An extended Boltzmann formalism for transport description in thin Fe–Cr–Fe trilayers

Abstract

We present the calculations of Giant Magnetoresistance (GMR) for thin trilayers of the type nFe/3Cr/nFe where 1 ≤ n ≤ 8 for the slab geometry. All parameters used for the calculations in Boltzmann approach like the potentials, relaxation times, effective masses and the Fermi energy are determined for the different spin polarisations from electronic structure of trilayer on the base of ab initio method. The value of the parameter P corresponds to the specularity factor in Fuchs-Sondheimer theory. It is responsible for scattering electron from the metallic surface determined in analytical way. The results show a strong dependence of GMR on the ferromagnetic layer thickness as well as on the concentration of scattering centers.Inspite of the fact that from the time of the discovery of giant magnetoresistance (GMR) effects in Fe/Cr/Fe multilayers [1, 2] almost 20 years have passed and many experimental and theoretical investigations have been conducted the description of the phenomenon is not completed and it still constitutes a challenge. We should remember that studies of transport properties in metallic superlattices are affected by many inherent complexities of the material. Many possible complications arise in these types of artificial material, among them, interfacial interdiffusion at various lateral length scales [3][4][5], bulk defects, structural changes of an individual layer and overall thicknesses. The last measurements reported [6] and extensively studied of the growth, structure, magnetization and magnetotransport in Fe/Cr/Fe superlattices show that the intrinsic GMR originates mainly from interfacial scattering and is determined by the interface width. This experimental fact confirms our earlier conclusion that the interface should be treated physically not as an ideal plane but as a transition zone between different materials where we can observe a mixture of two components close to the interface especially the significant increase of magnetic moment at interface for different spin orientation [7]. In semiclassical approach the contribution of surface scattering to thin films resistance is represented by the factor P σ belonging to the interval (0,1) in the Fuchs-Sondheimer theory [8]. In the present paper, the bulk scattering is taken into account by introducing spin-dependent (spinindependent) relaxation times in the ferromagnetic (nonmagnetic) layers. In semiclassical models, the number of free parameters becomes so large that they cannot be really used for the quantitative interpretation. The parameters like relaxation times, effective masses and the values representing the heigth of