Topological Hall effect in topologically trivial target skyrmions

Electrons moving through a noncoplanar magnetic order acquire a Berry phase effect akin to an effective magnetic field. This effect is also known as the topological Hall effect and has been observed in topological spin texture. Here starting from a classical picture, we showed that a target skyrmion, whose topological charge is zero, has a non-zero transverse current. We then evaluated the Hall angle using the Landauer-Buttiker formalism for various target skyrmion radii. We found non-monotonic Hall angles dependent on the Fermi energy and target skyrmion's radius. Finally, we show the results still respect the adiabatic approximation. It indicates the effect comes from the real-space topology of the spin texture.