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Theory of Perpendicular Magnetoresistance in Magnetic Multilayers
Valet, T. & Fert, A., 1993. Theory of Perpendicular Magnetoresistance in Magnetic Multilayers. Phys. Rev. B 48, 7099
Essay about this article
In bulk materials magnetoresistance is controlled by the angle between the current and magnetic field and by the orientation of the electric field or current relative to the crystalline axes. In multilayers, the orientation of the current relative to the plane of the layering is important. For this reason when Jack Bass and Bill Pratt Jr of Michigan State University (MSU) sat down to discuss their first results on magnetoresistance for current perpendicular to the planes of the layering with me at the end of 1991, we agreed on a new convention to describe GMR.
The geometry of the original experiments had the current parallel to the plane of the layers and was called CIP-MR; whereas a geometry with the current perpendicular to the plane of the layers was called CPP-MR. The reason why CPP-MR came later was due to the dimension of the multilayers. The plane of the layers are millimeters in size [10-3 meters], whereas the thicknesses of layers are nanometers in size [10 -9 meters]. For the CPP-MR geometry, the cross sectional area, A, for the current is millimeters squared, while the length, l, across which the resistance is measured, is in nanometers. Therefore the measured potential drop across the multilayer [the resistance R] is tiny, i.e., for a given resistivity, 
, the resistance is,
where R is in ohms, and is in micro-ohm-cm. To measure the small resistance of a multilayer in the CPP geometry, the MSU researchers incorporated it in a circuit with a superconducting quantum interference devise (SQUID). This limited CPP measurements to low temperatures. On the other hand CIP measurements do not have the handicap of the tiny l/A ratio, and CIP-MR can be measured at room temperature or low temperatures.
The first “theory” of CPP-MR was given by Shufeng Zhang and Peter Levy in terms of effective spin dependent electric fields [1]; these effective fields were predicated on the premise that there was no loss of spin current in each of the the two spin channels as the current moved across the layers. Two years later Valet and Fert developed a theory of CPP-MR based on the Boltzmann equation of motion. In this theory the origin of the effective spin dependent fields are clarified; they arise from the spin accumulation attendant to driving currents across interfaces between the magnetic and nonmagnetic layers and these fields appear as the electrochemical potentials induced by the accumulations. The theory of Valet and Fert also shows that the first calculation by Zhang and Levy is only valid in the limit when the loss of spin current density due to spin-flip scattering is small, i.e., where the spin diffusion length is long compared to the repeat distance of the multilayer, which is the thickness of the basic unit cell that consists of a magnetic and nonmagnetic layer.
Fortunately, the multilayers that first displayed CPP-MR had relatively thin layers, so that the repeat distance of the unit was indeed small compared to the spin diffusion length, and the basic idea of Zhang and Levy was applicable to the analysis of the CPP-MR data taken on the early samples. Later work in the CPP geometry used layers with thicknesses comparable to the spin diffusion length in order to probe the corrections introduced when the spin current in each channel did not remain constant as it traversed the multilayer. In these cases only the theory of Valet and Fert is applicable.
More recently several groups have adopted another nomenclature and use CIP-GMR and CPP-GMR. Finally, there is no reason to limit the geometries to currents in and perpendicular to the plane of the layers; in principle there can be any angle between the current and the direction of the layering. In 1995 Professor Shinjo’s group in Kyoto succeeded in growing corrugated multilayered structures on silicon substrates that had (111) faceted grooves etched on their surface; these structures can be probed by conventional means with current at an angle to the plane of the layer, CAP, [45º in this case] as well as currents in the plane [2].
References
1 S. Zhang and P.M. Levy, Conductivity Perpendicular to the Plane of Multilayered Structures, Journal of Applied Physics 69, 4786-4788 (1991).
2 P.M. Levy, S. Zhang, T. Ono, and T. Shinjo, Electrical Transport in Corrugated Multilayered Structures, Physical Review B 52, 16049-16054 (1995).
Discussion Question
Under what conditions is the electron’s mean free path irrelevant when describing conduction and GMR in magnetic multilayers?
The above article is reprinted with permission from Valet,T. & Fert, A. (1993) Phys. Rev. B 48, 7099. Copyright (1993) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
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