Abstract
AbstractThe resistance and magnetoresistance (MR) of three-dimensional current-perpendicular-to-plane (CPP) structures have been calculated via numerical finite element solutions of the Laplace equation. This model accounts for the non-uniform current paths in a four-probe geometry that can yield MR that differs from the intrinsic MR of the isolated CPP pillar with spatially uniform current flow. We calculated the four-probe MR for various geometries and resistivities of both the normal metal leads and the magnetoresistive pillar. From a single, unified approach, we are able to consistently account for the disparate behavior that has been previously published. In particular, we identify conditions that produce four-probe MR that differs from the intrinsic MR of the CPP pillar and highlight those situations where the four-probe resistance is negative. Finally, we present a simple analytical formula for the MR ratio that is applicable to narrow CPP pillars with wide, thin leads.
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