The longevity of Jacques Friedel's model of the virtual bound state

Peter M. Levy; Albert Fert

doi:10.1016/j.crhy.2015.12.011

Condensed matter physics in the 21st century: The legacy of Jacques Friedel

The longevity of Jacques Friedel's model of the virtual bound state
[La longévité du modèle d'état lié virtuel de Jacques Friedel]

Peter M. Levy ¹ ; Albert Fert ^2,³

¹ Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA
² Unité mixte de physique CNRS/Thales, 91767, Palaiseau, France
³ Université Paris-Sud, 91405 Orsay cedex, France

Comptes Rendus. Physique, Volume 17 (2016) no. 3-4, pp. 447-454.

Résumé
Abstract

Nous illustrons la pertinence toujours actuelle du modèle de l'état lié de Friedel pour décrire la diffusion des électrons dans les métaux. Ce modèle a été appliqué à des problèmes aussi différentes que la chiralité des interactions de spin dans les métaux ou l'effet Hall de spin causé par la diffusion d'impuretés avec couplage spin–orbite.

We illustrate the continuing pertinence of Friedel's model of the virtual bound state to describe electron scattering in metals. This model has been applied to such disparate studies as the chirality of spin interactions in metals, and the spin Hall effect caused by scattering from impurities with spin–orbit coupling.

Publié le : 2015-12-21

DOI : 10.1016/j.crhy.2015.12.011

Keywords: Virtual bound state (vbs), Phase shifts, Impurity scattering, Spin Hall effect, Dzyaloshinsky–Moriya Interaction (DMI), Skew scattering
Mot clés : Magnétisme, Conduction électrique, Impuretés

Affiliations des auteurs :

Peter M. Levy ¹ ; Albert Fert ^{2, 3}

¹ Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA
² Unité mixte de physique CNRS/Thales, 91767, Palaiseau, France
³ Université Paris-Sud, 91405 Orsay cedex, France

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Peter M. Levy; Albert Fert. The longevity of Jacques Friedel's model of the virtual bound state. Comptes Rendus. Physique, Volume 17 (2016) no. 3-4, pp. 447-454. doi : 10.1016/j.crhy.2015.12.011. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2015.12.011/

Bibliographie
Cité par

[1] J. Friedel Philos. Mag., 43 (1952), p. 153

[2] M. Gradhand; D.V. Fedorov; P. Zahn; I. Mertig; M. Gradhand; D.V. Fedorov; P. Zahn; I. Mertig; S. Lowitzer; M. Gradhand; D. Ködderitzsch; D.V. Fedorov; I. Mertig; H. Ebert; M. Gradhand; D.V. Fedorov; P. Zahn; I. Mertig; K. Tauber; M. Gradhand; D.V. Fedorov; I. Mertig; C. Herschbach; M. Gradhand; D.V. Fedorov; I. Mertig; D.V. Fedorov; C. Herschbach; A. Johansson; S. Ostanin; I. Mertig; M. Gradhand; K. Chadova; D. Ködderitzsch; H. Ebert Phys. Rev. B, 104 (2010), p. 27

[3] T. Seki; et al.; G.Y. Guo; S. Maekawa; N. Nagaosa; Bo Gu; Jing-Yu Gan; Nejat Bulut; Timothy Ziman; Guang-Yu Guo; Naoto Nagaosa; Sadamichi Maekawa; X. Wang; J. Xiao; A. Manchon; S. Maekawa Phys. Rev. B, 7 (2008), p. 125

[4] A. Fert; P.M. Levy; Peter M. Levy; H.X. Yang; M. Chshiev; Albert Fert Phys. Rev. B, 106 (2011)

[5] A. Fert; Peter M. Levy; P.M. Levy; A. Fert Phys. Rev. B, 44 (1980), p. 1538

[6] S. Heinze et al. Nat. Phys., 7 (2011), p. 713

[7] S. Lounis; et al.; L. Petersen et al. Phys. Rev. B, 108 (2012)

[8] E. Daniel; J. Friedel Columbus, Ohio, 1964 (J. Daunt; P. Edwards; F. Milford; M. Yaqub, eds.), Plenum, New York (1965), p. 933

[9] The derivation of Eq. (6) and details of the calculations is given in Ref. [5].

[10] Higher-order terms in $1 / R$ enter $E^{(3)}$ , as, for example, ones proportional to ${(R_{A} R_{B})}^{- 2}$ , but for large R, Eq. (8) is the leading term.

[11] A. Fert Mater. Sci. Forum, 59–60 (1990), p. 439

[12] S. Heinze et al. (see Ref. [6]. H. Yang, et al.) | arXiv

[13] A. Fert et al. Nat. Nanotechnol., 8 (2013), p. 152

[14] A. Thiaville; et al.; Emori et al. Nat. Mater., 100 (2012), p. 57002

[15] M.I. Dyakonov; V.I. Perel Phys. Lett. A, 13 (1971), p. 657

[16] A. Fert; A. Friederich; A. Hamzic J. Magn. Magn. Mater., 24 (1981), p. 231 (see Sec. 5)

[17] A. Messiah Quantum Mechanics, North-Holland, Amsterdam, 1961

[18] P.M. Levy Phys. Rev. B, 38 (1988), p. 6779

[19] P.W. Anderson Phys. Rev., l24 (1961), p. 41

[20] A. Fert; P.M. Levy Phys. Rev. Lett., 106 (2011) (see inset on Fig. 1)

[21] N.A. Sinitsyn J. Phys. Condens. Matter, 20 (2008)

[22] D.M. Brink; G.R. Satchler, Oxford University Press, Oxford, 1975 See Ref. [18], in particular see Eq. (3.2b). Also see Angular Momentum in particular p. 148 for the spherical tensor notation of vectors, p. 150 for the gradient formula, and pp. 136–144 for orthogonality and recoupling relations for the 3j symbols

[23] M. Yamanouchi; L. Chen; J. Kim; M. Hayashi; H. Sato; S. Fukami; S. Ikeda; F. Matsukura; H. Ohno Appl. Phys. Lett., 102 (2013)

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