Spin-density wave near the vortex cores in the high-temperature superconductor Bi₂Sr₂CaCu₂O_8+y

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 based upon NMR spin-lattice-relaxation spectroscopy. With this approach we have found a spin-density wave associated with the vortex core in Bi₂Sr ₂CaCu₂O_8+y, similar to checkerboard patterns in the local density of electronic states reported from scanning tunneling microscope experiments. We have determined both the spin-modulation amplitude and decay length from the vortex core in fields up to H=30T.