Asymmetric skyrmion Hall effect in systems with a hybrid Dzyaloshinskii-Moriya interaction

We examine the current-induced dynamics of a skyrmion that is subject to both structural and bulk inversion asymmetry. There arises a hybrid type of Dzyaloshinskii-Moriya interaction (DMI) which is in the form of a mixture of interfacial and bulk DMIs. Examples include crystals with symmetry classes C$_n$ as well as magnetic multilayers composed of a ferromagnet with a noncentrosymmetric crystal and a nonmagnet with strong spin-orbit coupling. As a striking result, we find that, in systems with a hybrid DMI, the spin-orbit-torque-induced skyrmion Hall angle is asymmetric for the two different skyrmion polarities ($\pm 1$ given by out-of-plane core magnetization), even allowing one of them t…