Topological Hall effect in Shastry-Sutherland lattice

We study the classical Heisenberg model on the geometrically frustrated Shastry-Sutherland lattice with additional Dzyaloshinskii-Moriya (DM) interaction. We show that several noncollinear and noncoplanar magnetic states such as flux, all-out, 3in-1out, canted-flux are stabilized over wide range of parametric space in the presence of DM interaction. We discuss the role of different DM vectors in the stabilization of these complex configurations of localized moments. These ordered states not only drive exotic magnetic properties but also anomalous magneto-transport. The spin of itinerant electron moving on the background of these localized spins acquires a Berry phase which manifests itself by contributing an extra term in Hall conductivity known as geometrical or topological Hall effect. We demonstrate this effect by calculating the energy bands and transverse conductivity for conduction electrons hopping on these localized moments. It is shown that transverse conductivity is non-zero for several of these noncoplanar ordered states even in the absence of magnetic field coupling to the conduction electrons.