiglio Nazionale delle Ricerche, Via E. Fermi 38, 00044 Frascati, Italy

(Received 22 July 1991 by R. Fieschi) The phonon lifetime of longitudinal and transverse phonons along the [1 00] direction in tantalum has been measured at 1.2, 4.2 and 6 K and room temperature by neutron inelastic scattering. An anomalous softening of acoustic phonons with energies between 6 and 12meV is observed when the temperature is lowered from 4.2 to 1.2 K. Such a softening is an indication that a lattice instability can be present at low temperatures in otherwise stable transition metals. THE STUDY OF the phonon lifetime is of great importance in order to obtain detailed information on the phonon-phonon as well as electron-phonon interactions. In principle the one-phonon response function can be measured by neutron inelastic scattering. However, this technique suffers from intensity and resolution limitations so it is rather time consuming to apply it for an extensive analysis of the effect of phonon interactions. Nevertheless, in view of the plentiful information obtainable from inelastic neutron scattering experiments, various studies have been performed in order to determine the phonon lifetime [1-3]. A detailed investigation of the phonon response function over a wide energy range is generally not necessary. However, when studying the effect of phonon interactions, the analysis of an extended energy range around the phonon peaks turns out to be very important as a consequence of the energy dependence of the phonon self-energy [4, 5]. This approach is particularly relevant when considering the electronphonon interaction in systems undergoing a transition, like a structural transition or a superconducting transition, Even though in such cases a lifetime measurement represents a very good means to study the transition [6], the possibility of analysing the whole response function would appear to be extremely desirable. In this paper we present the first study of the phonon line-shapes in tantalum at low temperature.

In this regime the phonon self-energy is dominated by the contribution from the electron-phonon interaction, which is quite complex in all transition metals and shows extended features when the system is close to a phase transition [7]. The average electron-phonon interaction is measured by the electron-phonon coupling parameter 2, which also appears in McMillan's equation [8] for the superconducting transition temperature. This coupling parameter can also be determined by a proper average of the phonon lifetime [9]. Among superconducting transition metals, tantalum shows a remarkable disagreement in 2 as deduced from the superconducting transition temperature through McMillan's equation and from electronic specific heat or resistivity measurements [10]. Such a discrepancy could be attributed to an anomalous behaviour of phonon lifetimes at low temperature. It should also be observed that the phonon density of states F(og) weighted with the electron-phonon coupling function 0t2(c0), as measured by a tunneling experiment [11], shows important differences when compared to the density of states derived from a room temperature neutron inelastic scattering experiment [12]. Such a discrepancy could be explained by a strong energy dependence of or(to), even though ~(to) has been found to be much more constant in other systems [9, 13]. Alternatively one can explain the anomalous tunneling results as due to a rather important renormalization of the phonon energy and lifetime at low temperature. In view of the discussed

195

P H O N O N S O F T E N I N G IN T A N T A L U M BELOW 4.2 K

196

disagreements found in this system, a low temperature study of the phonon lineshape seemed to be worthwhile. Recently, it has been shown that the PRISMA spectrometer [14, 15], installed at the ISIS Spallation Neutron Source (Chilton, UK), allows investigations of extended regions of momentum-energy space simultaneously with good performance characteristics. Moreover, thanks to the intrinsic nature of this time of flight instrument, it is possible to perform studies of temperature-dependent phenomena maintaining the sample in a fixed position, thus reducing incidental spurious effects introduced by possible instrumental misalignments during different scans. The experiment has been thus performed using the P R I M S M A spectrometer, employing 15 independent Ge(1 1 1) analysers [15] and 15 3He detectors. The sample was a cylinder, 1.2 cm in diameter and 5 cm in height, with the [0 0 1] axis vertical. The phonons were measured along the [1 0 0] direction around the (4 2 0) Bragg peak. The temperature was varied between 1.2K and room temperature and the stability was within + 0.1 K. Measurements have been performed at four temperatures, namely: 1.2, 4.2, 6 K and room temperature. The data collected at room temperature have been compared to the older data of [12] and a reasonable agreement between the two sets of data is found, although the transverse branch of previous data [12] is systematically l meV lower than the present data. The reason of such a disagreement is not clear but we are confident that the present data are correct since both energy gain and energy loss data belonging to different detectors give the same dispersion curve. In Fig. 1 we report some of the experimental peaks corrected for background and for the incoming spectrum, as a function of temperature. These data show a clear trend in going from 4.2 to 1.2K; in particular, very evident is the damping of the longitudinal phonon at about 6 meV when the temperature is lowered below 4.2 K. On the other hand this damping effect is present at higher energy too, where also the transverse phonon lineshape shows a temperature dependence. Since the spectrometer configuration is held fixed in all scans, the resolution effects are essentially temperature independent considering that the dispersion curves do not show any remarkable change between 6 and 1.2 K. Therefore, it is rather useful to derive quantitative information on the phonon lifetime. To this purpose we fitted the present data with simple model functions of the form: f(to)

=

[n(to) + 11

)'to (to _ to0)2 + (yto)2,

(1)

Vol. 81, No. 2

where n(to) is the Bose factor and )' and too are left as free parameters. This function takes into account the relevant features of the scattered intensity and it has been found to fit very well the data also in the tails of the phonon groups. Then the temperature dependence of the half width at half maximum ( H W H M ) of the fitted function can be considered as representative of the inverse phonon lifetime. The H W H M thus obtained exhibits the expected decreasing trend between room temperature and 4.2 K, whereas a quite puzzling behaviour is found when the temperature is lowered from 4.2 to 1.2 K. The difference between the H W H M at 1.2 and 4.2 K is shown in Fig. 2 in the energy range 0-15 meV for both transverse and longitudinal phonons. As it can be seen, there is a maximum increase of the phonon damping around 7.5 meV when the temperature is lowered. The observed trend suggests a resonant behaviour of the phonon states with some other excitation localized around 7.5 meV. Considering that the increase in the damping is present for transverse as well as longitudinal phonons, the process should be similar to the scattering process giving rise to resonances in the phonon spectrum of disordered alloys [16]. A deep analysis of the mechanism giving rise to such a damping is beyond the purpose of the present paper, even though some considerations can be attempted. One could think of the phonon lifetime decrease observed between 4.2 and 1.2 K as related to the transition to the superconducting phase which takes place at 4.37 K. Indeed this would have been the case if the superconducting energy gap were about 3meV as the effect is actually expected when the phonon energy is slightly larger than twice the gap. However, the isotropic gap in Ta is about 0.7 meV, so that a very large anisotropy is necessary to explain the present data in terms of electron-phonon interactions in the superconducting phase. Alternatively the observed effect could be related to some other kind of transition. We do not think that a magnetic phase transition could be present in Ta, therefore, a structural transition could be responsible for the observed behaviour. On the other hand, a preliminary analysis of the structure of the present sample, on the same spectrometer used as a diffractometer, has shown that the sample preserves its b.c.c, structure over the whole temperature range, so that the observed phonon damping is more likely to be due to a structural instability rather than to a true transition. A similar situation has been already observed in different systems [17-20] and seems to be related to a structural transition close to the working point in the phase space. Finally, we observe that as the present data do not

Vol. 81, No. 2 A

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P H O N O N SOFTENING IN T A N T A L U M BELOW 4.2 K A

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gratefully acknowledged. Technical assistance from A.J. Chappell is also acknowledged.

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REFERENCES

~ 0.2-

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Fig. 2. Difference between the H W H M at 1.2 and 4.2 K as a function of phonon energy. Transverse and longitudinal phonons are not distinguished. The full line is a guide to the eye. rule out the possibility of a strongly anisotropic superconducting gap, further investigation is necessary: measurements with a magnetic field applied to the sample in order to induce the transition to the normal state at the lowest temperature should be done.

Acknowledgements - Assistance in measurements of the room temperature data from U. Steigenberger is

5. 6. 7. 8. 9. 10. 1 !. 12. 13.

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PHONON SOFTENING IN TANTALUM BELOW 4.2 K (1980). C. Andreani, C.J. Carlile, F. Cilloco, C. Petrillo, F. Sacchetti, G.C. Stirling & C.G. Windsor, Nuclear Instrum. and Methods A254, 333 (1987). U. Steigenberger, M. Hagen, R. Caciuffo, C. Petrillo, F. Cilloco & F. Sacchetti, Nuclear Instrum. and Methods B53, 87 (1991). D.W. Taylor in Excitations in Disordered Systems, (Edited by M.F. Thorpe), p. 297, Plenum, New York (1982).

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F. Sacchetti, P. Bosi, F. Dupr6, G. Frollani, F. Menzinger & M.C. Spinelli, Phys. Status Solidi 96, 77 (1978). J.D. Axe, D.T. Keating & S.C. Moss, Phys. Rev. Lett. 35, 530 (1975). Y. Noda, Y. Yamada & S.M. Shapiro, Phys. Rev. B40, 5995 (1989). Y. Yamada & K. Fuchizaki, Phys. Rev. B42, 9420 (1990).