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

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 ${\mathrm{La}}_{1.905}{\mathrm{Ba}}_{0.095}{\mathrm{CuO}}_4$. Furthermore, we observe that both the low-energy magnetic spectral weight and the spin incommensurability are enhanced with 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 ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$.

Figure 1

Constant-energy slices through $S(\mathbf{Q},\omega )$. On the left are measurements at $T\lesssim 5\mathrm{K}$ for excitation energies (a) 1 meV, (b) 3 meV, (c) 6 meV, (d) 12 meV, (e) 35 meV, (f) 110 meV. On the right are measurements at $\hslash \omega =1\mathrm{meV}$ for temperatures of (g) 1.5 K, (h) 32 K, (i) 50 K, together with corresponding fits of symmetrically positioned Gaussian peaks in (j)–(l). Data in (a)–(c) and (g)–(i) were obtained at the MACS spectrometer at NCNR; data in (d)–(f) were measured at SEQUOIA (SNS). The units of $S(\mathbf{Q},\omega )$ are determined by Eq. (1).

Figure 2

Summary of fitted parameters: (a) ${\chi }^{\prime \prime }(\omega )$, (b) $\delta$, and (c) $\kappa$ vs $\hslash \omega$, for temperatures of $\le 5\mathrm{K}$ (violet circles), 32 K (red diamonds), 60 K (orange squares), 120 K (yellow triangles); (d) ${\chi }^{\prime \prime }(\omega )$, (e) $\delta$, and (f) $\kappa$ vs $T$ for energies of 1 meV (blue circles), 6 meV (green squares). Dashed line indicates $T_c=32\mathrm{K}$.

Figure 3

(a) Wave-vector-integrated local susceptibility ${\chi }^{\prime \prime }(\omega )$ measured at temperatures of $\le 6\mathrm{K}$ (violet), 32 K (red), and 100 K (orange). (b) Difference in ${\chi }^{\prime \prime }(\omega )$ between $\sim 6$ and 32 K (violet) and between 32 and 100 K (red). In (a) and (b), diamonds were measured on MACS (base $T=1.5\mathrm{K}$), circles on BT7 (base $T=5\mathrm{K}$), squares on SEQUOIA (base $T=6\mathrm{K}$).