Distribution of current in spin valves (abstract)

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Abstract
We present a model describing the distribution of spin up and spin down currents within the layers of spin valve structures. With this model and experimentally determined bulk mean free paths we successfully describe a variety of experimental results, including the variation of resistance and magnetoresistance with both ferromagnetic and nonferromagnetic layer thicknesses, and the current-induced field acting on the ferromagnetic layers versus overall current. Our model is based on an approximate path integral solution of the Boltzmann equation for in-plane transport in a multiply layered structure. For a given orientation of the magnetizations it calculates the current density jσ(r) at each point r for each spin σ throughout the structure. From jσ(r) it is straightforward to obtain the current in each layer for parallel versus antiparallel magnetizations, or of the current density near interfaces relevant to electromigration. Included in our model are both spin dependent bulk scattering as well as scattering at interfaces, which are treated as thin layers. For example, in order to obtain quantitative agreement with experiments with permalloy based structures it is essential to include spin independent scattering arising from Fe and Ni atoms rendered nonferromagnetic next to the spacer due to interfacial intermixing. Our results bear directly on the fundamentals of GMR by successfully describing transport in spin valves using the measured bulk spin dependent mean free paths of the individual layers. Our results are also of technological interest because they predict how current affects the MR response to an external field.

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