Nature and impact of stripe freezing in ${\mathrm{La}}_{1.67}{\mathrm{Sr}}_{0.33}{\mathrm{NiO}}_4$

${\mathrm{La}}_{1.67}{\mathrm{Sr}}_{0.33}{\mathrm{NiO}}_4$ develops charge and spin stripe orders at temperatures of roughly 200 K, with modulation wave vectors that are temperature independent. Various probes of spin and charge response have provided independent evidence for some sort of change below $\sim 50$ K. In combination with a new set of neutron scattering measurements, we propose a unified interpretation of all of these observations in terms of a freezing of Ni-centered charges stripes, together with a glassy ordering of the spin stripes that shows up in neutron scattering as a slight rotation of the average spin direction.

Figure 1

Temperature dependence of various measured quantities for LSNO $x=0.33$: Blue circles, magnetic susceptibility $\chi \left(T\right)$, measured with an in-plane field of 1 T [10], divided by ${\chi }_0=C/(T+18.6\text{K})$ with $C=0.28$ emu ${\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$; gray line, fit to the real part of the dielectric function, ${\epsilon }^{\prime }$, measured at a frequency of 10 kHz with the electric field parallel to the planes [14]; purple diamonds, spin-flip neutron cross section relative to the non-spin-flip response measured with neutron polarization analysis at $\mathbf{Q}=(\frac{2}{3},0,1)$, normalized at the base temperature [13]; violet squares, peak intensity of the 1D magnetic scattering measured for excitations of 2 meV, normalized at 2 K [9].

Figure 2

(a) Schematic diagram of features in reciprocal space: Black circles, nuclear Bragg peaks; red circles, overlapping spin and charge stripe Bragg peaks; orange dashed lines, intersection of the sheets of scattering from individual spin stripes with the $L=0$ plane; gray shading indicates the region probed experimentally. (b) Inelastic scattering at $\hslash \omega =3\pm 1$ meV and $T=5$ K. (c) Difference between the scattering measured at 5 K and 70 K for $\hslash \omega =3\pm 1$ meV. (d) Similar to (c), but plotting in the $(H,-0.8,L)$ plane, providing evidence that there are 2D sheets of scattering.

Figure 3

Schematic diagrams of charge and spin order for (a) Ni-centered stripes and (b) O-centered stripes. Circles indicate Ni sites and arrows indicate ordered moments; ellipses correspond to O sites and gray shading indicates location of doped holes. The intensity of the gray shading reflects the number of O sites over which a single hole is shared: Four in (a) and two in (b). Red filled/open arrows indicate antiphase spin stripes. Gray arrows in (a) indicate relative spin correlations along the charge stripes; these correlations are purely dynamic [9]. Height of arrows indicates effective spin size, as discussed in the text.

Figure 4

Color map of measured magnetic peak intensities at $T=5$ K for (a) $L=0$ and (b) an average of $L=\pm 1$; also included are fitted intensities for (c) $L=0$ and (d) $\left|L\right|=1$. For (a), three measured points with anomalously large intensities, possibly from charge-order contributions, have been excluded.

Figure 5

Top: Temperature dependence of intensity ratios $R_0$ (green) and $R_1$ (blue), defined in the text. Filled circles: Data; open diamonds: Fit to $R_0$ and $R_1$ using a single $\theta$ at each temperature; open squares: Results from fitting entire set of peaks at each temperature. Bottom: Values of $\theta$ obtained by fitting just $R_0$ and $R_1$ (diamonds) and from fitting the entire data set (squares).

Figure 6

Fit to integrated intensities from measurements at 5 K for (a) $L=0$ and (b) average of intensities at $L=\pm 1$. Filled circles are data points used in the fit and open circles are measurements not included in fitting; gray stars represent calculated intensities for a model with $p\equiv 1$, while black stars correspond to the model with variable $p$ and resulting parameter values $p=0.863\pm 0.015$ and $\theta =46.6^{\circ }\pm 2.3^{\circ }$.