Objectives:

Novel magnetotransport phenomena such as giant magnetoresistance (GMR) (in magnetic multilayers) and tunnel magnetoresistance (TMR) (in ferromagnetic tunnel junctions) appear when the size scale of the magnetic materials becomes nanolevel. Therefore, it is required to understand the spin-dependent scattering process in magnetic multilayer structure and here we shall cover the spin dependent scattering process in multilayer structure films.

Spin dependent scattering of electrons:

At first, we shall focus on different types of scatterings that the electrons may experience in magnetic multilayers. In the Boltzmann equation approach, we are mainly concerned with elastic (energy conserving) scattering, i.e., in each scattering the direction of propagation of electrons changes. Therefore, it is necessary to distinguish between spin dependent and spin flip scatterings. These two types of scattering are illustrated in Fig. 9.1. In the case of spin dependent scattering the orientation of the electron spin is conserved in each scattering event but the probabilities of scattering for electrons with ↑ and ↓ spin projections are different. On the other hand, when an electron undergoes a spin-flip scattering, its spin orientation changes from ↑ ( ) to ↓( ) or vice versa and, at the same time, the spin of the scattering centre changes by so that the total spin is conserved.

There are several sources of spin flip scattering. During the fabrication process, some of the magnetic atoms may enter the non-magnetic spacer layer to form magnetic impurities. When an electron is scattered off a magnetic impurity the spins of the electron and that of the impurity can interchange provided the impurity spin is free to rotate. This occurs when the impurity spin is not strongly coupled to the spins of the ferromagnetic layers, i.e., the impurity is not near the ferromagnet / spacer interface. Electrons can also be scattered from spin waves in the ferromagnet layers. Spin waves are quasiparticles with spin one and, therefore, creation (annihilation) of a spin wave in a collision with an electron leads to a flip of the electron spin. Since it involves the spin-wave energy, this is an inelastic process which is only important at elevated temperatures. Finally, when impurities with a strong spin-orbit interaction, such as gold, are present in the multilayer, the spin of an electron incident on such an impurity may be reversed due to the spin-orbit interaction. Since all these processes mix ↑and ↓ spin channels, they are detrimental to the large magnetoresistance.

In the case of spin dependent scattering, the key feature is that electrons with different spin orientations ( ↑, ↓) are scattered at different rates when they enter the ferromagnetic layers. Given that electrons obey the Pauli's exclusion principle, an electron can be scattered from an impurity only to quantum states that are not occupied by other electrons. At zero (low) temperatures, all the states with energies E below the Fermi energy E_F are occupied and those with E > E_F are empty. Since scattering from impurities is elastic, electrons at the Fermi level can be scattered only to states in the immediate vicinity of the Fermi level. For example, the Fermi level in copper (and other noble metals) intersects only the conduction band whose density of states D(E_F ) is low. It follows that the scattering probability in copper is also low. On the other hand, the d band in transition metals is only partially occupied and, therefore, the Fermi level in these metals intersects not only the conduction but also the d bands. Moreover, since the atomic wave functions of d levels are more localized than those of the outer s levels, they overlap much less, which means that the d band is narrow and the corresponding density of states is high. This opens up a new very effective channel for scattering of conduction electrons into the d band.