Neutron scattering study of spin ordering and stripe pinning in superconducting ${\mathrm{La}}_{1.93}{\mathrm{Sr}}_{0.07}{\mathrm{CuO}}_4$

The relationships among charge order, spin fluctuations, and superconductivity in underdoped cuprates remain controversial. We use neutron scattering techniques to study these phenomena in ${\mathrm{La}}_{1.93}{\mathrm{Sr}}_{0.07}{\mathrm{CuO}}_4$, a superconductor with a transition temperature of $T_c=20$ K. At $T\ll T_c$ we find incommensurate spin fluctuations with a quasielastic energy spectrum and no sign of a gap within the energy range from 0.2 to 15 meV. A weak elastic magnetic component grows below $\sim 10$ K, consistent with results from local probes. Regarding the atomic lattice, we have discovered unexpectedly strong fluctuations of the ${\mathrm{CuO}}_6$ octahedra about Cu-O bonds, which are associated with inequivalent O sites within the ${\mathrm{CuO}}_2$ planes. Furthermore, we observed a weak elastic $\left(3\overline{3}0\right)$ superlattice peak that implies a reduced lattice symmetry. The presence of inequivalent O sites rationalizes various pieces of evidence for charge stripe order in underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$. The coexistence of superconductivity with quasistatic spin-stripe order suggests the presence of intertwined orders; however, the rotation of the stripe orientation away from the Cu-O bonds might be connected with evidence for a finite gap at the nodal points of the superconducting gap function.

Figure 1

Diagrams indicating out-of-plane displacements of the in-plane oxygens in the low-temperature orthorhombic (LTO), low-temperature less-orthorhombic (LTLO), and low-temperature tetragonal (LTT) phases; space groups listed under acronyms. $+$ ($-$) indicates displacement above (below) plane; line thickness reflects magnitude of displacement. There are two inequivalent in-plane O positions in LTLO and LTT, but all are equivalent in LTO.

Figure 2

(a) Bulk susceptibility of the LSCO $x=0.07$ sample measured with a 20 G magnetic field applied along the $c$ axis both for field cooling (FC) and zero-field cooling (ZFC) conditions. (b) Comparison of magnetic susceptibility measured in a 1-T field applied either along an in-plane Cu-O direction (open circles, labeled $H\parallel a$) or along the $c$ axis (filled circles) after scaling by the anisotropic $g$ factors taken from [30]. Inset shows the difference between these scaled susceptibilities, indicating that diamagnetism within the ${\mathrm{CuO}}_2$ planes sets in below $\sim 80$ K. [To convert the susceptibility to SI units of $\mathrm{H}{\mathrm{m}}^2$/mol, multiply emu/mol by ${\left(4\pi \right)}^2\times {10}^{-13}$.]

Figure 3

Arrows indicate schematically the orientations of (200) and (020) fundamental Bragg peaks of the two main twin domains. Image plots show the results of mesh scans performed around these Bragg peaks. Upper right inset is a photo of the co-mounted crystals, each wrapped in Al foil.

Figure 4

Elastic intensities around the antiferromagnetic wave vector at 1.5 K, (a) measured (with background subtracted) and (b) fit, as described in text.

Figure 5

Temperature dependence of the intensity of elastic magnetic scattering, as described in the text. Filled symbols represent results obtained with $E_f=3.7$ meV; (blue) squares for integrated intensity, (black) circles for peak amplitude; results normalized to 1 at the lowest temperature. Open circles (red) indicate peak amplitude obtained with $E_f=5$ meV. Error bars here and elsewhere correspond to $1\sigma$ determined from counting statistics.

Figure 6

Image plots of intensity vs $E$ and Q for (a) SPINS with $E_f=3.7$ meV, (b) SPINS with $E_f=5$ meV, (c) HYSPEC with $E_i=8$ meV, and (d) HYSPEC with $E_i=27$ meV. Representative scans for (e) $E_f=3.7$ meV and (f) $E_f=5$ meV. Cuts integrated over $0.9\le h\le 1.1$ and $-0.25\le l\le 0.25$ for (g) $E_i=8$ meV and (h) $E_i=27$ meV. Lines in (e)–(h) represent fits of a pair of symmetric Gaussian peaks on a Q-independent background. Scans are vertically offset for clarity. In (c) there is a spurious feature (of undetermined origin) at $E\approx 1.7$ meV.

Figure 7

Compilation of the Q-integrated magnetic intensity (normalized as discussed in the text) as a function of excitation energy. The line through the data is a fit to a constant plus a Lorentzian centered at $E=0$; the half-width at half-maximum of the Lorentzian is $1.3\left(2\right)$ meV.

Figure 8

Measurements of phonons in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ with $x=0.07$ at $T=150$ K. (a) Constant-energy slice ($\hslash \omega =5\pm 2$ meV with $L$ integrated from $-0.25$ to 0.25), showing strong acoustic phonons about the $(2,-2,0), (2,-4,0)$, and $(4,-2,0)$ Bragg points, and soft tilt fluctuations at $(3,-3,0)$. Dashed lines indicate the directions and widths of the slices through $(3,-3,0)$ shown in (b) (longitudinal direction) and (c) (transverse direction). (d) Intensity of the phonon signal at $(3,-3,0)$ integrated from 3 to 7 meV [as in (a)] and multiplied by 2.5 (red squares) and at $(2,-2,0)$ (blue circles), corrected for background measured in between these positions.

Figure 9

Elastic scattering ($\hslash \omega =0\pm 0.5$ meV) about the $(3,-3,0)$ position along the (a) transverse and (b) longitudinal directions. In each case, the red curve is a Gaussian fit to the $(3,-3,0)$ peak. The extra peaks in (b) are powder diffraction peaks from the Al sample holder.

Figure 10

Elastic scattering along $\mathbf{Q}=(3,-3,l)$. Based on a comparison with a cut along $(2,-2,l)$, we conclude that the peak shape and width are due to the vertical focusing and the sample geometry.

Figure 11

Integrated intensity of the $(3,-3,0)$ superlattice peak as a function of temperature. The vertical dashed line indicates the transition to the HTT phase based on an interpolation formula [46].