Theory of Giant Magnetoresistance and Tunneling Magnetoresistance

Abstract

This chapter describes the theory of the giant magnetoresistance effect and the tunneling magnetoresistance effect. Giant magnetoresistance and tunneling magnetoresistance arise when a magnetic field reorients the magnetization in different regions of a specimen causing a change in electrical resistance. Typically these regions are different ultrathin layers. Giant magnetoresistance can occur in metallic multilayers. Two geometries are important. Current-in-plane GMR was the first “spintronic” effect and was discovered in 1988. Current-perpendicular-to-plane GMR was observed a few years later and is conceptually easier to understand than current-in-plane GMR. In this chapter both of these phenomena are treated in a semiclassical approximation. For current-in-plane GMR, it is necessary to treat the transport as nonlocal. For current-perpendicular-to-plane GMR, a local approximation is often adequate. Tunneling magnetoresistance arises when quantum mechanical tunneling between ferromagnetic electrodes through an insulating layer depends on the relative orientation of the magnetizations of the two electrodes. In this chapter, tunneling magnetoresistance is treated using the Landauer approach which envisions ballistic electrons traveling between reservoirs with given chemical potentials being transmitted or reflected by the insulating layer. The tunneling current through the layer is carried by the evanescent states. The properties of these evanescent states and how they join to those electronic states near the Fermi energy of the electrodes for the majority and minority spin channels can be important for the size of the tunneling magnetoresistance effect.