Fig. 4: Examples of architectures for SOT induced by FMs.

a Illustration of field-free switching of a FM (FM₁) assisted by another FM (FM₂). When an external current is applied along the x direction, the z spins generated by the magnetization-dependent spin Hall effect in FM₂ as well as the y spins generated by the spin Hall effect in the heavy metal enable deterministic switching without the help of an external magnetic field. The switching process is not deterministic if it relies solely on the spin Hall effect in the heavy metal. b Illustration of self-generated SOT driven by the spin Hall effect in a FM. The spin Hall currents outgoing from the FM are reflected at outer boundaries and lead spin torque to the FM itself. The imbalance between the re-entering spin angular momenta from top and bottom interfaces results in a non-zero SOT. Here the gradual decreases in the size of electrons represent the decay of the magnitudes of non-equilibrium spins. Although the spin sink layers are denoted by gray layers, they are not necessary to be non-magnets but can be antiferromagnets, artificial superlattices, or even vacuums.