Intrinsic nonadiabatic topological torque in magnetic skyrmions and vortices

Abstract

We propose that topological spin currents flowing in topologically nontrivial magnetic textures, such as magnetic skyrmions and vortices, produce an intrinsic nonadiabatic torque of the form T t ∼ [(∂ x m × ∂ y m)·m]∂ y m. We show that this torque, which is absent in one-dimensional domain walls and/or nontopological textures, is responsible for the enhanced nonadiabaticity parameter observed in magnetic vortices compared to one-dimensional textures. The impact of this torque on the motion of magnetic skyrmions is expected to be crucial, especially to determine their robustness against defects and pinning centers.

Tuning the Skyrmion Hall Effect via Engineering of Spin-Orbit Interaction

“…Indeed, previous studies have incorporated the textured-induced magnetic and electric fields and shown that this gives raise to the so-called topological torque and topological damping that directly influence the mobility of skyrmions. 52,53…”

Current-driven skyrmion depinning in magnetic granular films

“…Their rich topological properties combined with the ultralow energy required to manipulate them give them an edge over their predecessors such as domain walls and magnetic vortices 3,20,23,[33][34][35][36][37] . Since their discovery, considerable research has been devoted to understand their topological properties, room temperature stability and robustness against disorder 3,[18][19][20][33][34][35][36][37][38] . Still, a deep understanding of their dynamic behavior in real thin films characterized by granular boundaries, is lacking.…”

Cooperative Charge Pumping and Enhanced Skyrmion Mobility

“…We propose that the cooperative electronic pumping arising from a train of skyrmions in a racetrack enhances the collective skyrmion mobility. Notice that each moving skyrmion also pumps a nonequilibrium spin density locally that enhances the magnetic damping but does not affect our conclusions [21]. This prediction calls for experimental verification and has the potential to foster the development of skyrmion racetracks [2,3].…”

“…where m is the unit magnetization vector, ijk is Levi-Cevita symbol, e i is the i-th unit vector in cartesian coordinates and s = ±1 accounts for spin projection on m. When the skyrmion is static, E s em → 0 and the emergent magnetic field B s em is responsible for the deviation of the flowing electron trajectory, resulting in topological charge and spin Hall effects [13,19], as well as topological torque [20,21]. As a reaction, the skyrmion experiences a Magnus force that pushes it sideway, as observed experimentally [23][24][25].…”

“…In contrast, a skyrmion is a 2D object such that the pumped current arises from the cooperation between the spin-motive force (∼ E s em ) and the topological Hall effect (∼ B s em ). Indeed, in the adiabatic limit the semiclassical spin-dependent pumped current reads [21], where S is the waveguide area and σ s H is the ordinary Hall conductivity for spin s. As a result, the total charge current is…”