Diagrammatic analysis of the dynamics of localized moments in metals

Stewart Barnes, J. Zitkova-Wilcox

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

Using the conventional exchange Hamiltonian Hes, together with an additional model Hamiltonian which provides a source of lattice relaxation for the conduction-electron magnetization, the coupled local-moment-conduction- electron transverse dynamic susceptibility is calculated. Feynman temperature-ordered Green's functions are used and are "dressed" with self-energies which are correct to second order in interaction parameters. A pair of coupled vertex equations are constructed which includes all diagrams correct to second order in the interaction parameters. In order to obtain the desired two-particle characteristics of the response function, some new manipulative and mathematical methods are introduced. These enable the vertex equations to be reduced to a coupled pair of linear equations which determine the coupled susceptibility. At sufficiently high temperatures the Kondo "g shifts" and the weak frequency dependence of the self-energies can be ignored. These linear equations are then equivalent to the linearized version of the following Bloch equations: ddtMs=gs[Ms×(HextMe)]-(1Tse)[Ms-s0(HextMe) ]+(gsgeTes)[Me-e0(HextMs)], ddtMe=ge[Me×(HextMs)]-(1Tes+1Te1)[Me- e0(HextMs)]+(gegsTse)[Ms-s0(HextMe)]+D2[Me-e0(HextMs)], where Tse, Tes, and Te1 are the relaxation times for the local-moment-conduction-electron-spin, the conduction-electron-spin-local-moment, and the conduction-electron-spin-lattice systems. The diffusion constant is D=13vF2Ti, where Ti is the nonmagnetic-impurity scattering time, and Me and Ms are, respectively, the conduction-electron and local-moment magnetizations. The spin-orbit scattering in the presence of large-potential-impurity scattering results in relaxation effects identical to those obtained above with the model electron-lattice Hamiltonian. Hext is the external static and rf field, e0 and s0 are the conduction-electron and local-moment-unenhanced (by the s-d exchange) susceptibilities, and ge and gs are the respective g factors (and B have been set equal to unity). These Bloch equations show that the relaxation destination vectors are those appropriate to the total internal field. The presence of the g-factor ratios are consistent with the fact that Hes transfers spin, rather than magnetization, from the conduction electrons to local moments and vice versa. For temperatures kT

Original languageEnglish (US)
Pages (from-to)2163-2192
Number of pages30
JournalPhysical Review B
Volume7
Issue number5
DOIs
StatePublished - 1973
Externally publishedYes

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conduction electrons
Metals
moments
Electrons
metals
Hamiltonians
electron spin
Magnetization
linear equations
magnetic permeability
Scattering
magnetization
Linear equations
apexes
scattering
impurities
Impurities
Green's function
unity
Relaxation time

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Diagrammatic analysis of the dynamics of localized moments in metals. / Barnes, Stewart; Zitkova-Wilcox, J.

In: Physical Review B, Vol. 7, No. 5, 1973, p. 2163-2192.

Research output: Contribution to journalArticle

Barnes, Stewart ; Zitkova-Wilcox, J. / Diagrammatic analysis of the dynamics of localized moments in metals. In: Physical Review B. 1973 ; Vol. 7, No. 5. pp. 2163-2192.
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