Circuit model for spin-bottleneck resistance in magnetic-tunnel-junction   devices
  Spin-bottlenecks are created in magnetic-tunnel-junction devices by spatial inhomogeneity in the relative resistances for up and down spins. We propose a simple electrical circuit model for these devices which incorporates spin-bottleneck effects and can be used to calculate their overall resistance and magnetoresistance. The model permits a simple understanding of the dependence of device magnetoresistance on spin diffusion lengths, tunneling magnetoresistance, and majority and minority spin resistivities in the ferromagnetic electrodes. The circuit model is in a good quantitative agreement with detailed transport calculations. 
T. Jungwirth and A.H. MacDonald