Staging superstructures in high-$T_c$ Sr/O codoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_{4+y}$

We present high-energy x-ray diffraction studies on the structural phases of an optimal high-$T_c$ superconductor ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_{4+y}$ tailored by co-hole-doping. This is specifically done by varying the content of two very different chemical species, Sr and O, respectively, in order to study the influence of each. A superstructure known as staging is observed in all samples, with the staging number $n$ increasing for higher Sr dopings $x$. We find that the staging phases emerge abruptly with temperature, and can be described as a second-order phase transition with transition temperatures slightly depending on the Sr doping. The Sr appears to correlate the interstitial oxygen in a way that stabilizes the reproducibility of the staging phase both in terms of staging period and volume fraction in a specific sample. The structural details as investigated in this paper appear to have no direct bearing on the electronic phase separation previously observed in the same samples. This provides evidence that the electronic phase separation is determined by the overall hole concentration rather than specific Sr/O content and concomitant structural details.

Figure 1

Illustration of relevant structures, with only ${\mathrm{CuO}}_6$ octahedra and interstitial oxygen shown. (a) Tetragonal F4/mmm and (b) orthorhombic Bmab structures of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ seen along the $a$ axis. (c) Example of a staged structure caused by layers of favorable positions for interstitial oxygen due to tilt flip domain borders. Figure inspired by [13, 17, 18]. (d) Map of investigations of the $\left[0KL\right]$ plane for the $x=0.04$ sample at $T=10$ K, close to Bmab allowed positions (012), (014), and (032). The intensity of each pair of peaks has been scaled for visibility. Blue dashed arcs are centered in origo, showing how the resolution function is widest transverse to $q$. Green lines mark out the FWHM of the long axis for each peak.

Figure 2

Low-temperature data for the four samples. The plots for the $x=0.00$, 0.065, and 0.09 samples are cut off from the maximum intensities of 101.4, 196.5, and 196.9, respectively, to show the staging peaks. The inset plot in the bottom panel shows a zoom for clarity. Black lines indicate error bars, and are in general smaller than the data symbols. Red thick curves show full fits of the spectra, composed of the sum of individual peaks (thin orange curves) and a flat background. Vertical green lines indicate integer $n$ staging. The relative intensity $r_I$ is calculated from the integrated intensities as given in Eq. (2).

Figure 3

Temperature dependence of integrated intensities of staging peaks (red triangles for low $l$ and yellow squares for high $l$) and central peaks (blue circles). Lines for the staging data are power-law fits to the filled markers only. Empty markers are excluded from the fits due to order-parameter saturation (low temperatures) and critical scattering (close to transition temperatures).

Figure 4

Overview of peak positions (left) and staging peak widths (right) for the $x=0.04$ sample. Blue circles show the position of the central Bmab peak while green diamonds show the midpoint of the staging peaks, which are in turn positioned at the yellow squares and red triangles. There is a clear difference between the blue circles and the green diamonds, indicating different $c$-axis lengths for the Bmab and the staged structures. Note that the Bmab peak position was held fixed in the fit to the $T=60$ K value above this temperature. The widths show a clear increase around the phase transition, as expected for a second-order phase transition.

Figure 5

Cooling history dependency of the measured signals for the $x=0.00$ (top) and $x=0.04$ (bottom) samples. The top scattering pattern is changed remarkably from the one shown in the top plot of Fig. 2 because of the initial fast cool.