Detailed structure of the low-energy magnetic dispersion of the diagonal incommensurate phase in La${}_{1.975}$Sr${}_{0.025}$CuO${}_4$

Inelastic neutron scattering experiments have been performed on lightly doped La${}_{1.975}$Sr${}_{0.025}$CuO${}_4$, which contains a hole concentration slightly higher than the critical concentration for three-dimensional long-range antiferromagnetic order. We previously found that the magnetic excitation spectrum in the insulating phase with a diagonal incommensurate spin modulation has similarities to that in the superconducting regime, where the spin modulation is bond parallel. In this study, we investigate the excitations in detail around $E_{\mathrm{cross}}$, at which the excitations become most nearly commensurate. It is found that both the magnitude and the anisotropy of the momentum width of the excitations change abruptly at $E_{\mathrm{cross}}$. Our experimental results suggest that the magnetic excitations rising from the pair of (diagonally) incommensurate wave vectors merge at $E_{\mathrm{cross}}$ into isotropic excitations.

Figure 1

Diagram of the reciprocal lattice in the ($H,K$, 0) scattering zone in the orthorhombic phase for a crystal with a single domain (a) and with two domains (b). The results of elastic neutron scans A, B, C, and D, whose trajectories are indicated in (b), are plotted in (c), (d), (e), and (f), respectively. Solid curves in (e) and (f) indicate the weight from the main domain, A.

Figure 2

Neutron inelastic scans at 3, 9, and 11 meV along $(0,K,0)$ and $(H,0,0)$ and at 30 meV along $(2,K,0)$ in La${}_{1.975}$Sr${}_{0.025}$CuO${}_4$. Scans along $(0,K,0)$ and $(H,0,0)$ correspond to those parallel and perpendicular to the incommensurate wave vector, respectively, as indicated in the inset. Solid lines are the results of fits as discussed in the text. Horizontal bars represent instrumental resolutions.

Figure 3

Magnetic dispersion relation along $q_K$ (a) and $q_H$ (c) in La${}_{1.975}$Sr${}_{0.025}$CuO${}_4$ at 10 K. Data plotted here were determined using the model of two 2D squared Lorentzians. As discussed in the text, the scans along $q_K$ at $10\le \hslash \omega \le 12$ meV can be fitted with a single isotropic 2D squared Lorentzian equally well. The line widths, which are shown by shaded horizontal bars, are fixed values for the fits along $K$ shown in (a) but are fitted values for the data along $H$ as presented in (b) and (c). (a) Dashed lines indicate the spin-wave dispersion in pure La${}_2$CuO${}_4$ with the spin-wave velocity[36] of 850 meV Å. (b) Dashed lines are visual guides. Insets: Peak configuration in momentum space for two magnetic excitation rods below $\sim$10 meV (left) and 2D isotropic excitation above $\sim$10 meV (right). The peak separation (2$\epsilon$) and full width at half-maximum (1.3$\kappa$) of the peak are also indicated.

Figure 4

Plot of $E_{\mathrm{cross}}$ vs $x$ in LSCO (filled circles), Zn-doped LSCO (filled triangle), and La${}_{2-x}$Ba${}_x$CuO${}_4$ (open circle), including results from Refs. 2,4,5,15,37, and38. The present result in La${}_{1.975}$Sr${}_{0.025}$CuO${}_4$ is shown by the open square. The dashed line is a guide for the eye.

Figure 5

Neutron inelastic scans at 3 meV along $(0,K,0)$ and $(H,0,0)$ in La${}_{1.975}$Sr${}_{0.025}$CuO${}_4$ measured at 10, 50, and 150 K. Solid lines are the results of fits of a convolution of the resolution function with two 2D squared Lorentzians.