  Analytical calculations and micromagnetic simulations are used to determine
the Berry curvature and topological Hall effect (THE) due to conduction
electrons in small ferromagnetic particles. Our focus is on small particles of
nonellipsoidal shapes, where noncoplanar spin structures yield a nonzero
topological Hall signal quantified by the skyrmion number Q. We consider two
mechanisms leading to noncoplanarity in aligned nanoparticles, namely
flower-state spin configurations due to stray fields near corners and edges,
and curling-type magnetostatic selfinteractions. In very small particles, the
reverse magnetic fields enhance Q due to the flower state until the reversal
occurs, whereas for particles with a radius greater than coherence radius Rcoh
the Q jumps to a larger value at the nucleation field representing the
transition from the flower state to the curling state. We calculate the
Skyrmion density (average Berry curvature) from these spin structures as a
function of particle size and applied magnetic field. Our simulation results
agree with analytical calculations for both flower state and flux closure
states. We showed the presence of Berry curvature in small particles as long as
the size of the particle is less than the single domain limit. Using magnetic
force microscopy (MFM), we also showed that in a nanodot of Co with a suitable
size, a magnetic vortex state with perpendicular (turned-up) magnetization at
the core is realized which can be manifested for Berry curvature and emergent
magnetic field in confined geometries for single domain state at room
temperature.
