Perpendicular spin valves with ultrathin ferromagnetic layers: Magnetoelectronic circuit investigation of finite-size effects

We address two finite-size effects in perpendicular transport through multilayers of ferromagnetic and normal metal layers: (i) the transport properties depend on the magnetic layer thickness when of the order or thinner than the spin-flip diffusion length and (ii) magnetic layers with thickness approaching the magnetic coherence length become transparent for spin currents polarized perpendicular to the magnetization. We use magnetoelectronic circuit theory to investigate both effects on angular magnetoresistance (aMR) and spin-transfer torque in perpendicular spin valves. We analyze recent aMR experiments to determine the spin-flip diffusion length in the ferromagnet permalloy as well as the Py £ Co interface spin-mixing conductance and propose a method to measure the ferromagnetic coherence length.