Scanning ion microscopy with polarization analysis is utilized for three-dimensional spin mapping of the surface magnetization (SM) of circular Co dots created in situ by focused ion beam etching of 30 nm thin Co=Si100 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. DOI: 10.1103/PhysRevLett.97.107201 PACS numbers: 75.60.Ch, 07.78.+s, 75.70.Rf Recently, broad and intense scientific interest has focused on the physics of magnetism at the nanometer and micrometer scales. Studies of the surface magnetic structure (SMS) of small magnetic elements receive great attention. They allow the exploration of a wealth of new, fundamental SMSs that emerge when the thickness of the sample is of the order of or below the bulk Bloch wall thickness. Central to the fundamental understanding of these small magnetic elements is the precise knowledge of their three-dimensional (3D) SMSs and their dependence on the shape and size of the elements. Of further importance are the interactions between these small elements in patterned magnetic materials. This requires shapes of elements that exhibit minimized stray fields; for example, circular disks should possess flux-closure vortex states with only small external stray fields at remanence.In recent years, the existence of S, C, flower, edgepinning, vortex, antivortex, and other so-called micromagnetic ground states has been predicted and to some extent directly or indirectly observed [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. For many SMSs, however, their detailed 3D, spin-, and spatially resolved SMS is presently not yet known. Among these SMSs, fluxclosure magnetic vortex states, existing in circular magnetic elements, are paid great attention, because they are not only proposed for use in data storage [16], they are reported to possess some unique physical features, such as an overall in-plane circular SMS profile with a central nanometer-sized core possessing a perpendicular magnetization [6,9,15], which plays an important role in the dynamics of microscopic magnets [17,18].Using magnetic force microscopy [6], Lorentz microscopy [9,15], a combination of surface magneto-optical Kerr effect (SMOKE) hysteresis loops and micromagnetic simulations [4,8], off-axis holography in transmission electron microscopy [10], and scanning electron microscopy with polarization analysis [13], the presence of magnetic vortices in patterned magnetic permalloy and Co elements was indirectly or directly verified. For Fe quantum dots, the existence of curling spin structures in vortex cores is also predicted from full-potential linear augmented-plane-wave calculations [19]. To the best of our knowledge, there is presently no fundamental information available about the detailed 3D spin structure of magnetic vortices which could help to obtai...