Fig. 1: Energy-efficient switching of a PMA nanoelement on a topological insulator.

The magnetization switching in the nanoelement is driven by Dirac spin-orbit torque induced by an optimal 2D electric current pulse (\({\overrightarrow{j}}_{m}\)) flowing at the surface of a topological insulator substrate. The calculated optimal control path for switching, with α = 0.1, ξD = ξF, and T = 50τ0, is shown with the green line. The directions of the normalized magnetic moment \(\overrightarrow{s}\) and the optimal current \({\overrightarrow{j}}_{m}\) are indicated by the blue and red arrows, respectively.