Polarized light scattering studies of heavy fermion superconductors

Abstract Polarized light scattering measurements of some heavy fermion superconductors are presented and discussed. Light scattering affords a unique opportunity to study both the f electrons, which are thought to participate in the formation of the superconducting state, and the lattice excitations, which can demonstrate strong electron-phonon interactions and elastic anomalies in these compounds. These points are illustrated by presenting the results of light scattering experiments on single crystal samples of CeCu2Si2, UBe13, UPt3, and URu2Si2.

The use of polarized light scattering has recently proven useful for studying the complex excitation spectra of heavy fermion systems. For example, this q = 0 probe can provide information about crystal field excitations and spin fluctuations which is complementary to that provided by neutron scattering at higher q. Additionally, the high resolution of light scattering allows a careful study of strong electron-phonon coupling effects, which are anticipated in these compounds due to the existence of electronic energies on the order of typical phonon frequencies.
A number of interesting phonon properties have been revealed in these materials by light scattering. For example, the phonon spectra of both UPt 3 [1], and URuzSi 2 [2] are characterized by an extremely intense Alg breathing mode (at 150cm ~ in UPt3, and at 430cm -1 in URu2Si2), which dwarfs the other phonons observed in these materials. The huge intensities of these modes illustrate the large breathing-type deformation potential coupling of the phonons to the electronic configuration of U, consistent with the elastic anomalies [3,4} observed in these compounds. Furthermore, the A~g phonon in URu2Si 2 is particularly notable in that it demon-0378-4363/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) and Yamada Science Foundation strates a strong increase in scattering intensity with decreasing temperature. This behavior is thought to reflect a strong magnetoelastic coupling of this Alg mode to a crystal field level near 400 cm-1 (50 meV) [5].
As alluded to previously, a number of interesting electronic and magnetic excitations have also

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Temperature dependence of the T~g + T:g spectra of Ugel3, illustrating the spin fluctuation spectrum. The hatched area shows the quasielastic contribution as described in the text, the dotted line shows the linear (inelastic) contribution, and the solid line is the sum of these contributions with a small offset. The spectra have been offset.
been observed in our studies. In CeCu2Si 2 [6], for example, crystal field excitations are evident, 1 displaying a broad peak centered at 290cm (see fig. 1). That this peak results from electronic transitions is clear from its increasing intensity with decreasing temperature, its absence in isostructural LaCuzSi2, and its antisymmetric symmetry, Azg , which is characteristic of electronic or magnetic scattering. From this symmetry assignment, we can further deduce that these excitations involve transitions between two F 7 levels of the tetragonally split Ce3+j = ~ multiplet (inset, fig. 1).
In UBe~3 [7], strong quasielastic scattering from spin fluctuations is evident, displaying the symmetry of the antisymmetric representation, Tlg (see fig. 2). It was initially found that the spectral response of this scattering could not be fit well to a simple relaxational model as would be expected of quasielastic scattering. However, as shown in fig. 2, by presuming a rather large linear term, ~ (1 + n(oo))w (dotted lines), in addition to the quasielastic response (hatched area), the observed response can be fit nicely (solid line). This linear term is also observed to a lesser extent in the spectra of UPt 3 and URu2Si 2 (see figs. 3 and 4), and is presumed to arise from very broad crystal field scattering centered at higher energies (>1000 cm-1). Quasielastic light scattering from spin fluctuations has also been observed in UPt 3 [1,8] (hatched area in fig. 3), similarly displaying the symmetry of an antisymmetric representation, A2g. It should be noted that the quasielastic scattering in UBe~3 is much greater than that  observed in either UPt 3 or WRu2Si 2 (see figs. 3 and 4). Indeed, the unexpectedly large scattering intensity of the response observed in UBe13 has led to the suggestion that the observed scattering possibly results from low energy, highly damped crystal field excitations [7]. However, it is likely that the large spin fluctuation scattering strength in UBel3 arises instead from a larger magnetooptical coupling in UBe13 than in UPt 3 and The spin fluctuation scattering we observe in URu2Si 2 [2] (see fig. 4) is interesting in that it demonstrates a strongly temperature dependent linewidth. In fact, a detailed study of the linewidth with temperature indicates a single-ion, linear regime above 70K, and an exchange dominated, temperature independent regime between 70K and 23 K. Furthermore, a careful inspection of the linewidth through the magnetic transition at T N = 17 K shows an abrupt decrease in the linewidth, consistent with critical slowing. Indeed, by 5 K no quasielastic scattering is observed within our experimental resolution (<6cm 1), as shown in the bottom spectrum of fig. 4. This dramatic change in the damping rate is thought to corroborate earlier specific heat evidence [9] for a gap opening transition, which removes relaxation channels along with the Fermi surface.
It is interesting to compare the spin fluctuation linewidths we observe at q = 0 in these materials, with higher q neutron scattering results. For example, the q = 0 spin fluctuation linewidth we see in UBe13 is much larger than that reported at the zone boundary by recent neutron scattering results on single crystals [10]. Such narrowing of the linewidth towards the zone boundary indicates that correlations exist with a critical q [11] near the zone boundary. A large q dependence of the spin fluctuation linewidth is also observed in URu2Si 2 [2], although in this system the low temperature linewidths we observe at q = 0 are roughly half those seen by neutron scattering at higher q [12]. This suggests longer wavelength correlations in URu2Si2, with a critical q closer to the zone center. Finally, in UPt3, the spin fluctuation linewidth we observe at q = 0 is comparable to that found at higher q by neutron scattering [11], indicating the absence of any q dependence in the linewidth. However, in this material, a q dependence in the spin fluctuation intensity, i.e. the static susceptibility, x(q), has been observed by neutron scattering, suggesting the presence of antiferromagnetic correlations in UPt 3 [11].
Furthermore, the very existence of low temperature spin fluctuations in our q = 0 Raman studies is notable, inasmuch as non-interacting Fermi liquid theory sets the energy scale of the imaginary part of the susceptibility at vFq--(VF/2pr)q 2 (where v v and Pv are the Fermi velocity and momentum, respectively). Therefore, nonzero spin fluctuation scattering at q--0 alludes to an absence of simple Fermi liquid effects in these materials. This finite spin fluctuation scattering at q = 0 is allowed because the mag-netization is not conserved in these systems due to their strong spin-orbit interactions. This issue, therefore, demands further theoretical guidance [13].
In conclusion, we have been able to observe a number of interesting excitations in the heavy fermion superconductors. Particularly interesting is the presence of finite spin fluctuation scattering at q=0, and the consequent absence of simple Fermi liquid behavior, noted for the spin fluctuation scattering in UBe13, UPt3, and URu2Si 2. Finally, a number of novel features in the phonon spectrum have been observed, including evidence for magnetoelastic coupling to crystal field levels.