Correlation Between Chiral Fluctuations and Topological Hall Effect Above Room Temperature

The topological Hall effect is used exclusively as a signature of the magnetic skyrmions in a material. However, this phenomenon might have originated from other mechanisms such as thermally driven topology in chiral magnets. The relationship between topological spin structures and Hall conductivity were investigated at low temperatures; however, much remained unknown for the emergent topology at elevated temperatures. In this project, we performed the Monte Carlo simulation of a two-dimensional model of the chiral magnet and studied the correlation between Hall conductivity and the chiral fluctuations at elevated temperatures. We used both the topological charge and scalar chirality to characterize the topology of the spin-lattice. The Hall conductivity was calculated by applying the Kubo formula to the tight-binding model. Massive ensemble averages were taken to derive the thermal average of both the chirality and Hall conductivity. The results show there is a correlation between the topology and the Hall conductivity for a large number of averages.