Optimal magnetization switching via spin-orbit torque on the surface of a topological insulator

An optimal protocol for the current-induced switching of a perpendicularly magnetized nanoelement placed on the surface of a topological insulator is presented. The time dependence of both in-plane components of the surface current that induces the magnetization reversal via Dirac spin-orbit torque with minimal Joule heating is derived analytically as a function of the required switching time and material properties. It is demonstrated that a particularly energy-efficient switching is realized for vanishing dampinglike torque. The optimal reversal time providing a tradeoff between the switching speed and energy efficiency is derived. The obtained switching protocol is contrasted with the one realized in heavy-metal systems. Topological insulators provide a highly tunable platform for the realization of energy-efficient magnetization switching.