Critical current of spin-transfer-torque-driven magnetization dynamics in magnetic multilayers

The critical current of the spin-transfer-torque-driven magnetization dynamics was studied by taking into account both spin pumping and the finite penetration depth of the transverse spin current. We successfully reproduced the recent experimental results obtained by Chen [Phys. Rev. B 74, 144408 (2006)] and found that the critical current remains finite even in the zero-thickness limit of the free layer. We showed that the remaining value of the critical current is determined mainly by spin pumping. We also showed that we could control the critical current by varying the spin-diffusion length of the nonmagnetic electrode adjacent to the free layer.