Charge Excitations in the Stripe-Ordered ${\mathrm{La}}_{5/3}{\mathrm{Sr}}_{1/3}{\mathrm{NiO}}_4$ and ${\mathrm{La}}_{2-x}(\mathrm{Ba},\mathrm{Sr}{)}_x{\mathrm{CuO}}_4$ Superconducting Compounds

Charge excitations in stripe-ordered 214 compounds ${\mathrm{La}}_{5/3}{\mathrm{Sr}}_{1/3}{\mathrm{NiO}}_4$ and $1/8$-doped ${\mathrm{La}}_{2-x}(\mathrm{Ba}\mathrm{\text{or}}\mathrm{Sr}{)}_x{\mathrm{CuO}}_4$ are studied using resonant inelastic x-ray scattering in the hard x-ray regime. We observe $\simeq 1\mathrm{eV}$ excitation with a momentum transfer corresponding to the charge stripe spatial period both for the diagonal (nickelate) and parallel (cuprates) stripes. They are interpreted as collective stripe excitations or anomalous softening of the charge excitonic modes of the in-gap states.

Figure 1

Diagonal charge stripes in (a) LSNO $x=1/3$ and parallel stripes in (b) LBCO $x=0.125$ and LSCO $x=0.12$ in the basal (Ni or Cu) ${\mathrm{O}}_2$ plane. Stripes are marked by shaded belts. (c) and (d) depict momentum space for the (Ni or Cu) ${\mathrm{O}}_2$ square lattice in unit of $1/a$ ($a$ is the lattice constant of the square lattice). Arrows connecting the stripes in (a) and (b) indicate spatial periods of stripes. Arrows in (c) and (d) indicate characteristic momentum transfer ${\mathbf{q}}_{\mathbf{s}}$. The period of ($3a/2$, $3a/2$) in (a) gives characteristic momentum transfer ${\mathbf{q}}_{\mathbf{s}}=(2\pi /3,2\pi /3)$, and the period of ($4a$, 0) in (b) gives ${\mathbf{q}}_{\mathbf{s}}=(\pi /2,0)$. Circles in (c) and (d) indicate equivalent ${\mathbf{q}}_{\mathbf{s}}$ points due to the stripe domains whose stripes run perpendicular with each other.

Figure 2

RIXS spectra of LSNO $x=1/3$ measured at different momentum transfer $\mathbf{q}$. The spectra are shown shifted by 300 each in intensity, for clarity. Measured $\mathbf{q}$ positions are indicated in the right top inset by circles labeled $A$ through $G$ and connected by arrows, showing the order of spectra from bottom to top. Point $F$ corresponds to ${\mathbf{q}}_{\mathbf{s}}$. The shaded ellipsoid around point $F$ shows $\mathbf{q}$ resolution. The right bottom inset shows elastic line tails on the energy gain side of the RIXS spectra for positions $E$, $F$, and $G$.

Figure 3

A contour plot of RIXS intensity in the momentum transfer range between ($2\pi$, 0) and (0, $2\pi$). The RIXS intensity is normalized to the in-gap peak intensity at $\sim 1.5\mathrm{eV}$. The white area has intensity of more than 250 due to the elastic peak or filled dip at ${\mathbf{q}}_{\mathbf{s}}$ positions. The shaded rectangular area has not been measured.

Figure 4

(a) RIXS intensity map of LBCO $x=0.125$ along $(\pi ,\pi )\to (\pi ,0)\to (0,0)\to (\pi ,\pi )$. (b) RIXS spectrum—the cross section $A$ in (a). (c) Close-ups of RIXS spectra around 1 eV of LBCO $x=0.125$ (top) and LBCO $x=0.08$ (bottom)—the cross sections $A$ and $B$ in (a). The cross section $B$ corresponds to ${\mathbf{q}}_{\mathbf{s}}=(\pi /2,0)$ of LBCO $x=0.125$. The RIXS intensities in (c) are normalized to the maximum of the CT peak at $\sim 4\mathrm{eV}$. (d) Momentum transfer dependence of the RIXS signal averaged in the energy region between 1 and 1.25 eV. These profiles correspond to the cross section $C$ in (a). Each spectrum is shifted for clarity. The arrows indicate ${\mathbf{q}}_{\mathbf{s}}$ positions. Although LBCO $x=0.08$ does not have a robust stripe order, we show ${\mathbf{q}}_{\mathbf{s}}=2\pi (2x,0)=(0.32\pi ,0)$ by a dashed arrow estimated from a very small neutron diffraction signal reported in Ref. 35.