Evidence for Short-Range-Ordered Charge Stripes Far above the Charge-Ordering Transition in ${\mathrm{La}}_{1.67}{\mathrm{Sr}}_{0.33}{\mathrm{NiO}}_4$

The temperature evolution of structural effects associated with charge order (CO) and spin order in ${\mathrm{La}}_{1.67}{\mathrm{Sr}}_{0.33}{\mathrm{NiO}}_4$ has been investigated using neutron powder diffraction. We report an anomalous shrinking of the $c/a$ lattice parameter ratio that correlates with $T_{\mathrm{CO}}$. The sign of this change can be explained by the change in interlayer Coulomb energy between the static-stripe-ordered state and the fluctuating-stripe-ordered state or the charge-disordered state. In addition, we identify a contribution to the mean-square displacements of Ni and in-plane O atoms whose width correlates quite well with the size of the pseudogap extracted from the reported optical conductivity, with a non-Debye-like component that persists below and well above $T_{\mathrm{CO}}$. We infer that dynamic charge-stripe correlations survive to $T\sim 2T_{\mathrm{CO}}$.

Figure 1

PDF (top) and Rietveld (bottom) fits to 80 K data. In both panels, structure models are shown as red solid lines, while the data are shown as circles. Difference curves are offset for clarity.

Figure 2

The temperature evolution of $c/a$ ratio (bottom curve with red solid circles) in comparison with the volume expansion (top curve with blue solid circles). Dotted lines indicate $T_{\mathrm{SO}}=190\mathrm{K}$ and $T_{\mathrm{CO}}=240\mathrm{K}$. In the inset, the red solid circles represent a normalized long-range-order (LRO) parameter calculated from $c/a$, and the black open circles represents the $T$ evolution of the normalized integrated intensity of the single crystal CO peak from Du et al. [31].

Figure 3

Anisotropic ADPs that are not along in-plane Ni-O bonds are shown in (a), while the ADPs that lie along these bonds are shown in (b). The structure is shown in the inset of (a) to illustrate the atoms and the directions of the different anisotropic ADPs that are plotted in the main panels, with Ni in blue, apical oxygen (${\mathrm{O}}_a$) in orange, and in-plane oxygen (${\mathrm{O}}_p$) in red. Vertical dotted lines indicate the spin- and charge-ordering temperatures, $T_{\mathrm{SO}}$ and $T_{\mathrm{CO}}$. Dashed lines represent calculated Debye behavior. The dotted lines in (b) represent calculated Debye behavior with different offsets that are appropriate to fit the high-$T$ ADPs. The inset contains the same ADP data converted to a short-range-order (SRO) parameter, which is the normalized difference from the high-$T$ Debye fit as described in the text, where the symbols used are the same as in the main panel. Plotted on top is a similar SRO parameter for the energy of the pseudogap as determined from optical conductivity measurements as described in the text.

Figure 4

Comparison of the temperature evolution of the squared inverse height of the nearest neighbor Ni-Ni PDF peak (blue solid circles) and of the in-plane oxygen $U_{22}$ (red triangles).