High-Energy Spin Dynamics in ${\mathrm{L}\mathrm{a}}_{1.69}{\mathrm{S}\mathrm{r}}_{0.31}{\mathrm{N}\mathrm{i}\mathrm{O}}_4$

To test the prediction that the dispersion of the magnetic resonance in superconducting ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{6+x}$ is similar to magnons in an incommensurate antiferromagnet, we have mapped out the spin dynamics in a stripe-ordered nickelate, ${\mathrm{L}\mathrm{a}}_{2-x}{\mathrm{S}\mathrm{r}}_x{\mathrm{N}\mathrm{i}\mathrm{O}}_4$, with $x\simeq 0.31$, using inelastic neutron scattering. We observe spin-wave excitations up to 80 meV emerging from the incommensurate magnetic peaks with a surprisingly large and almost isotropic spin velocity: $\hslash c_s\sim 0.32\mathrm{e}\mathrm{V}\AA$. A comparison indicates that the inferred spin-excitation spectrum is not, by itself, an adequate model for the magnetic resonance feature of the superconductor.

Figure 1

Upper panel: Sketch of the Brillouin zone in the reciprocal $(HK0)$ plane. Full circles indicate the location of the incommensurate magnetic peaks, ${\mathbf{Q}}_{\delta }$. The circles (around ${\mathbf{Q}}_{\delta }$) show the cut of the spin-wave cones at a constant energy, defining $Q_{\omega }$ ($\equiv \omega /c_s$ in the low-energy regime). Full bars represent the directions of the scans shown in the lower panel; the arrow shows the direction of the scans shown in Fig. 2. Lower panels: Constant energy scans at $E=28.1\mathrm{m}\mathrm{e}\mathrm{V}$ (measured with $E_f=14.7\mathrm{m}\mathrm{e}\mathrm{V}$) at two temperatures along the two directions sketched in the upper panel, probing fluctuations along wave vectors perpendicular (left) and parallel (right) to the stripes. Lines represent best fits of the extended Gaussian model described in the text.

Figure 2

(a) Dispersion relation of the spin excitations in ${\mathrm{L}\mathrm{a}}_{1.69}{\mathrm{S}\mathrm{r}}_{0.31}{\mathrm{N}\mathrm{i}\mathrm{O}}_4$. The solid line is a fit by a simple $|\sin (3\pi H)|$ function. The two dashed lines correspond to the spin-wave dispersion relation in undoped ${\mathrm{L}\mathrm{a}}_2{\mathrm{N}\mathrm{i}\mathrm{O}}_4$, but shifted to the incommensurate wave vectors. (b)–(d) Constant energy scans at (b) $E=75\mathrm{m}\mathrm{e}\mathrm{V}$, (c) $E=65\mathrm{m}\mathrm{e}\mathrm{V}$, and (d) $E=55\mathrm{m}\mathrm{e}\mathrm{V}$ along $(H,-H,0)$ (i.e., perpendicular to the stripes) around $Q=(1.5,1.5,0)$. Scan (b) was measured with $E_f=41\mathrm{m}\mathrm{e}\mathrm{V}$ (as in Fig. 3), while (c) and (d) were measured with $E_f=30.5\mathrm{m}\mathrm{e}\mathrm{V}$. The error bars reflect a total counting time of $15\mathrm{m}\mathrm{i}\mathrm{n}/\mathrm{p}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}$ in (b) and $10\mathrm{m}\mathrm{i}\mathrm{n}/\mathrm{p}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}$ in (c)–(d). Full lines represent best fits of the extended Gaussian model described in the text.

Figure 3

Energy scans at (a) $\mathbf{Q}=(1.175,1.825,0)$, (b)–(d) $\mathbf{Q}=(1.5,1.5,0)\equiv {\mathbf{Q}}_{\mathrm{A}\mathrm{F}}$, after subtraction of background measured either at $\mathbf{Q}=(1,2,0)$ or by rocking the sample by $\pm 15°$. The data have been obtained with $E_f=41\mathrm{m}\mathrm{e}\mathrm{V}$. The solid lines represent best fits of a damped harmonic oscillator function, with a dispersion relation as shown in Fig. 2a, convolved with the spectrometer resolution. The line in (a) is the same as in (b) except for a scale factor.

Figure 4

Temperature dependence of various fitting parameters: Spin-wave energy maximum (left scale) and damping energy at ${\mathbf{Q}}_{\mathrm{A}\mathrm{F}}$ (right scale). Vertical lines indicate the magnetic and charge-order transitions.