Spatially-resolved NMR is used to probe the magnetism in and around vortex cores of nearly optimally-doped Tl2Ba2CuO 6+δ (Tc=85 K). The NMR relaxation rate T −1 1 at 205 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 TN =20 K. Above TN 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.PACS numbers: 74.20. Rp, 74.25.Fy, 74.25.Jb, 74.70.Tx In high-T c cuprates (HTC) the superconductivity with d-wave symmetry appears when carriers are doped into the antiferromagnetic (AF) Mott insulators. It is well established that the strong AF fluctuation plays a crucial role in determining many physical properties. Therefore the relation between superconductivity and magnetism has been a central issue in the physics of HTC. Especially, how the antiferromagnetism emerges when the dwave superconducting order parameter is suppressed is a fundamental problem in the superconducting state [1,2]. In this respect, the microscopic structure of vortex core, which is a local normal region created by destroying the superconductivity by magnetic field, turns out to be a very interesting subject.Within the framework of the semiclassical approximation, in which the electron correlation effects are ignored, vortex cores in d-wave superconductors are in the normal metallic state which is same as the state above T c , similar to s-wave superconductors [3]. However, recent high resolution STM experiments have revealed many unexpected properties in the spectrum of vortex cores, which are fundamentally different from these semiclassical dwave vortex cores [4]. For instance, a checkerboard halo of the local density of states (LDOS) around the core has been reported in Bi 2 Sr 2 CaCu 2 O 8+δ [5]. A new class of theories has pointed out that the strong electron correlation effects change the vortex core structure dramatically. For example, possible competing orders, such as AF [6], staggered flux [7], and stripe [2,8] orderings in and around cores have been discussed. Therefore it is crucial for gaining an understanding of the vortex state of HTC to clarify how the AF correlation and pseudogap phenomena, which characterize the magnetic excitation in the normal state, appear in and around vortex cores.Despite extensive studies, little is known about the microscopic electronic structure of the vortices, especially concerning the magnetism. The main reason for this is that STM experiments do not directly reflect the magnetism. Neutron scattering experiments on La 2−x Sr x CuO 4 have reported that an applied magnetic field enhances the AF correlation in the superconducting state [9]. However, the relation between the observed AF ordering and the magnetism within vortex cores is not clear, because the neutron experiments lack spatial resolution. Recent µSR experime...