Raman scattering from spin fluctuations and phonons in the heavy-fermion superconductor UPt3

Abstract Quasielastic scattering from spin fluctuations has been observed in UPt3 by Raman spectroscopy. The experiments for wave vectors q≈0 show a nearly temperature independent linewidth for 5 K ⩽ T ⩽ 300 K Complementary to neutron scattering results this establishes the q independence of the spin relaxation rate, indicating the localized nature of the spin fluctuations. A Raman-active phonon near 79 cm-1 (10 meV) shows a drastic increase in line-width with decreasing temperature, demonstrating strong electron-phonon coupling.

Quasielastic scattering from spin fluctuations has been observed in UPt 3 by Raman spectroscopy.The experiments for wave vectors q~O show a nearly temperature independent linewidth for 5 K~ T 4 300 K. Complementary to neutron scattering results this establlshes the q independence of the spin relaxation rate, indicating the localized nature of the spin fluctuations.A Raman-active phonon near 79 cm -I (10 meV) shows a drastic increase in llnewidth with decreasing temperature, demonstrating strong electronphonon coupling .
There has been considerable interest recently in the u~usual proper~igs of heavy fermlon materials" such as UPtR"2 , which is a superconductor and exhibit~ spin fluctuations.The latter have been inferred from specific heat Z, magnetic susceptibility S, and resistivity measurements% From neutron scattering measurements ~ on polycrystals of UPt~ one has deduced an energy scale of the spin-fluctuations of about 9 meV (100K) independent of momentum transfers q )I ~-I.Fermi liquid theory predicts this energy scale to be determined by vF.q , where v F is the Fermi velocity.An important question is whether this linear q dependence can be observed in q~0 Raman scattering.
Moreover, since it has been suggested that the electron pairing in heavy fermlcn superconductors may not be due to t~e usual BCS-type electron-phonon interaction v, any phonon spectroscopy is highly desirable.
In UPt 3 we have observed by means of Raman spectroscopy (a true q = 0 probe) quasielastic scattering from spin fluctuations and a temperature dependent, anomalous broadening of the llnewidth of the A I (f +) phonon The result I for the spin fluctuations complements neutron scattering investigations and establishes the q independence of the spin relaxation rate.In analogy to findings in A15 superconductors 7 we observe an increasing broadening of the phonon mode with decreasing temperature, reflecting strong electron-phonon coupling.UPt 3 crystallizes in. the hexagonal Ni~Sn-structure (space group D~6h , P63/mmc).T~e sample was made by arc melting of the pure elements on a water-cooled copper hearth in a zirconiumgettered argon atmosphere.Raman measurements have been carried out between 5 and 300 K, using 5309 ~ Kr+-laser excitation with 150 mW incident power.The Raman spectra were taken on a fractured surface of the polycrystalllne sample where the laser beam was focussed onto a (001) cleavage plane of a single crystal grain.
d2° ~ d~d~S i,J X"iJ(q,hw) where X"ij is the imaginary part of the susceptibility.If we are dealing with uncorrelated spins, i.e. which relax exponentially in time with a q-independent relaxation rate F, it should be possible to separate x"i I into q and dependent factors.We use a Kralers-Kronig relation and assume x"4q,~) = #~x'(q,O) P(w) where P(~) and X' denote the spectral function and the real part of the susceptibility, respectively.
We now assume a Lorentzian for P(~), since we expect the 5f spins to fluctuate statistically.Thus we find the magnetic scattering intensity These Haman measurements, complementing the neutron scattering results for large q (> I ~-1), establish the q independence of the spin relaxation rate within the large error bars of the neutron data.Hence we conclude that the spin fluctuations are localized in space as expected for well separated U atoms.Coherence and Fermi liquid effects, which lead to a q dependence of the spin relaxation rate for q~0, can be ruled out for temperatures down to 5 K as a consequence of our results.In addition to our findings for UPt~ we have reanalyzed magnetic Haman scatterihg data of UBe13 , reported I0 recently for 40 K and 350 K.We w~re able to fit these data to the form of Eq. ( 4) and the result is shown in Fig. 2 by the hatched area.For both tem~peratures f/2 is found to be 110 4±20) cm-' 413.6 meV), in good agreement with neutron scattering results (13 ± 2 meV) 11.
In addition to the magnetic Raman scattering in UPt3, we were able to investigate one of the five Raman-active phonons.Fig. 3 shows unpolariled Haman spectra of UPtsat 300 K, 77 K, and 5 K.The phonon mode at 79 cm -I appears only for parallel polarizations of the incident and scattered light and has A~ symmetry The llne-] width of the phonon peak i~creases with deeressing temperature from 10 cm -I at 300 K to ~0 where A denotes the magnetic scattering intensity and S(~) is the surface roughness scattering contribution (Lorentzian line shape), which is superimposed on the magnetic excitations.We have fit our data to Eq. ( 4) and subtracted S(~) to yield the pure spin fluctuation contribution to the spectra 4shown by the hatched area in Fig. I).From the fit, the half width F/2 at half maximum of the quasielastic intensity is found to decrease from 110 cm -I (13.6 meV) at 300 K to 85 cm-I(I0.5 meV) at 5 K.

Eq. (~).
cm -I at 5 K.The weak excitation near 150 cm -I appearing in the spectrum for 77 K is attributed to a scattering process of second order.
We ascribe the phenomenon of increasing width of the optical phonon in UPt 3 to strong electron-phonon coupling, in analogy to observations in superconducting A15 compounds'.Assuming that this discrete phonon interacts with a continuum of electronic excitations leads to a phonon linewidth, which is proportional to the s~uare of the electronphonon coupling constant 7. Hence we conclude an increase in the electron-phonon coupling constant with decreasing temperature.The anomalous behavior observed for the phonon mode of AI~ symmetry is consistent with the dominant deformation potential type electron-pho~qn coupling concluded from elastlc anomalies '~.This most likely explains the strong Raman scattering intensities of the A phonon compared to the other unobservabl~ g Raman-active modes (E1g , 3 E2g).(cm-1) The scatterir~ intensity of the A I_ phonon is separated from the background ~y the dashed lines.
Further evidence for strong electron-phonon coupling is given by the occ~rence of the two phonon-process near 150 cm'" for intermediate temperatures between 300 K and 5 K, i.e. for 77 K. On the one hand the electron-phonon coupling increases with decreasing temperature, but on the other hand the phonon population decrease~s drastically according to the Boltzmann factor v.
In conclusion, we would like to emphasize that spin fluctuations of heavy fermion U-compounds can be seen by Raman scattering.This is indicative of large magneto-optical coupling already observed for non-heavy fermion U-compounds 13 and perhaps characteristic for any Ucompound.This may be due to the large spinorbit coupling in U itself.Moreover the q~0 measurements of the spin fluctuations in UPt 3 and UBe13 show the same characteristic energy scale as the neutron data for q >I ~-I.The absence of any Fermi liquid behavior of the spin fluctuation rate remains an openquestio~ Any p~'oposed theory for heavy fermlons must be able to account for this disagreement.Furthermore our measurements give evidence for a strong electron-phonon coupling, which has to be taken into acccount by any theory explaining the unusual superconductivity.
A coupling of the observed A I phonon of UPt 3 to the electronic syste~ seems even more probable because its frequency is of the same order as the spin fluctuation rate.The q = 0 Alg phonon coincides with a flat optical phonon branch near 10 meV (80 cm -1 ) measured for q >1 ~-1 (Ref.5) and establishes the existence of an Einstein mode in UPt 3. The coincidence of an Einstein mode with the spin relaxtion rate is a stri~n~, similarity between UPt 3 and OBe1~'','~.

Fig. I showsTemperature
Fig. I shows Raman spectra of UPt 3 at 300, 77 and 5 K, obtained in backscatterln-g geometry using perpendicular polarizations of incident and scattered light.This choice of polarizations reduces (100 % in the case of ideal polarizations) the fraction of light scattered elastically due to surface imperfections and strongly indicates the qu~slelastic scattering extending beyond 200 cm-" in Fig.I to be of magnetic origin8 The elastically scattered light has been accounted for by a Lorentzian fit to the laser line and shows a cut-off near +30 cm -I.Moreover 0 elastic scattering should show no temperature dependence, i.e. no increasing Stokes/anti-Stokes asymmetry with decreasing temperature as seen in Fig. I. Finally, the residual Stokes scattering intensity at 5 E cannot be due to second order phonon difference processes since these processes die ou~t very rapidly with decreasing temperature v.The quaslelastic scattering intensity in Fig.I (given by the hatched area) is interpretedas due to spin fluctuations as will be described below.
Fig 3: Raman spectra of UPtR for parallel polarizations of incidefit (5309 ~) and scattered light.The scatterir~ intensity of the A I_ phonon is separated from the background ~y the dashed lines.