Model calculations of line shapes and amplitudes appropriate to radio-frequency size effect resonances on “small” Fermi surface sheets in complex metals have been carried out using a perturbative technique. Detailed results are presented for high-symmetry sheets, with emphasis on the sphere and the circular cylinder; some discussion is also given to suggest what changes may occur in less regular cases. The calculated line shapes are in good agreement with experiment, both for diffuse surface scattering of the resonating electrons and also for specular surface scattering. The behavior of the amplitudes as a function of the mean free path indicates that the expression customarily used in analyzing data for the temperature dependence of the resonance strength should be modified. Except for the field region near onset, where the behavior is more complicated, we find % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabiqaaiaacaGaaeqabaWaaeaaeaaakeaacaWGZbGaeyyhIu% RaamyzamaaCaaaleqabaGaeyOeI0IaamiEaaaakiaac+cacaGGOaGa% aGymaiabgkHiTiaadwgadaahaaWcbeqaaiabgkHiTiaaikdacaWG4b% aaaOGaaiykaaaa!3F57!\[s \propto e^{ - x} /(1 - e^{ - 2x} )\] where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabiqaaiaacaGaaeqabaWaaeaaeaaakeaacaWG4bGaaeiiai% abggMi6MaaGnaalaaabaGaaGymaaqaaiaaikdaaaGaaeiuaiaac+ca% cqaH7oaBaaa!3AEC!\[x{\rm{ }} \equiv \frac{1}{2}{\rm{P}}/\lambda \], with P the orbit perimeter and λ the mean free path. This replaces the usually adopted form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabiqaaiaacaGaaeqabaWaaeaaeaaakeaacaWGZbGaeyyhIu% RaamyzamaaCaaaleqabaGaeyOeI0IaamiEaaaakiaac+cacaGGOaGa% aGymaiabgkHiTiaadwgadaahaaWcbeqaaiabgkHiTiaaikdacaWG4b% aaaOGaaiykaaaa!3F57!\[s \propto e^{ - x} /(1 - e^{ - 2x} )\]. Furthermore, the mean free path dependence is found to be essentially independent of the degree of specularity, in contrast to previous theoretical results for “simple” metals. While the difference between the usual and the revised expressions for S(x) is not large at modest mean free paths (that is, for x ≳ 1), it can be quite substantial at larger values of λ. This is of importance when dealing with very pure metals at the lowest temperatures or when trying to assess the residual mean free path in samples of moderate purity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. F. Koch and R. E. Doezema, in Proc. 14th Int. Conf. Low Temp. Phys. (North-Holland, Amsterdam, 1975), Vol. 5, p. 134.
V. F. Gantmakher, Rep. Prog. Phys. 37, 317 (1974); see also Ref. 1.
E. A. Kaner and V. L. Fal'ko, Sov. Phys.—JETP 24, 392 (1967).
G. E. Juras, Phys. Rev. 187, 784 (1969).
D. K. Wagner and R. Cochran, J. Low Temp. Phys. 18, 549 (1975); see also D. K. Wagner and R. C. Albers, J. Low Temp. Phys. 20, 593 (1975).
G. E. Juras, Phys. Rev. B 2, 2869 (1970).
P. B. Johnson and R. G. Goodrich, Phys. Rev. 14, 3286 (1976); V. A. Gasparov, Sov. Phys.—JETP 41, 1129 (1976); V. F. Gantmakher and V. A. Gasparov, Sov. Phys.—JETP 37, 864 (1973).
D. A. Boudreau and R. G. Goodrich, Phys. Rev. B 3, 3086 (1971).
D. G. de Groot, Thesis, Free University of Amsterdam (1974).
J. F. Koch and C. C. Kuo, Phys. Rev. 143, 470 (1966); M. S. Khaikin, Adv. Phys. 18, 1 (1969); see also Ref. 1.
P. M. Marcus, Nat. Bur. Std. Circ. 519, 265 (1952).
R. E. Prange and T. W. Nee, Phys. Rev. 168, 779 (1968).
G. E. Juras, Phys. Rev. Lett. 24, 390 (1970).
P. H. Haberland and C. A. Shiffman, Phys. Rev. Lett. 19, 1337 (1967).
M. S. Khaikin, Sov. Phys.—JETP 14, 1269 (1962).
W. A. Reed, Phys. Rev. 188, 1184 (1969); J. H. Wood, Phys. Rev. 146, 432 (1966); A. Goldstein and S. Foner, Phys. Rev. 146, 442 (1966).
A. Fukumoto and M. W. P. Strandberg, Phys. Rev. 155, 685 (1967); P. H. Haberland, J. F. Cochran, and C. A. Shiffman, Phys. Rev. 184, 655 (1969).
D. G. Chatjigiannis, Thesis, Northeastern University (1974).
J. E. Neighbor, C. A. Shiffman, D. G. Chatjigiannis, and S. P. Jacobsen, Phys. Rev. Lett. 27, 929 (1971).
D. Duchardt and C. A. Shiffman, in Proc. 14th Int. Conf. Low Temp. Phys. (North-Holland, Amsterdam, 1975), Vol. 4, p. 325.
G. E. H. Reuter and E. H. Sondheimer, Proc. Roy. Soc. 195A, 336 (1948); see also E. A. Kaner and V. L. Fal'ko, Sov. Phys.—JETP 22, 1294 (1966).
M. Yaqub and J. F. Cochran, Phys. Rev. 137, A1182 (1965).
J. F. Koch and T. E. Murray, Phys. Rev. 186, 722 (1969).
J. R. Peverley, Phys. Cond. Matter 19, 51 (1975).
W. F. Druyvesteyn and A. J. Smets, J. Low Temp. Phys. 2, 619 (1970).
P. B. Johnson, J. C. Kimball, and R. G. Goodrich, Phys. Rev. B 14, 3282 (1976).
B. Castaing and P. Goy, J. Phys. C: Solid State Phys. 6, 2040 (1973).
A. B. M. Hoff and D. G. de Groot, J. Low Temp. Phys. 29, 467 (1977).
Author information
Authors and Affiliations
Additional information
Work supported by the National Science Foundation under Grant DMR76-12573.
Rights and permissions
About this article
Cite this article
Duchardt, D., Neighbor, J.E. & Shiffman, C.A. Calculation of the radiofrequency size effect in complex metals. I. Mean free path dependence of the resonance strength for diffuse or specular surface scattering. J Low Temp Phys 35, 53–87 (1979). https://doi.org/10.1007/BF00121722
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00121722