Scanning ion microscopy with polarization analysis is utilized for three-dimensional spin mapping of the surface magnetization (SM) of circular Co dots created inﾠsitu by focused ion beam etching of 30ﾠnm thin Co/Si(100) films. From 3D scanning ion microscopy with polarization analysis spin maps, direct evidence is found for the existence of vortex-antivortex states with in-plane circular or hyperbolic SM components and a wide core with perpendicular SM components which oscillate in the outer region and become zero.