Nature of the magnetic stripes in fully oxygenated ${\mathrm{La}}_2{\mathrm{CuO}}_{4+y}$

We present triple-axis neutron scattering studies of static and dynamic magnetic stripes in an optimally oxygen-doped cuprate superconductor, ${\mathrm{La}}_2{\mathrm{CuO}}_{4+y}$, which exhibits a clean superconducting transition at $T_c=42\mathrm{K}$. Polarization analysis reveals that the magnetic stripe structure is equally represented along both of the tetragonal crystal axes and that the fluctuating stripes display significant weight for in-plane as well as out-of-plane spin components. Both static magnetic order as well as low-energy fluctuations are fully developed in zero applied magnetic field and the low-energy spin fluctuations at $\hslash \omega =0.3\text{–}10\mathrm{meV}$ intensify on cooling. We interpret this as an indication that superconductivity and low-energy spin fluctuations coexist microscopically in spatial regions which are separated from domains with static magnetic order.

Figure 1

(a) The real part of AC magnetic susceptibility, ${\chi }^{\prime }$, showing the sharp transition to a diamagnetic state on cooling below the superconducting critical temperature. $T_c$ is indicated by the yellow stripe which spans a temperature range $41.3\pm 0.8\mathrm{K}$. The steps followed in the conversion from emu to SI units are presented in Appendix pp1. (b) Temperature dependence of magnetic order measured as 1-point scans on top of one of the IC peaks $(1.115,0.108,0)$. The incoherent background has not been subtracted. The dashed line indicates the background level extracted from an energy scan taken away from the incommensurate peak position, at $(1.1,-0.24,0)$. (c) Temperature dependence of magnetic fluctuations with energy 0.3 and 1.5 meV. Data were measured as three-point scans with $k_f=1.2$ Å${}^{-1}$ $[\mathrm{\Delta }E=0.070(1\left)\mathrm{meV}\right]$ and the intensity is obtained as the difference between the point on top of the peak, at $(0.875,-0.125,0)$, and the average of the two background points.

Figure 2

[(a) and (b)] Representative inelastic scans through the incommensurate positions ($\pm \delta ,1-\delta ,0$) where $\delta =0.125$, collected at 1.5 and $7\mathrm{meV}$ with fixed outgoing wave vectors $k_f=1.55{\AA }^{-1}$ and $k_f=1.5{\AA }^{-1}$, respectively. The data were collected at ThALES (a) and IN12 (b) at two temperatures: Blue diamonds show data in the superconducting state (2 K) and orange circles show data within the normal state (45 K). The solid lines are Sato-Maki function fits to the raw data as described in the text. (c) Dynamic susceptibility ${\chi }^{″}({\mathbf{Q}}_{IC},\omega )$ measured inside ($2\mathrm{K}$, blue) and outside ($45\mathrm{K}$, orange) the superconducting dome. Solid lines are guides to the eye. Each data point represents an average of values obtained at different $k_f$ values and on different instruments (ThALES and IN12). In gray symbols, we show for comparison the magnetic susceptibility measured inside and outside the superconducting state by Lake et al. [33] on a optimally doped $x=0.163$ LSCO sample.

Figure 3

(a) Magnetic field dependence of low-energy spin excitations measured at $2\mathrm{K}$. Representative (b) inelastic constant energy scan ($\hslash \omega =1\mathrm{meV}$) and (c) elastic scans collected in the superconducting phase ($2\mathrm{K}$) with and without applied magnetic field. The solid lines are Gaussian fits to the raw data.

Figure 4

(a) Inelastic constant energy scan ($\hslash \omega =1.5\mathrm{meV}$) and (b) elastic scans collected in the superconducting phase (30 K and 5 K, respectively) in SF, with three spin configurations, and NSF mode. The scan direction is represented in the inset of subplot (b). In panel (a) the NSF data are displaced by a factor $-0.7\times {10}^{-5}$ for better visualisation. $S$ denotes the incoming neutron beam spin direction. The solid lines are Gaussian fits to the raw data.

Figure 5

(a) A cartoon illustration of the neutron scattering signal generated by the incommensurate AFM spin structure including contributions from all four crystal twins. (b) Twinning of a structural peak into two domains each composed of a pair of twins. The direction of the orthorhombic $b$ axis, which corresponds to the spin direction, is shown by a double-arrow for each twin peak. $\mathrm{\Delta }$ is the angular separation between two twin reflections [77] and in our orthorhombic system has a value $\mathrm{\Delta }={90}^{\circ }-2arctan\left(\frac{a}{b}\right)\sim 0.8^{\circ }$, a splitting too small to be resolved given our $Q$ resolution. $a^{*}$ and $b^{*}$ are the reciprocal lattice constants in orthorhombic notation. Image adapted from the Supplemental Material of Ref. [65]. (c) The stripe pattern arising from charge stripes running along the tetragonal $a_T$ axis (Charge A) and the tetragonal $b_T$ axis (Charge B). The triangles and circles indicate how the charge orientations corresponds to the incommensurate peak structures in (a) for the local coordinate system of each twin type, which are rotated by ${90}^{\circ }$ with respect to each other.

Figure 6

Measured intensity of the spin flip channel at $(2,0,0)$ Bragg position as a function of temperature.

Figure 7

Dynamic susceptibility ${\chi }^{″}\left(\omega \right)$ measured at temperatures inside ($2\mathrm{K}$) and outside ($45\mathrm{K}$) the superconducting dome. All data has been measured at Thales (Th1) with constant $k_f=1.55{\AA }^{-1}$. In gray and black symbols, we show the magnetic susceptibility measured inside and outside the superconducting state by Xu et al. [45] on an underdoped $x=0.095$ LSBCO sample with $T_c=32\mathrm{K}$. The shaded area indicates the magnitude of the spin waves in the parent compound LCO, as presented by Xu et al. [45], and is connected to the right-hand side axis.