Phase diagram of charge order in La${}_{1.8-x}$Eu${}_{0.2}$Sr${}_x$CuO${}_4$ from resonant soft x-ray diffraction

Resonant soft x-ray scattering experiments with photon energies near the O $K$ and the Cu $L_3$ edge on the system La${}_{1.8-x}$Eu${}_{0.2}$Sr${}_x$CuO${}_4$ for $0.1⩽x⩽0.15$ are presented. A phase diagram for stripelike charge ordering is obtained together with information on the structural transition into the low-temperature tetragonal phase. A clear dome for the charge ordering around $x=\frac{1}{8}$ is detected well below the structural transition. This result differs substantially from other systems in which static stripes are detected. There the charge order is determined by the structural transition appearing at the same temperature. Furthermore, we present results for the coherence length and the incommensurability of the stripe order as a function of Sr concentration.

Figure 1

X-ray absorption spectrum of La${}_{1.65}$Eu${}_{0.2}$Sr${}_{0.15}$CuO${}_4$ near the O $K$ edge measured in the fluorescence yield mode (FY) in light gray (blue). Also shown in black is the (001) superstructure reflection intensity as a function of the photon energy. The inset shows the (001) reflection measured with a photon energy of 533 eV at $T=6$ K.

Figure 2

Temperature dependence of the intensities of the superstructure reflections of La${}_{1.65}$Eu${}_{0.2}$Sr${}_{0.15}$CuO${}_4$ normalized to the intensity at $T=6$ K. (Squares) (001) reflection measured with photon energies $h\nu =533.2$ eV near the O $K$ edge. (Circles) (0.254 0 0.75) reflection measured with photon energies $h\nu =529.2$ eV near the O $K$ edge. (Diamonds) (0.254 0 1.6) reflection measured with photon energies $h\nu =929.8$ eV near the Cu $L_3$ edge.

Figure 3

Phase diagram of La${}_{1.8-x}$Eu${}_{0.2}$Sr${}_x$CuO${}_4$ showing transition temperatures for the LTT phase $T_{\mathrm{LTT}}$, the antiferromagnetic structure $T_{\mathrm{AF}}$, the magnetic stripe order $T_{\mathrm{SO}}$, the stripe like charge order $T_{\mathrm{CO}}$, and the superconducting transition temperature $T_C$. Closed circles from the present RSXS experiments. Open circles from Ref. 6. Closed diamond from neutron diffraction data presented in Ref. 7.

Figure 4

(Upper panel) Concentration dependence of the coherence length in units of the lattice constant $a$ of static stripe order in La${}_{1.8-x}$Eu${}_{0.2}$Sr${}_x$CuO${}_4$. (Lower panel) Concentration dependence of the incommensurability wave vector $\delta$ for the stripe order which is one half of the wave vector for charge order. The assignment to the symbols is the same as in Fig. 2.