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We report spatially resolved nuclear magnetic resonance measurements on a high temperature superconductor that indicate the presence of correlated antiferromagnetic fluctuations in the vortex core. The nuclear spin-lattice relaxation rate, , of planar , in near-optimally doped YBCuO (YBCO), was measured. Outside of the core, is independent of temperature consistent with theoretical predictions for a {\it d}-wave superconductor. In the vortex core increases with decreasing temperature following an antiferromagnetic Curie-Weiss law.

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