Weak localization magnetoresistance is used to investigate spin-orbit and the phase relaxation rates. The spin-orbit rate is independent of temperature. By plotting the spin-orbit rate as a function of the inverse thickness of the films, we separate the spin-orbit relaxation into two parts: one from the scattering off the bulk imperfections, and one from the scattering against the two surfaces. The ratio between the spin-orbit and the impurity relaxation rates in the bulk was found to be close to 2 × 10−5 for all the different samples. The influence of implanted heavy ions on the spin-orbit relaxation was also investigated. The dependence of the phase relaxation rate on resistivity, film thickness, and temperature has been studied. Theoretical results for electron-electron and electron-phonon scattering are compared to our data. We consider two novel temperature-independent phase relaxation mechanisms which may explain the residual rate we observe. The influence of a high-frequency electromagnetic field on the phase relaxation rate was investigated. For small microwave power levels the phase relaxation rate was found to increase linearly with microwave power. In the absence of a magnetic field and for samples having a dominating spin-orbit interaction (antilocalization) the resistance increases with microwave power, but turns into a decrease at high microwave power levels. For those samples having very weak spin-orbit interaction the resistance decreases continuously as we apply microwaves. This is roughly the expected behavior, but the observed change in resistance was larger than that calculated at small microwave power levels.
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References
E. Abrahams, P. W. Anderson, D. C. Licciadello, and T. W. Ramakrishnan, Phys. Rev. Lett. 43, 718 (1979).
B. L. Altshuler, A. G. Aronov, and P. A. Lee, Phys. Rev. Lett. 44, 1288 (1980).
B. L. Altshuler, D. E. Khmelnitskij, A. I. Larkin, and P. A. Lee, Phys. Rev. B 22, 5142 (1980).
S. Hikami, A. I. Larkin, and Y. Nagaoka, Prog. Theor. Phys. 63, 707 (1980).
S. Maekawa and H. Fukuyama, J. Phys. Soc. Japan 50, 2516 (1981).
G. Bergmann, Phys. Rep. 107, 1 (1984).
S. Kobayashi and F. Komori, Prog. Theor. Phys. (Suppl.) 84, 224 (1985).
S. Chakravarti and A. Schmid, Phys. Rep. 140, 193(1986).
P. E. Lindelof, J. Nørregaard, andJ. Bindslev Hansen, Z. Phys. B Condensed Matter 59, 423 (1985).
P. E. Lindelofand S. Wang, Phys. Rev. B 33, 1478 (1986).
S. Wang and P. E. Lindelof, Phys. Rev. Lett. 59, 1156 (1987).
L. P. Gorkov, A. I. Larkin, and D. E. Khmelnitskij, Pis'ma Zh. Eksp. Teor. Fiz. 30, 248 (1979) [JETP Lett. 30, 228 (1979)].
G. Bergmann, Phys. Rev. B 28, 2914 (1983).
S. Kobayashi, F. Komori, Y. Ootuka, and W. Sasaki, J. Phys. Soc. Japan 49, 1635 (1980).
G. Bergmann, Phys. Rev. B 25, 2937 (1982).
B. L. Altshuler and A. G. Aronov, Solid State Commun. 38, 11 (1981).
P. A. Lee and T. V. Ramakrishnan, Phys. Rev. B 26, 4009 (1982).
M. Gijs, C. van Haesendonck, and Y. Bruynseraede, J. Phys. F: Met. Phys. 16, 1227 (1986).
D. E. Khmelnitskij, Physica 126B, 235 (1984).
D. Y. Sharvin and Y. V. Sharvin, Pis'ma Zh. Eksp. Teor. Fiz. 34, 285 (1981) [JETP Lett. 34, 272 (1981)].
N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976), p. 15.
R. P. Peters and G. Bergmann, J. Phys. Soc. Japan 54, 3478 (1985).
P. Renucci, L. Gaudart, J. P. Petrakian, and D. Roux, Thin Solid Films 130, 75 (1985).
K. L. Chopra, Thin Film Phenomena (McGraw-Hill, New York, 1969), p. 344.
M. B. Walker, Phys. Rev. B 3, 30 (1971).
R. T. Schumacher and S.-K. Wang, Phys. Rev. B 10, 2129 (1974).
G. Bergmann and C. Horriar-Esser, Phys. Rev. 31, 1161 (1985).
A. A. Abrikosovand L. P. Gorkov, Zh. Eksp. Teor. Fiz. 42, 1088 (1962) [Sov. Phys. JETP. 15, 752 (1962)].
R. Merservey and P. M. Tedrow, Phys. Rev. Lett. 41, 805 (1978).
M. Gijs, C. van Haesendonck, Y. Bruynseraede, and G. Deutscher in Proceedings International Conference on LITPIM, Braunschweig, 1984, Schweitzer and Kramer, eds. (PTB, 1984), p. 139.
G. Bergmann, Phys. Rev. Lett. 48, 1046 (1982).
G. Bergmann, Phys. Rev. Lett. 53, 1100 (1984).
B. L. Altshuler, A. G. Aronov, and D. E. Khmelnitskij, Solid State Commun. 39, 619 (1981).
S. Shelenko and J. Rammer, to be published.
J. Rammerand A. Schmid, Phys. Rev. B 34, 1352 (1986).
A. Schmid, Z. Phys. 271, (1973).
B. L. Altshuler, A. G. Aronov, and D. E. Khmelnitskij, J. Phys. C: Solid State 15, 7367 (1982).
W. Eiler, J. Low Temp Phys. 56, 481 (1984).
G. Bergmann, Phys. Rev. B 28, 515 (1983).
A. E. White, R. C. Dynes, and J. P. Garno, Phys. Rev. B 29, 3694 (1984).
J. Kästner and R. Mölleken, in Proceedings International Conference in LITPIM, Braun-schweig, 1984, Schweitzer and Kramer, eds. (PTB, 1984), p. 177.
V. V. Afonin, Yu. M. Galperin, and R. N. Ignatjev, Fiz. Tverd. Tela 28, 1063 (1986) [Sov. Phys. Solid State 28, 594 (1986)].
P. A. Vorobjev, Fiz Tverd, Tela. 27, 545 (1985) [Sov. Phys. Solid State 27, 336 (1985)].
M. E. Gershenzon and V. N. Gubankov, Pis'ma Zh. Eksp. Teor. Fiz. 34, 32 (1981) [JETP Lett. 34, 30 (1981)].
S. A. Vitkalov, G. M. Gusev, Z. D. Kvon, and G. I. Levjev, Pis'ma Zh. Eksp. Teor. Fiz. 43, 145 (1986) [JETP Lett. 43, 185 (1986)].
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Wang, S., Lindelof, P.E. Weak localization experiments on magnesium films: effects of substrate, ion implantation, microwaves, temperature, and resistivity/thickness on the phase and spin-orbit relaxation. J Low Temp Phys 71, 403–444 (1988). https://doi.org/10.1007/BF00116871
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DOI: https://doi.org/10.1007/BF00116871