Quantum Well Theory of the Exchange Coupling in Co/Cu/Co(001)

Mathon, J.; Villeret, Murielle; Muniz, R. B.; Castro, J. d'Albuquerque e; Edwards, D. M.

doi:10.1103/physrevlett.74.3696

Cited by 82 publications

(64 citation statements)

References 12 publications

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“…GMR ratios in Co/ Cu are as large as 65%, 28 whereas Fe/ Cu and Fe/ Au multilayers are only a few percent. The important difference between these systems is that the Co majority-electron band is well matched to the Cu s-p band, 20,29,30 whereas the minority band is not. It was suggested by Dieny 31 that the source of the small GMR in Fe/ Cu is due to the poor mismatch between the Fe and Cu band structures for both majority and minority electrons.…”

Section: Discussion Of the Scattering At The Au/ Fe Interfacesmentioning

confidence: 99%

Spin-dependent transport in Fe andFe∕Aumultilayers

et al. 2005

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Section: Discussion Of the Scattering At The Au/ Fe Interfacesmentioning

confidence: 99%

Spin-dependent transport in Fe andFe∕Aumultilayers

et al. 2005

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“…2,4,[7][8][9] Good agreement between total-energy calculations and the SP approximation were obtained in these systems. However, as we show here, there are cases in which this method is inadequate for spacer thicknesses and temperatures of experimental interest.…”

Section: ͓S0163-1829͑99͒04738-4͔mentioning

confidence: 99%

Section: ͓S0163-1829͑99͒04738-4͔mentioning

confidence: 99%

“…They express the coupling asymptotically ͑i.e., for large values of N) as a sum of contributions coming from extremal wave vectors of the spacer Fermi surface ͑FS͒ in the direction perpendicular to the layers. 6,7,4 The oscillation period of each contribution is determined by the spacer FS, whereas the amplitude and phase are regulated also by the degree of confinement of the carriers within the spacer layer.The stationary phase method has been successfully applied to analyze both experimental data and results of full numerical calculations of J in several systems, such as Co/ Cu/Co ͑001͒ and Fe/Cu/Fe ͑001͒ multilayers. 2,4,[7][8][9] Good agreement between total-energy calculations and the SP approximation were obtained in these systems.…”

mentioning

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“…6,7,4 The oscillation period of each contribution is determined by the spacer FS, whereas the amplitude and phase are regulated also by the degree of confinement of the carriers within the spacer layer.…”

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Inadequacy of the asymptotic approximation for the interlayer coupling in Fe/Ag/Fe and Fe/Au/Fe (001) trilayers

et al. 1999

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We discuss the basic assumptions underlying the stationary phase approximation to the interlayer exchange coupling between magnetic materials across nonmagnetic spacers. We show that, for temperatures and spacer thicknesses of interest, it cannot be applied to systems such as Fe/Ag/Fe and Fe/Au/Fe ͑001͒ trilayers. Such inadequacy results from particular confinement effects caused by the Fe layers in the Ag and Au extremal Fermi-surface ''neck'' states. This is of special relevance to the interpretation of experimental data. ͓S0163-1829͑99͒04738-4͔The bilinear exchange coupling J between magnetic materials across nonmagnetic metallic spacers oscillates with decaying amplitude between positive ͑ferromagnetic͒ and negative ͑antiferromagnetic͒ values, as the spacer layer thickness N is increased. For systems with crystalline layers and sharp interfaces, J can be calculated at any temperature T from an expression of the form 1-5where f (E) is the Fermi-Dirac distribution function, k ជ ͉͉ is a wave vector parallel to the layers, F(E,k ជ ͉͉ ,N) is given in terms of the electronic Green functions of the system, and the sum over k ជ ͉͉ is restricted to the two-dimensional Brillouin zone ͑BZ͒. The prominent features of the oscillatory behavior of J, i.e., period, phase, and amplitude, are related to the electronic structure of the multilayered system. While numerical evaluations of Eq. ͑1͒ do not highlight this relationship, simple approximations, currently referred to as the stationary phase ͑SP͒ method, allow semianalytical expressions for J to be derived. They express the coupling asymptotically ͑i.e., for large values of N) as a sum of contributions coming from extremal wave vectors of the spacer Fermi surface ͑FS͒ in the direction perpendicular to the layers. 6,7,4 The oscillation period of each contribution is determined by the spacer FS, whereas the amplitude and phase are regulated also by the degree of confinement of the carriers within the spacer layer.The stationary phase method has been successfully applied to analyze both experimental data and results of full numerical calculations of J in several systems, such as Co/ Cu/Co ͑001͒ and Fe/Cu/Fe ͑001͒ multilayers. 2,4,[7][8][9] Good agreement between total-energy calculations and the SP approximation were obtained in these systems. However, as we show here, there are cases in which this method is inadequate for spacer thicknesses and temperatures of experimental interest. This is precisely what happens in Fe/Ag/Fe ͑001͒ and Fe/Au/Fe ͑001͒ trilayers. To understand why this is so, it is instructive to review the basic assumptions of the method.The SP method relies on the fact that, for fixed E and k ជ ͉͉ , the function F in the integrand of Eq. ͑1͒ oscillates with N. Thus, F can be expanded in a Fourier series in N, whose coefficients c s and corresponding wave vector k Ќ are functions of E and k ជ ͉͉ . The following approximations are then introduced to allow an analytical evaluation of the integrals over these variables. The first one is based on the fact that t...

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Exchange Coupling in Magnetic Multilayers

Edwards

Umerski

2007

Handbook of Magnetism and Advanced Magnetic Materials

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After a brief historical introduction, the origin of interlayer exchange coupling (IEC) in magnetic multilayers is explained with an emphasis on the role of quantum well states in the nonmagnetic spacer layers. Analytic results for a simple model are given and techniques for quantitative calculation of IEC in real systems are described. A full discussion is given on mechanisms for biquadratic exchange coupling and the temperature dependence of IEC arising from single‐electron and spin‐wave excitations. Theory and experiment are compared for systems with noble metal, transition metal, antiferromagnetic metal, and insulating spacers. Open questions are identified, particularly an order‐of‐magnitude discrepancy between theory and experiment for the strength of IEC in the case of transition‐metal spacers.

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Quantum Well Theory of the Exchange Coupling in Co/Cu/Co(001)

Cited by 82 publications

References 12 publications

Spin-dependent transport in Fe andFe∕Aumultilayers

Spin-dependent transport in Fe andFe∕Aumultilayers

Inadequacy of the asymptotic approximation for the interlayer coupling in Fe/Ag/Fe and Fe/Au/Fe (001) trilayers

Exchange Coupling in Magnetic Multilayers

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