We have investigated the magnetic structure of self-organized Fe islands on W(001) by means of spin-polarized scanning tunneling spectroscopy (Sp-STS). Single-domain, simple vortex, and distorted vortex states have been observed. The high resolution magnetic images were used to experimentally determine the single-domain limit. The experimental structures were compared with results of micromagnetic calculations confirming the ground state nature of the experimental configurations. The single-domain limit directly observed with Sp-STS is consistent with theoretical predictions.