Spin-Density Wave near the Vortex Cores in the High-Temperature Superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+y}$

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 ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+y}$, 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 $H=30\mathrm{T}$.

Figure 1

The local field distribution and relaxation rate distribution at $H=14.9\mathrm{T}$. The relaxation rates across the ${}^{17}\mathrm{O}$ NMR spectrum (green curve) at $T=4.2\mathrm{K}$ for a Bi2212 single crystal. At low frequency there is an unexpected increase in the spin-lattice relaxation rate, $T_1^{-1}$, mirrored in spin-spin relaxation, $T_2^{-1}$.

Figure 2

The NMR linewidth, defined as the square root of the second moment of the spectrum, versus applied magnetic field at $T=4.2\mathrm{K}$. The contribution from supercurrents was calculated from GL theory [28] (solid curve) and was subtracted from the data points. Inset: The experimental spectrum (solid, black curve) is much broader as compared to the calculated spectrum (dashed, blue line) for a perfect vortex lattice at $H_0=14.9\mathrm{T}$ and $T=4.2\mathrm{K}$.

Figure 3

The calculated [gray (red)] and experimental (black) results for the spectra (curves) and relaxation rates (dots, model; squares, experiment) for various fields, (a)–(d) for ($H=4,10,15,25\mathrm{T}$). At low magnetic field there is a near monotonic relationship for $T_1^{-1}$ as a function of frequency (local field) as expected for the case $A_{\mathrm{SDW}}\le A_{\mathrm{dia}}$. At high magnetic fields the SDW dominates producing a nonmonotonic distribution of relaxation rates. The spectra are normalized to peak height and the calculated $T_1^{-1}$ is offset vertically and scaled to compare with experiment.

Figure 4

The amplitude $A_{\mathrm{SDW}}$ (squares) and decay length $\tau$ (circles) for the best fit from Eq. (1) to our measured spectra. There is an increase in $A_{\mathrm{SDW}}$ with increasing magnetic field while $\tau$ is nearly constant. Inset: The spatial distribution of the local magnetic fields near a vortex within a ${\mathrm{CuO}}_2$ plane calculated from Eq. (1) for a spin-density wave with these parameters at $H=15\mathrm{T}$.