  Spin-orbit torques in ferromagnet/nonmagnet/ferromagnet trilayers are studied
using a combination of symmetry analysis, circuit theory, semiclassical
simulations, and first-principles calculations using the non-equilibrium
Green's function method with supercell disorder averaging. We focus on
unconventional processes involving the interplay between the two ferromagnetic
layers, which are classified into direct and indirect mechanisms. The direct
mechanism involves spin current generation by one ferromagnetic layer and its
subsequent absorption by the other. In the indirect mechanism, the in-plane
spin-polarized current from one ferromagnetic layer ``leaks'' into the other
layer, where it is converted into an out-of-plane spin current and reabsorbed
by the original layer. The direct mechanism results in a predominantly
dampinglike torque, which damps the magnetization towards a certain direction
$\mathbf{s}_d$. The indirect mechanism results in a predominantly fieldlike
torque with respect to a generally different direction $\mathbf{s}_f$. Similar
to the current-in-plane giant magnetoresistance, the indirect mechanism is only
active if the thickness of the nonmagnetic spacer is smaller than or comparable
to the mean-free path. Numerical calculations for a semiclassical model based
on the Boltzmann equation confirm the presence of both direct and indirect
mechanisms of spin current generation. First-principles calculations reveal
sizeable unconventional spin-orbit torques in Co/Cu/Co, Py/Cu/Py, and Co/Pt/Co
trilayers and provide strong evidence of indirect spin current generation.
