Topological spin textures and topological Hall effect in centrosymmetric magnetic nanoparticles

Although topological spin textures are not commonly found in centrosymmetric magnetic systems, noncoplanar monodomain magnetic states such as flower and curling states do emerge due to the contribution of surfaces and edges in nanoparticles. In this work, we studied the topological nature of these intriguing noncoplanar spin textures and their manifestation in electric transport phenomena due to the Berry phase accumulation. Specifically, we calculated the topological charges $Q$ associated with these spin textures and the corresponding topological Hall effect. We assessed these spin textures across various particle sizes and along magnetic hysteresis loops and mapped the spin structures in confined geometries using magnetic force microscopy. We show that $Q$, as a fractional number, increases with particle size and saturates as the system transits from the flower state to the curling state. Along magnetic hysteresis loops, smaller particles that show flower states in zero field, exhibit a peak in $Q$ near the coercive field, a signature of the topological Hall effect demonstrated in other systems. In contrast, larger particles that show curling states during the magnetization reversal, exhibit transitions between the homogeneous state, flower state, and curling state, which generates jumps in $Q$ and the topological Hall effects. These results reveal the rich topological nature of centrosymmetric magnetic nanoparticles, offer control using magnetic field and probe using electric transport, suggesting promising potential applications.