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Spin-Density Wave near the Vortex Cores of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$

Competition with magnetism is at the heart of high temperature superconductivity, most intensely felt near a vortex core. To investigate vortex magnetism we have developed a spatially resolved probe using nuclear magnetic resonance. Our spin-lattice-relaxation spectroscopy is spatially resolved both within a conduction plane as well as from one plane to another. With this approach we have found a spin-density wave associated with the vortex core in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, which is expected from scanning tunneling microscope observations of "checkerboard" patterns in the local density of electronic states.[1] We determine both the spin-modulation amplitude and decay length from the vortex core in fields up to H=30 T.