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Prog. Theor. Phys. Vol. 43 No. 3 (1970) pp. 601-620

Anomalies and Bound State Due to the Anisotropic s-d Exchange Interaction

Hiroyuki Shiba

Department of Physics, Osaka University, Toyonaka

(Received November 22, 1969)

Abstract:

The Kondo problem for the anisotropic s-d exchange interaction is investigated in detail. The scattering amplitude of a conduction electron is calculated in the most divergent approximation (Abrikosov's approximation). The importance of some types of terms overlooked in the previous work by Miwa and Nagaoka is pointed out. By changing the degree of anisotropy of the exchange integral the behaviors of the obtained scattering amplitude–especially the divergence difficulties–are examined. To see physical meaning of the divergence difficulties the problem of the existence of the bound state realized as the ground state of this coupled many-body system is discussed by extending the Yosida-Okiji-Yoshimori theory to the anisotropic case. It is shown that the exact solution of the bound state can be obtained also for the anisotropic s-d interaction, and that the divergence difficulties stated above are closely connected with the existence of the bound state.

URL : http://ptp.ipap.jp/link?PTP/43/601/
DOI : 10.1143/PTP.43.601

[ Full Text PDF : FREE ACCESS (1017K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. J. Kondo, Prog. Theor. Phys. 32 (1964), 37[PTP].
2. See for example:
   P. W. Anderson, Localized Moments in Many Body Physics, ed. by R. Balian and C. de Witt.
   J. Kondo, “Theory of Dilute Magnetic Alloys” (Researches of the Electrotechnical Laboratory No. 688).
   M. D. Daybell and W. Steyert, Rev. Mod. Phys. 40 (1968), 380[APS].
3. A. A. Abrikosov, Physics 2 (1965), 39.
4. H. Miwa and Y. Nagaoka, Phys. Lett. 22 (1969), 394[CrossRef].
5. K. Yosida, Phys. Rev. 147 (1966), 223[APS].
6. A. Okiji, Prog. Theor. Phys. 36 (1966), 712[PTP].
7. A. Yoshimori, Phys. Rev. 168 (1968), 493[APS].
8. A. Yoshimori and K. Yosida, Prog. Theor. Phys. 39 (1968), 1413[PTP].
9. S. Doniach, Phys. Rev. 144 (1966), 382[APS]; Bull. Am. Phys. Soc. Ser. II 11 (1966), 387.
10. See for example:
    E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge, 1963).
11. S. Nakajima, Prog. Theor. Phys. 39 (1968), 1402[PTP].

Citing Article(s) :

1. Journal of the Physical Society of Japan 61 (1992) pp. 3239-3254 :

   Numerical Renormalization Group Study of Magnetic Impurities in Superconductors

   Koji Satori, Hiroyuki Shiba, Osamu Sakai and Yukihiro Shimizu

2. Journal of the Physical Society of Japan 61 (1992) pp. 3439-3442 :

   1/N and Quantum Monte Carlo Studies of a Magnetic Impurity in an Insulator with a Small Gap

   Tetsuro Saso

3. Journal of the Physical Society of Japan 62 (1993) pp. 4364-4372 :

   Magnetic Impurity in Insulators with Small Energy Gap

   Jun Ogura and Tetsuro Saso

4. Journal of the Physical Society of Japan 67 (1998) pp. 1332-1341 :

   Ground State Properties and Localized Excited States around a Magnetic Impurity Described by the Anisotropic s- d Interaction in Superconductivity

   Tomoki Yoshioka and Yoji Ohashi

5. Journal of the Physical Society of Japan 76 (2007) 023705 (5 pages) :

   Kondo Effect in an Electron System with Dynamical Jahn–Teller Impurity

   Takashi Hotta

6. Journal of the Physical Society of Japan 76 (2007) 084702 (8 pages) :

   Enhanced Kondo Effect in an Electron System Dynamically Coupled with Local Optical Phonon

   Takashi Hotta

7. Progress of Theoretical Physics Vol. 49 No. 5 (1973) pp. 1483-1502 :

   Singlet Ground State of the Localized d-Electrons Coupled with Conduction Electrons in Metals

   Isamu Okada and Kei Yosida

8. Progress of Theoretical Physics Vol. 50 No. 6 (1973) pp. 1777-1796 :

   Ground State of a Pair of Localized Spins in Metals

   Hiroumi Ishii

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