High-energy magnetic excitations from dynamic stripes in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}\mathrm{Cu}{\mathrm{O}}_4$

We use inelastic neutron scattering to study the temperature dependence of magnetic excitations (for energies up to $100\mathrm{meV}$) in the cuprate ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}\mathrm{Cu}{\mathrm{O}}_4$. This compound exhibits stripe order below a temperature of $\sim 50\mathrm{K}$; previous measurements have shown that the magnetic excitations of the stripe-ordered phase have an hour-glass-like dispersion, with a saddle point at $\sim 50\mathrm{meV}$. Here, we compare measurements in the disordered phase taken at 65 and $300\mathrm{K}$. At energies on the scale of $k_{B}T$, there is substantial momentum broadening of the signal, and the low-energy incommensurate features can no longer be resolved at $300\mathrm{K}$. In contrast, there is remarkably little change in the scattered signal for energies greater than $k_{B}T$. In fact, the momentum-integrated dynamic susceptibility is almost constant with temperature. The continuity of the magnetic excitations at $E>50\mathrm{meV}$ indicates that the character of the local antiferromagnetic spin correlations is independent of stripe ordering. Based on the smooth evolution of the lower-energy excitations into the spin waves of the stripe-ordered phase, we infer the existence of dynamic stripe correlations in the disordered phase. We reconsider the nature of the magnetic dispersion, and we discuss the correspondences between the thermal evolution of magnetic stripe correlations with other electronic properties of the cuprates.

Figure 1

(Color online) Constant-energy cuts around ${\mathbf{Q}}_{\mathrm{AF}}=(0.5,0.5)$ from data taken on MAPS at different temperatures. The bottom and middle rows are data taken with $E_i=80\mathrm{meV}$, and the top row is data taken with $E_i=140\mathrm{meV}$.

Figure 2

(Color online) Imaginary part of the spin susceptibility after $\mathbf{Q}$ integration over the antiferromagnetic Brillouin zone; ${\chi }^{″}\left(\omega \right)$ measured at $T=10\mathrm{K}$ (black open circles), $65\mathrm{K}$ (red diamonds), and $300\mathrm{K}$ (blue triangles). The solid gray circles represent data from Ref. 28. (Note that the two points near $47\mathrm{meV}$ in the latter data are contaminated by a phonon, as discussed in the text.)

Figure 3

(Color online) Linear intensity profiles measured through ${\mathbf{Q}}_{\mathrm{AF}}$ at different energy transfers. For each data set, we average linear cuts taken along the [100] and [010] directions to improve statistics. The solid lines are fits to the data using two symmetric Gaussians displaced equally from $H=0.5$ plus background. The peaks on the high-$Q$ side (e.g., at $\hslash \omega =16$, 32, 41, and $45\mathrm{meV}$) are due to phonon contributions.

Figure 4

(Color online) Two-dimensional maps plotted in energy-momentum space showing the fitted dispersions and $Q$ widths at $T=10$, 65, and $300\mathrm{K}$. The signal is sliced along the [100] direction in $\mathbf{Q}$ through ${\mathbf{Q}}_{\mathrm{AF}}$. As a reference, the solid lines denote the dispersion at low temperature obtained in Ref. 28.

Figure 5

(Color online) Measurements of $S\left(\mathbf{Q}\right)$. (a), (b), and (c) show the energy integrals (over the $4–110\mathrm{meV}$ interval) of the $E_i=140\mathrm{meV}$ data, corrected for the magnetic form factor, at temperatures of 10, 65, and $300\mathrm{K}$, respectively. A background varying as $Q^2$ has been subtracted in order to emphasize the magnetic response. The diagonal streaks near the upper left and lower right corners are artifacts due to spurious signals at the detector edges. (d) Cuts along the $\mathbf{Q}$ path are indicated by dashed lines in (a)–(c). Symbols represent the integral over the data, while the lines correspond to integration over the fitted magnetic signal (from Fig. 3). The difference in the two approaches is due to the differing treatments of the phonon background.