Theory of the Negative Magnetoresistance in Magnetic Metallic Multilayers
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THEORY OF THE NEGATIVE MAGNETORESISTANCE IN MAGNETIC METALLIC MULTILAYERS RANDOLPH Q. HOOD AND L. M. FALICOV Department of Physics, University of California at Berkeley, and Materials Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California, 94720, USA ABSTRACT The Boltzmann equation is solved for a system consisting of alternating ferromagnetic normal metallic layers. The in-plane conductance of the film is calculated for two configurations: successive ferromagnetic layers aligned (i) parallel and (ii) antiparallel to each other. The results explain the giant negative magnetoresistance encountered in these systems when an initial antiparallel arrangement is changed into a parallel configuration by application of an external magnetic field. The calculation depends on (A) geometric parameters (the thicknesses of the layers); (B) intrinsic metal parameters (number of conduction electrons, magnetization and effective masses in the layers); (C) bulk sample properties (conductivity relaxation times); and (D) interface scattering properties (diffuse scattering versus potential scattering at the interfaces). It is found that a large negative magnetoresistance requires, in general, considerable asymmetry in the interface scattering for the two spin orientations. All qualitative features of the experiments are reproduced. Quantitative agreement can be achieved with sensible values of the parameters. The effect can be conceptually explained based on considerations of phase-space availability for an electron of a given spin orientation as it travels through the multilayer sample in the various configurations and traverses the interfaces.
1. INTRODUCTION Ferromagnetic-normal metallic superlattices and sandwiches [1,2] display a number of interesting properties, such as a varying interlayer magnetic coupling [3] and a negative, sometimes very large magnetoresistance (MR) effect [4-15]. Examples are (NiFe/Cu/NiFe), (NiFe/Ag/NiFe), (Fe/Cr),,, (Co/Cu),,, (Fe/Cu),,, and (Co/Ru),,, to name just a few. It has been found that the magnetic moment of each ferromagnetic layer is arranged with respect to that of the neighboring ferromagnetic layers either in a parallel fashion, or in an antiparallel one, depending on the thickness of the metal spacers and on the quality of the interfaces. When the conditions are such that the consecutive moments are arranged antiparallel to each other, the application of an external magnetic field to the sample results in two effects: (1) the moments rearrange themselves into a completely parallel arrangement in fields of the order of 1 T; and (2) the sample decreases its resistance -- negative MR -- in all directions (in-plane in particular) by varying amounts which can be as small as a few percent, and as large as 55% (for Co/Cu at liquid Helium temperatures) [13]. A decrease by more than 20% is generally known as the giant magnetoresistanceeffect (GMR). Even though the current knowledge of the MR effect is incomplete, one fact that has emerged is that spin-depend
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