FIG. 3.

Magnetic trilayer and perpendicular transport. The top and bottom ferromagnetic layers are separated by a nonmagnetic layer. In each layer, the charge current flows along the electric field, where flow directions are given as block arrows. In each ferromagnetic layer, the spin current flows along the charge current with spins aligned with the magnetization (red arrows). For spin currents, block arrows indicate electron flow direction and blue arrows indicate spin direction. Equivalently, block arrows could also indicate charge flow direction with blue arrows indicating magnetic moment. In the non-magnetic layer, the spins in the spin current are a combination of spins aligned with the lower layer magnetization and anti-aligned with the upper layer magnetization (here given by $\widehat{x}-\widehat{z}$). In the absence of spin-orbit coupling, the spin current with spin direction longitudinal to the magnetization is conserved across the interfaces. Note that spin currents are unchanged by flipping both the flow and spin directions. The discontinuity in the spin current at the interfaces, given by the spin direction transverse to the magnetization, is the spin transfer torque, indicated for the top and bottom layers by the green arrows. Typically, one layer will be able to respond to the torques and the other layer will be essentially fixed though one of several mechanisms.