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TEMPERATURE DEPENDENCE OF SCATTERING RATE IN TRANSITION METALS FROM
MAGNETOACOUSTIC EXPERIMENTS
J. Rayne, J. Leibowitz
To cite this version:
J. Rayne, J. Leibowitz. TEMPERATURE DEPENDENCE OF SCATTERING RATE IN TRANSI-
TION METALS FROM MAGNETOACOUSTIC EXPERIMENTS. Journal de Physique Colloques,
1978, 39 (C6), pp.C6-1066-C6-1067. �10.1051/jphyscol:19786472�. �jpa-00217953�
JOURNAL DE PHYSIQUE Colloque C6, supplimenr au no 8, Tome 39, aolit 1978, page C6-1066
TEMPERATURE DEPENDENCE OF SCATTERINS RATE I N T R A N S I T I O N METALS FROM MAGNETOACOUSTIC EXPERIMENTS
*
J.A. Rayne and J.R. ~eibowitz+
Carnegie-MeZZon University, Pittsburgh, PA 15213, U. S. A.
+CathoZic Unive~?sity, Washington, D. C. 20017, U.S.A.
Rbsum6.- La variation en fonction de la tempdrature du taux de diffusion associ6 aux ellipso'ides de lacunes pour le tungstsne, le molybdgne et le niobium a QtQ d6terminQe au moyen de mesures magnQto- acoustiques. Dans le molybdsne et le niobium une variation proportionelle au carrQ de la tempdrature est observQe jusque 12 K. Le coefficient du terme en T2 est en corrQlation avec la taille des ellip- so'ides et suggsre que la diffusion du type Qlectron-Qlectron est dominante aux basses tempbratures.
Abstract.- The temperature dependence of the scattering rate for the hole ellipsoids in tungsten, molybdenum and niobium has been determined from magnetoacoustic data. In molybdenum and niobium a T2 dependence is observed up to 12 K. The coefficient of the T2 term correlates with size of the rele- vant ellipsoids and suggests that electron-electron scattering is dominant at low temperatures.
INTRODUCTION.- The influence of electron-electron collisions on the transport properties of transition metals is of considerable interest. In this paper we report the temperature dependence of the scattering rate in tungsten, molybdenum and niobium obtained from magnetoacoustic experiments. All three metals have a bcc structure with Fermi surfaces containing ellipsoidal hole surfaces at the symmetry points N of the relevant Brillouin zone /l/. For both molyb- denum and niobium the scattering rate for the ellip- soids follows a T2 law. The coefficient of this T2 term appears to correlate with the ellipsoid volume, suggesting that the dominant scattering is due to electron-electron collisions.
EXPERIMENT.- The samples used in this work were sin- gle
-
crystal cylinders, oriented along [l 0 g , with resistance ratios in excess of 10 000 to l. Attenua- tion measurements up to 300 MHz were made in trans- mission for shear waves, using 10 MHz and 20 MHz Y- cut quartz transducers operated in an overtone mode.effect exhibits pronounced selectivity 12
1 . For all
field directions only the oscillations due to the hole ellipsoids in (010) are present. A mote limi- ted discrimination is observed in molybdenum /2/
and niobium 131 for the magnetic field H parallel
-
to
-
E, as can be seen from figure 1.Magnetoacoustic data were recorded automatically - Fig. 1 : Temperature dependence of magnetoacoustic shear-wave data in niobium at 255 ~ z - f o r q along using a Princeton Applied Research, Model 162boxcar
p 0 4 with E and H parallel to
Fog.
The Ziscon- signal averager. The temperature of the sample was t'inzty in "atenukion at low fields is due to the controlled electronically to better than 0.01 K. superconducting to normal transition.Again the oscillations are due to the ellipsoids in RESULTS AND DISCUSSION.- For shear waves propagating
the plane of q and E.
in tungsten with wave vector q
-
alongDO^
and pola- ...rization vector along [ o o ~ , the magnetoacoustic
The oscillatory attenuation for a given orbit
3 is given by
Work supported by U.S. National Science Foundation
a = a. exp (-m(T) /mc)
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786472
where V(T) is the temperature dependent contribu- tion to the scattering rate, a is the limiting at-
0
tenuation at T=O and U is the relevant cyclotron frequency. The above-mentioned selectivity allows the application of equation (1) to determine v(T) for the ellipsoidal orbits in all three metals.
Fig. 2 : Plot of log a/aO versus l'' for magneto- acoustic shear-wave data in niobium with $, and
&
parallel to
Fog.
Figure 2 shows that for the ellipsoids in niobium v(T) = c ~ T ~ . For molybdenum similar behavior is observed, but for tungsten the scattering rate above 6 K follows the relation v(T) = $T3. The values of a, B obtained from these measurements are smarized in Table I. For tungsten and molybdenum the results are in reasonable agreement with those obtained from radio-frequency size effect (RFSE) measurements 141. No comparison is possible for niobium, since RFSE experiments are not practicable with a reasonable specimen thickness owing to the high critical field of niobium.
The coefficients ci for niobium and molydbe- num appear to correlate with the ellipsoid volumes given in Table I, supporting the view that the dominant scattering is due to electron-electron collisions. Since the ellipsoids in tungsten are very small, it would be expected that a would be correspondingly reduced. The T~ dependence of V(T) in this case would then be attributable to small- angle electron-phonon scattering. A more general form for v is given by the expression
v = V
+
iy.'T2 + fi1T30 (2)
which takes into account both electron-electronand
electron-phonon scattering. Analysis of the avai- lable data for all three metals using this equation supports the correlation between the magnitude of a' and the ellipsoid volume. Rowever, the resulting values of B' for molybdenum and niobium are very small, in spite of the fact that all three metals have similar phonon spectra. Further experimental and theoretical work on this problem are clearly required.
ACKNOWLEDGEMENTS.- The .authors would like to thank Dr. Richard Reed of Oak Ridge National Laboratory for the niobium sample used in these experiments.
t
TABLE I
Fit of Scattering Rates to Equations V = V + a~~
0
and V = V. + $ T ~
Ellipsoid
Metal Volume
-
C1 1 -1 B(K2
S X 10-') (K-~ S X ') 10-( i 3
X 103)References
/l/ See for example Mattheiss, L. R., Phys. Rev. B1 (1970) 373.
/2/ Rayne, J.A., IEEE Ultrasonics Symposium edited by J. de Klerk and B.R. McAvoy (1 977) p 321.
/3/ Leibowitz, J.R., Blessing, G.V., Alexander, E.M Phys. Rev. B9 (1974) 2457.
/4/ Boiko, V.V., Gantmakher, V.F., Gasparov, V.A., Sov. Phys-JETP 38 (1974) 604.
