Relation between giant magnetoresistance and critical current for spin precession in magnetic multilayers

In a spin valve with current perpendicular to layers, the electrical resistance with antiparallel magnetic layers differs from the value with parallel layers, by an amount Delta R. Also, above a certain critical value I-c, a dc current induces a precession of the magnetization in the free magnetic layer, through s-d exchange. Using a local mechanism where current-induced torques depend only on the spin polarization of the current, we show that the average of I-c over parallel and antiparallel states is inversely proportional to Delta R when almost any parameter of the spin valve is varied. This prediction agrees with the experimental results of Urazhdin and of Emley On the other hand, the kind of relation predicted in the case of the nonlocal mechanism, where current-induced torques are mediated by the spin accumulation of Johnson and Silsbee, is inconsistent with some of the Urazhdin experiments. This shows that the local mechanism is dominant over the nonlocal one in these experiments.