Abstract
The impurity spin polarization, static susceptibility, and longitudinal impurity spin relaxation rate are calculated for thes-d model as function of temperature and magnetic field for ferromagnetic and antiferromagnetic exchange coupling. The thermodynamic functions and the dynamical susceptibility are obtained from the impurity relaxation spectrum, which is approximated by taking into account the infrared-like singularities. For antiferromagnetic coupling the zero-field susceptibility obeys a Curie-Weiss law1/χ∼4.6(T+θ) for high and intermediate temperatures and it approaches the finite value1/χ∼3.8θ for zero temperature. The zero-field relaxation rate is much larger than the Korringa value; it decreases with temperature and approaches the nonzero value1/T 1∼1.2θ for zero temperature. The relaxation rate decreases with increasing field. The results for the spin polarization agree well with the experimental data for the Cu:Fe alloy.
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References
A. Abragam,The Principles of Nuclear Magnetism (Clarendon Press Oxford, England, 1961); C. P. Schlichter,Principles of Magnetic Resonance (Harper and Row, New York, 1963).
K. Yoshida and A. Okiji,Progr. Theor. Phys. (Kyoto)34, 505 (1965).
M. B. Walker,Phys. Rev. 176, 432 (1968); R. Orbach and H. J. Spencer,Phys. Rev. 179, 690 (1969).
J. Kondo,Advances in Solid State Physics (Academic Press, New York, 1969), Vol. 23, p. 183;Progr. Theor. Phys. (Kyoto)32, 37 (1964).
Y. Nagaoka,Phys. Rev. 138, A1112 (1965).
H. Suhl,Phys. Rev. 141, 483 (1966).
J. Zittartz,Z. Physik 217, 43 (1968).
K. Fischer,Springer Tracts Mod. Physics 54, 1 (1970).
R. More and H. Suhl,Phys. Rev. Letters 20, 500 (1968).
P. Wölfle, W. Brenig, and W. Götze,Physics Letters 30A, 448 (1969);Z. Physik 235, 59 (1970).
W. Brenig, J. A. Gonzalez, W. Götze, and P. Wölfle,Z. Physik 235, 52 (1970); C. S. Ting,Physics Letters 32A, 21 (1970);J. Phys. Chem. Sol. 32, 395 (1971).
W. Götze, inProc. Conf. on EPR in Metals, Haute-Nendaz, September 1973.
F. Bloch and A. Nordsieck,Phys. Rev. 52, 54 (1937).
P. Nozières and C. T. de Dominicis,Phys. Rev. 178, 1097 (1969).
K. D. Schotte and U. Schotte,Phys. Rev. 182, 479 (1969).
P. W. Anderson and G. Yuval,Phys. Rev. Letters 23, 89 (1969); P. W. Anderson, G. Yuval, and D. R. Hamann,Phys. Rev. B 1, 4464 (1970).
M. Fowler and A. Zawadowski,Solid State Comm. 9, 471 (1971); M. Fowler,Phys. Rev. B 6, 3422 (1972).
A. A. Abrikosov and A. A. Migdal,J. Low Temp. Phys. 3, 519 (1970).
V. Emery and A. Luther,Phys. Rev. B9, 215 (1974).
K. D. Schotte and U. Schotte,Phys. Rev. B 4, 2228 (1971).
W. Götze and P. Schlottmann,Solid State Comm. 13, 17 (1973).
W. Götze and P. Schlottmann,Solid State Comm. 13, 511 (1973).
W. Götze and P. Schlottmann,Solid State Comm. 13, 861 (1973).
W. Wilson, preprint, to be published in the Proc. of the Nobel Symposium 24.
E. C. Hirschkoff, O. G. Symko, and J. C. Wheatley,Physics Letters 33A, 19 (1970).
J. L. Tholence and R. Tournier,Phys. Rev. Letters 25, 867 (1970).
P. Steiner, W. v. Zdrojewski, D. Gumprecht, and S. Hüfner,Phys. Rev. Letters 31, 355 (1973).
R. B. Frankel, N. A. Blum, B. B. Schwartz, and D. J. Kim,Phys. Rev. Letters 18, 1051 (1967).
P. Steiner, W. v. Zdrojewski, D. Gumprecht, and S. Hüfner, private communication.
H. Alloul and P. Bernier, preprint.
W. Götze and P. Wölfle,J. Low Temp. Phys. 5, 575 (1971);6, 455 (1972).
H. Mori,Progr. Theor. Phys. (Kyoto)34, 399 (1965).
W. Götze and P. Schlottmann,J. Low Temp. Phys. 12, 149 (1973).
K. D. Schotte,Z. Physik 230, 99 (1970).
C. M. Hurd,J. Phys. Chem. Solids 28, 1345 (1967).
W. Götze and P. Wölfle,Physics Letters 40A, 249 (1972).
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Götze, W., Schlottmann, P. On the longitudinal static and dynamic susceptibility of spin-1/2 Kondo systems. J Low Temp Phys 16, 87–118 (1974). https://doi.org/10.1007/BF00655861
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DOI: https://doi.org/10.1007/BF00655861