---

Prog. Theor. Phys. 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

Institute for Solid State Physics, University of Tokyo, Roppongi, Tokyo

(Received December 23, 1972)

Abstract:

The theory of the singlet ground state for the s-d exchange model is extended to the core of d-electrons with orbital degeneracy. The effective s-d Hamiltonian is derived from the extended Anderson Hamiltonian by the Schrieffer-Wolff canonical transformation. On the basis of the effective Hamiltonian, the ground-state wave function and the ground-state energy are calculated. The anomalous part of the ground-state energy is given by -Dexp[N/(2l+1)ρJ], independently of the d-electron number, when the Hund coupling is neglected compared with the effective s-d interaction. This binding energy is much larger than that for a localized s-electron because of an extra factor of 1/(2l+1) in the exponent. This large value is caused mainly by the orbital quenching. For a more realistic case in which the Hund coupling is larger than the s-d interaction, it reduces to a smaller value of -Dexp[(2l+1)N/ρJ] for a half-filled shell in which orbital exchange does not exist. This value is due purely to the spin quenching. Qualitative discussion is given about the spin quenching and orbital quenching on the effective Hamiltonian derived for n=2l, n being the number of d-electrons.

URL : http://ptp.ipap.jp/link?PTP/49/1483/
DOI : 10.1143/PTP.49.1483

[ Full Text PDF : FREE ACCESS (1443K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

---

References:

1. K. Yosida and A. Okiji, Prog. Theor. Phys. 34 (1965), 505[PTP].
2. K. Yosida, Phys. Rev. 147 (1966), 223[APS].
3. A. Okiji, Prog. Theor. Phys. 36 (1966), 712[PTP].
4. K. Yosida, Prog. Theor. Phys. 36 (1966), 875[PTP].
5. K. Yosida, Phys. Rev. 164 (1967), 879[APS].
6. A. Yoshimori, Phys. Rev. 168 (1968), 493[APS].
7. A. Yoshimori and K. Yosida, Prog. Theor. Phys. 39 (1968), 1413[PTP].
8. K. Yosida and A. Yoshimori, Prog. Theor. Phys. 42 (1969), 753[PTP].
9. P. W. Anderson, Phys. Rev. 124 (1961), 41[APS].
10. J. R. Schrieffer and P. A. Wolff, Phys. Rev. 149 (1966), 491[APS].
11. P. W. Anderson and A. M. Clogston, Bull. Am. Phys. Soc. 6 (1961), 124.
    J. Kondo, Prog. Theor. Phys. 28 (1962), 846[PTP].
12. T. Moriya, Prog. Theor. Phys. 33 (1965), 157[PTP].
13. K. Yosida, A. Okiji and S. Chikazumi, Prog. Theor. Phys. 33 (1965), 559[PTP].
14. J. R. Schrieffer, J. Appl. Phys. 38 (1967), 1143[CrossRef].
15. L. Dworin and A. Narath, Phys. Rev. Lett. 25 (1970), 1287[APS].
16. B. Coqblin and J. R. Schrieffer, Phys. Rev. 185 (1969), 847[APS].
17. H. Shiba, Prog. Theor. Phys. 43 (1970), 601[PTP].
18. A. A. Abrikosov, Physics 2 (1965), 5.
19. S. Nakajima, Prog. Theor. Phys. 39 (1968), 1402[PTP].
20. P. W. Anderson, Phys. Rev. 164 (167), 352[APS]; Phys. Rev. Lett. 18 (1967), 1049[APS].

Citing Article(s) :

1. Journal of the Physical Society of Japan 64 (1995) pp. 4345-4362 :

   Kondo Effect Due to Impurities with (5f)ⁿ Configuration: Fermi Liquid Versus Non-Fermi Liquid

   Mikito Koga and Hiroyuki Shiba

2. Journal of the Physical Society of Japan 66 (1997) pp. 3551-3557 :

   Effect of Hund's Rule Coupling on the Kondo Effect

   Youichi Yanase and Kosaku Yamada

3. Journal of the Physical Society of Japan 67 (1998) pp. 1431-1439 :

   s- f Exchange Interaction and RKKY Interaction for Hyperfine-Enhanced Nuclear Magnets of Pr

   Takehiro Nagasima and Hiroumi Ishii

4. Journal of the Physical Society of Japan 67 (1998) pp. 2444-2454 :

   Kondo Effect in Single Quantum Dot Systems – Study with Numerical Renormalization Group Method –

   Wataru Izumida, Osamu Sakai and Yukihiro Shimizu

5. Journal of the Physical Society of Japan 68 (1999) pp. 2317-2325 :

   Effects of the Hund's Rule Coupling in an Orbitally Degenerate Anderson Model

   Katsunori Kubo and Dai S. Hirashima

6. Journal of the Physical Society of Japan 70 (2001) pp. 186-191 :

   Orbital Dependence in Kondo Effect Enlarged by Hund's-Rule Coupling

   Satoshi Yotsuhashi, Hiroaki Kusunose and Kazumasa Miyake

7. Journal of the Physical Society of Japan 74 (2005) pp. 95-102 :

   Enhancement of Kondo Effect in Multilevel Quantum Dots

   Mikio Eto

8. Journal of the Physical Society of Japan 74 (2005) pp. 103-109 :

   Kondo Effect in Quantum Dot Systems –Numerical Renormalization Group Study–

   Wataru Izumida and Osamu Sakai

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

   Ground State of a Pair of Localized Spins in Metals

   Hiroumi Ishii

10. Progress of Theoretical Physics Vol. 53 No. 2 (1975) pp. 315-325 :

    Effects of Anisotropy Energy on the Ground State of Ce Impurities in Metals

    Akio Ogawa and Akio Yoshimori

11. Progress of Theoretical Physics Vol. 53 No. 2 (1975) pp. 366-385 :

    Bound State Due to a Pair of Interacting Magnetic Impurities in Metals. II

    Koi Sato and Yosuke Nagaoka

12. Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 967-981 :

    The Korringa Relation for the Impurity Nuclear Spin-Lattice Relaxation in Dilute Kondo Alloys

    Hiroyuki Shiba

13. Progress of Theoretical Physics Vol. 71 No. 3 (1984) pp. 450-457 :

    Comments on the Dense Kondo State

    Kosaku Yamada, Kei Yosida and Katsuro Hanzawa

14. Progress of Theoretical Physics Vol. 77 No. 5 (1987) pp. 1097-1115 :

    Fermi Liquid Theory on the Basis of Periodic Anderson Hamiltonian with Orbital Degeneracy

    Kosaku Yamada, Kozo Okada, Kei Yosida and Katsurou Hanzawa

15. Progress of Theoretical Physics Supplement No.106 (1991) pp. 129-135 :

    Magnetic Ordering with Small Moments

    Kosaku Yamada and Satoru Inagaki

16. Progress of Theoretical Physics Supplement No.108 (1992) pp. 141-171 :

    Fermi Liquid Theory on Heavy Electron Systems

    Kosaku Yamada, Kei Yosida and Katsurou Hanzawa

---

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.