Skyrmion Hall effect and shape deformation of current-driven bilayer skyrmions in synthetic antiferromagnets

The commonly believed absence of skyrmion Hall effect for topologically trivial magnetic skyrmions is reconsidered for bilayer skyrmions in synthetic antiferromagnets driven by spin-transfer and spin-orbit torques. Using a general Lagrangian formalism, we show that Bloch-type bilayer skyrmions acquire a finite Hall angle when driven by spin-orbit torque, while N\'eel-type skyrmions do not, in agreement with micromagnetic simulations. Both types of skyrmions exhibit current-induced elliptical deformation with minor and major axes aligned longitudinally and transversely to their velocity, respectively. A linear relation between velocity and longitudinal radius is derived with a coefficient proportional to the strength of spin-orbit torque. These effects are critical for antiferromagnetic skyrmion-based applications such as skyrmion racetrack memory. The Lagrange equations also reproduce the linear Hall-angle--helicity relation reported by Msiska et al. [Phys. Rev. Appl. 17, 064015 (2022)]. An intuitive explanation of the skyrmion Hall effect for arbitrary helicity based on the antiferromagnetic exchange torque is also provided.