We have derived the expression of the Ruderman-Kittel-Kasuya-Yosida coupling between two ferromagnetic layers separated by a nonmagnetic spacer, for arbitrary crystal structure and Fermi surface. For the first time, quantitative predictions of the interlayer coupling for Cu, Ag, and Au spacers are given. The results are in good agreement with recent experimental data for fcc Co/Cu and Fe/Cu systems.

Oscillatory coupling between ferromagnetic layers separated by a nonmagnetic metal spacer.

A theory of interlayer exchange coupling is presented. A detailed and comprehensive discussion of the various aspects of the problem is given. The interlayer exchange coupling is described in terms of quantum interferences due to confinement in ultrathin layers. This approach provides both a physically transparent picture of the coupling mechanism, and a suitable scheme for discussing the case of a realistic system. This is illustrated for the Co/Cu/Co(001) system. The cases of metallic and insulating spacers are treated in a unified manner by introducing the concept of the complex Fermi surface.

Theory of interlayer magnetic coupling

The phenomenon of electron tunnelling has been known since the advent of quantum mechanics, but continues to enrich our understanding of many fields of physics, as well as creating sub-fields on its own. Spin-dependent tunnelling (SDT) in magnetic tunnel junctions (MTJs) has recently aroused enormous interest and has developed in a vigorous field of research. The large tunnelling magnetoresistance (TMR) observed in MTJs garnered much attention due to possible applications in non-volatile random-access memories and next-generation magnetic field sensors. This led to a number of fundamental questions regarding the phenomenon of SDT. In this review article we present an overview of this field of research. We discuss various factors that control the spin polarization and magnetoresistance in MTJs. Starting from early experiments on SDT and their interpretation, we consider thereafter recent experiments and models which highlight the role of the electronic structure of the ferromagnets, the insulating layer, and the ferromagnet/insulator interfaces. We also discuss the role of disorder in the barrier and in the ferromagnetic electrodes and their influence on TMR.

https://iopscience.iop.org/article/10.1088/0953-8984/15/4/201/pdf

Spin-dependent tunnelling in magnetic tunnel junctions

(1993). Ultrathin metallic magnetic films: magnetic anisotropies and exchange interactions. Advances in Physics: Vol. 42, No. 5, pp. 523-639.

Ultrathin metallic magnetic films: magnetic anisotropies and exchange interactions

We present a Ruderman-Kittel approach to the problem of oscillatory exchange coupling between ferromagnetic layers separated by a nonmagnetic metal spacer. This model provides a very simple explanation for the occurrence of long periods as well as multiperiodic oscillations, and is valid for arbitrary crystal structure and Fermi surface. The role of defects, such as misfit dislocations and interfacial roughness, is discussed.

Ruderman-Kittel theory of oscillatory interlayer exchange coupling.

Interface roughness, magnetic moments, and couplings in (A)m/(Cr)n (001) superlattices (A=Fe, Co, Ni).

The general trends for the electronic structure of perfect model superlattices AmBn are calculated using a real-space tight·binding model. The magnetic moments distribution and the interlayer magnetic couplings between ferromagnetic layers Am (A=Fe or Co) coupled by non-magnetic (B=V or Ru), nearly ferromagnetic (B=Pd) or antiferromagnetic (B=Cr) spacer layers Bn are obtained as a function of the spacer thickness n. In a first part, we present the model we used for the calculation and the crystallographic structure of the considered superlattices (Fe/V, Fe/Cr, Co/Ru and Co/Pd). These considera­ tions will be applied to the non·magnetic and nearly ferromagnetic cases to derive general trends for the magnetic interlayers couplings. In a second part, we apply the method we presented previously to the superlattices with an antiferromagnetic spacer (Fe,Cr.). Using first a "d" band calculation we show that the interlayer coupling energy can be understood in terms of a strong interfacial antifer­ romagnetic coupling and of a constrained magnetic wall in the Cr layer giving a rapidly oscillating coupling energy. An extension of the previous calculation taking into account the "spd" hybridization does not affect the previous conclusion. Finally we examine the distribu­ tion of magnetic moments and the stability of tilted antiferromagnetic Cr layers and we find that this magnetic structure is nearly degenerate with the collinear antiferromagnetic arrangement.

Electronic Structure, Magnetic Order and Interlayer Magnetic Couplings in Metallic Superlattices

Theoretical investigations of the magnetic behaviour of Cr monolayers deposited on a Fe(001) substrate: Role of a mono-atomic step

Interfacial alloying and interfacial coupling in Cr/Fe(001)

Electronic structure, magnetism and growth of ultrathin films of transition metals

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