Magnetism in the vortex core state has been studied by spatially-resolved NMR. The nuclear spin lattice relaxation rate T1-1 of 205Tl in nearly optimal-doped Tl2Ba2CuO6+\delta (Tc=85 K) is significantly enhanced in the vortex core region. The NMR results suggest that the suppression of the d-wave superconducting order parameter in the vortex core leads to the nucleation of islands with local antiferromagnetic (AF) order.
PACS numbers: 74.72.Jt, 76.50.+g, 76.60.Jx
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