i wonder if there is a "best" way to interprete the figure of interlayer exchange coupling (IEC).
i present the IEC as function as spacer tickness for metal/MgO interface, the strength of the interaction decreases linearly from the thickness of n=3 to the thickness of n=7 where it becomes zero. What is the reason for this linear dependence? Does this dependence depend on the MgO gap width?
best regards
Consult the paper by P Bruno (Phys. Rev. B 52, 411 (1995)) [1]. See in particular Eq. (3.24) herein and the relevant discussions regarding the dependence of the exchange coupling on the spacer thickness in the cases where the spacer is metallic / insulating. In your case, where the spacer consists of a metallic layer on an insulating layer, the dependence of the exchange coupling on the spacer thickness appears to be dominated by the metallic part of the spacer (you have not specified the thickness of each part of the spacer). I think you will have to carry out an independent theoretical calculation (along the lines described in the above-mentioned paper by Bruno) in order to gain physical insight into your observations.
[1] http://journals.aps.org/prb/abstract/10.1103/PhysRevB.52.411
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.52.411
Thank you for your reply.
i read the paper but the relation between the IEC and the gap of the spacer is still not clear for me.
You are welcome Taoufik.
As regards the band gap, have you paid attention to the concept of complex Fermi surface, discussed extensively in the paper by Bruno? See, for example, Fig. 3, p. 417, in the paper by Bruno. For the background, I refer you to the book The Theory of the Properties of Metals and Alloys, by NF Mott, and H Jones (Oxford University Press, 1945 - first published in 1936), the paper Analytic Properties of Bloch Waves and Wannier Functions, by W Kohn (Phys. Rev. 115, 809 (1959)), and the excellent PhD thesis of Johan Cuypers, Scattering of electrons at heterostructure interfaces (Eindhoven University of Technology, 1992), the link to which I attach below.
http://repository.tue.nl/386541
http://journals.aps.org/pr/abstract/10.1103/PhysRev.115.809
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