Spin–orbit torque in a three-fold-symmetric bilayer and its effect on magnetization dynamics

Field-free switching of perpendicular magnetization has previously been observed in an epitaxial L1₁-ordered CoPt/CuPt bilayer and attributed to spin-orbit torque (SOT) arising from the crystallographic 3<i>m</i>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 3<i>m</i>SOT is about 20% of the conventional dampinglike SOT. We further study the magnetization dynamics in perpendicularly magnetized films in the presence of 3<i>m</i>SOT and Dzyaloshinskii-Moriya interaction, using the equations of motion for domain wall dynamics and micromagnetic simulations. For systems where strong interfacial DMI results in the Néel character of domain walls, we find that 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, deterministic switching is possible at much smaller current densities, which may explain the recent experimental findings.