  Spatially-resolved NMR is used to probe the magnetism in and around vortex
cores of nearly optimally-doped Tl_2Ba_2CuO_{6+x} (Tc=85 K). The NMR relaxation
rate 1/T_1 at Tl site provides a direct evidence that the AF spin correlation
is significantly enhanced in the vortex core region. In the core region Cu
spins show a local AF ordering with moments parallel to the layers at T_N=20K.
Above T_N the core region is in the paramagnetic state which is a reminiscence
of the state above the pseudogap temperature (T*~120 K), indicating that the
pseudogap disappears within cores.
