  We propose an experimental scheme to determine the spin-transfer torque
efficiency excited by the spin-orbit interaction in ferromagnetic bilayers from
the measurement of the longitudinal magnetoresistace. Solving a diffusive
spin-transport theory with appropriate boundary conditions gives an analytical
formula of the longitudinal charge current density. The longitudinal charge
current has a term that is proportional to the square of the spin-transfer
torque efficiency and that also depends on the ratio of the film thickness to
the spin diffusion length of the ferromagnet. Extracting this contribution from
measurements of the longitudinal resistivity as a function of the thickness can
give the spin-transfer torque efficiency.
