Neutron Scattering Evidence for a Periodically-Modulated Superconducting Phase in the Underdoped Cuprate La$_{1.905}$Ba$_{0.095}$CuO$_4$

The role of antiferromagnetic spin correlations in high-temperature superconductors remains a matter of debate. We present inelastic neutron scattering evidence that gapless spin fluctuations coexist with superconductivity in La$_{1.905}$Ba$_{0.095}$CuO$_4$. Furthermore, we observe that both the low-energy magnetic spectral weight and the spin incommensurability are enhanced by the onset of superconducting correlations. We propose that the coexistence occurs through intertwining of spatial modulations of the pair wave function and the antiferromagnetic correlations. This proposal is also directly relevant to sufficiently underdoped La$_{2-x}$Sr$_x$CuO$_4$ and YBa$_2$Cu$_3$O$_{6+x}$.

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