PALE:ClassicArticles/GMR/Theory91011

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Theoretical Considerations

The next three sections are on the theoretical work that was done between 1989 and 2000 on GMR. In his first publication on GMR, in 1988, Professor Fert suggested an interpretation of his data based on (1) the strong spin dependent scattering of the conduction electrons in the ferromagnetic transition-metals, and (2) that the role of the external field is to switch the orientation of adjacent magnetic layers from antiparallel in zero field to parallel. With these two ingredients he reasoned that when the magnetization of the magnetic layers are parallel, the resistivity for one spin current is much lower than for the other. As the two spin currents conduct independently in the two-current model, as if they were conductors in a parallel circuit, one has a short-circuit effect inasmuch as the resistivity for the multilayer is controlled by the spin channel with the lower resistivity. However, when the magnetic layers are aligned antiparallel the resistivity of each spin channel is averaged [between the spin-up and spin-down scattering] and the short-circuit is suppressed, thereby raising the resistivity. The role of the external field in this explanation is solely to switch the magnetization of the layers from antiparallel to parallel and thereby produce a short-circuit in the multilayer, which lowers its resistivity.

Subsequent theoretical work built on and amplified this reasoning and was directed towards explaining the myriad of details that ensued in the years following discovery of GMR. The first work in 1989, by Camley and Barnas, was based on the Boltzmann equation for transport in the multilayer relevant to the geometry encountered in the original experiments [1]. At the time they worked on their calculation, Camley and Barnas were at the KFA in Jülich, Germany and worked closely with Peter Grünberg. To capture the scattering at interfaces they used the Fuchs-Sondheimer theory of surface roughness scattering; and while they were able to capture some aspects of the data their treatment was unable to obtain the appropriate weighting of the bulk and interface scattering to arrive at the correct mean free path of the electrons in the multilayer. This length was crucial for setting the scale by which to gauge the effect of the thickness of multilayers on the GMR.

A second attempt in 1990 by Levy, Zhang and Fert was more successful [2]. It was based on the Kubo formalism of electrical conductivity and gave a more balanced treatment of the effects on the mean free path of the electrons from the scattering in the bulk of the layers and the scattering at the interfaces. Consequently, it provided a more realistic length scale by which to ascertain the role of layer-thickness on the GMR. In the ensuing years Levy and his collaborators developed more insights on the different material aspects that impact on GMR. Their results are summarized in a review that appeared in 1994 [3]. Parenthetically, the observation of GMR was not confined to multilayered structures. In 1992 two groups observed GMR in granular materials in which magnetic grains are immersed in a nonmagnetic metallic matrix. Most of the treatments of GMR prior to 1995 were based on phenomenological model Hamiltonians with adjustable parameters, and many were based on the semi-classical equation of motion for the transport in which one could simultaneously specify the positions and momenta of electrons.

Since then there have been many treatments of electron transport in metallic multilayers which were first principle or ab-intio calculations where all the necessary parameters are detemined from knowledge of the atomic constituents in the structure, and which are based on the quantum theory of transport in solids.

1 R.E. Camley and J. Barnas, Physical Review Letters 63,664 (1989).

2 P.M. Levy, S. Zhang and A. Fert, Physical Review Letters 65, 1643 (1990).

3 Giant Magnetoresistance in Magnetic Layered and Granular Materials, Chapter in Solid State Physics Vol. 47, Edited by H. Ehrenreich and D. Turnbull, (Academic Press, Cambridge MA, 1994), 367-462.