Evidence for a Nematic Phase in ${\mathrm{La}}_{1.75}{\mathrm{Sr}}_{0.25}{\mathrm{NiO}}_4$

Determining the nature of electronic states in doped Mott insulators remains a challenging task. In the case of tetragonal ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_4$, the occurrence of diagonal charge and spin stripe order in the ground state is now well established. In contrast, the nature of the high-temperature “disordered” state from which the stripe order develops has long been a subject of controversy, with considerable speculation regarding a polaronic liquid. Following the recent detection of dynamic charge stripes, we use neutron scattering measurements on an $x=0.25$ crystal to demonstrate that the dispersion of the charge-stripe excitations is anisotropic. This observation provides compelling evidence for the presence of electronic nematic order.

Figure 1

(a) Schematic diagram indicating relative locations of fundamental Bragg peaks (black solid circles), charge-order peaks (red hollow diamonds), and spin-order peaks (black hollow squares) in the $(H,K,0)$ plane of ${\mathrm{La}}_{1.75}{\mathrm{Sr}}_{0.25}{\mathrm{NiO}}_4$. Shaded area illustrates the scanning range where data have been collected at 10 K. White arcs represent aluminum powder rings. (b) Constant energy slice of $(H,K,0)$ plane at 10 K. Elastic scattering intensities have been integrated, with $-0.2\le L\le 0.2$, $-1.5\le E\le 1.5\mathrm{meV}$. (c) Scans through magnetic peaks along $\mathbf{Q}=(1,K,0)$. (d) Scans through charge-order peaks along $\mathbf{Q}=(H,3,0)$. (e) Inelastic neutron scattering (integrated over $2\le E\le 5\mathrm{meV}$, $-0.2\le L\le 0.2$), measured at $T_{\mathrm{so}}=140\mathrm{K}$. Bright spots centered at fundamental Bragg wave vectors represent acoustic phonons. Weak spots circled in yellow (green) represent the dynamic spin (charge) stripes at small (large) $\mathbf{Q}$.

Figure 2

(a) Elastic scattering ($-0.2\le L\le 0.2$, $-1\le E\le 1\mathrm{meV}$) associated with static charge order along $(H,3,0)$, measured at different temperatures. The temperature-independent peaks around (5.1,3,0) are powder diffraction from the aluminum sample holder. (b) Inelastic signal from dynamical charge order ($-0.2\le L\le 0.2$, $2\le E\le 5\mathrm{meV}$), measured at different temperatures. In both (a) and (b), intensities are normalized to incident flux. Data sets have been shifted for clarity; solid lines represent Gaussian fits. (c) Temperature dependence of the integrated intensity of static (blue filled circles) and dynamic (red filled squares) charge-stripe correlations. For comparison, triple-axis results of static charge order (blue open circles) from Anissimova et al. [28] are included.

Figure 3

Constant energy slice ($2\le E\le 5\mathrm{meV}$, $-0.2\le L\le 0.2$) around the charge-stripe peak at ${\mathbf{Q}}_{\mathrm{co}}^{*}=(4.44,3,0)$ at 160 K, plotted in the $(HK0)$ plane. The strongest scattering, centered at $\mathbf{G}=(4,4,0)$ and (2,4,0), comes from acoustic phonons. White dashed lines and letters indicate the direction of corresponding slices in Fig. 4.

Figure 4

Low-energy excitations of lattice and charge stripes in ${\mathrm{La}}_{1.75}{\mathrm{Sr}}_{0.25}{\mathrm{NiO}}_4$ at 160 K. (a) Acoustic phonons dispersing from the Bragg peak $\mathbf{Q}=(4,2,0)$ along [100], integrated over $1.9\le K\le 2.1$, and (b) from $\mathbf{Q}=(4,4,0)$ along [010], integrated over $3.75\le H\le 4.25$. (c),(d) Scattered intensity as a function of $E$ vs $\mathbf{Q}$ through ${\mathbf{Q}}_{\mathrm{co}}^{*}$ along [100], integrated over $2.9\le K\le 3.1$ (c), and along [010], integrated over $4.1\le H\le 4.7$ (d). Charge-stripe fluctuations are indicated by white ovals. (e) Cuts through the charge-stripe fluctuations in (c), integrated over fixed energy bands, as noted in the labels; (f) cuts through the charge-stripe fluctuations in (d). In all cases, data have been integrated over $-0.2\le L\le 0.2$. In (a)–(d), a $\mathbf{Q}$-independent incoherent elastic scattering contribution, broadened by instrumental energy resolution, has been subtracted. Lines through the data points in (e) and (d) are fitted Gaussian peaks plus background; in (e), the background is linear in $H$, while in (f), the background is a constant plus the tail of a Gaussian peak at large $K$ to account for the neighboring acoustic phonons.