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Abstract Field-free switching of perpendicular magnetization has been observed in an epitaxial L1$$_1$$-ordered CoPt/CuPt bilayer and attributed to spin-orbit torque (SOT) arising from the crystallographic $3m$ point group of the interface. Using a first-principles nonequilibrium Green’s function formalism combined with the Anderson disorder model, we calculate the angular dependence of the SOT in a CoPt/CuPt bilayer and find that the magnitude of the $3m$$ SOT is about 20\% of the conventional dampinglike SOT. We further study the magnetization dynamics in perpendicularly magnetized films in the presence of $$3m$ SOT and Dzyaloshinskii-Moriya interaction, using the equations of motion for domain wall dynamics and micromagnetic simulations. We find that for systems with strong interfacial DMI characterized by the N'eel character of domain walls, a very large current density is required to achieve deterministic switching because reorientation of the magnetization inside the domain wall is necessary to induce the switching asymmetry. For thicker films with relatively weak interfacial DMI and the Bloch character of domain walls the deterministic switching with much smaller currents is possible, which agrees with recent experimental findings. 

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 nonequilibrium 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 𝐬_𝑑. The indirect mechanism results in a predominantly fieldlike torque with respect to a generally different direction 𝐬_𝑓. Similarly 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 sizable 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.