Anomalous High-Energy Spin Excitations in the High-$T_c$ Superconductor-Parent Antiferromagnet ${\mathrm{La}}_2{\mathrm{CuO}}_4$

Inelastic neutron scattering is used to investigate the collective magnetic excitations of the high-temperature superconductor-parent antiferromagnet ${\mathrm{La}}_2{\mathrm{CuO}}_4$. We find that while the lower energy excitations are well described by spin-wave theory, including one- and two-magnon scattering processes, the high-energy spin waves are strongly damped near the $(1/2,0)$ position in reciprocal space and merge into a momentum dependent continuum. This anomalous damping indicates the decay of spin waves into other excitations, possibly unbound spinon pairs.

Figure 1

The measured ${\chi }^{\prime \prime }(\mathbf{q},\omega )$ in ${\mu }_B^2{\mathrm{eV}}^{-1}\mathrm{f}.\mathrm{u}{.}^{-1}$ at $T=10\mathrm{K}$. For $E\ge 320\mathrm{meV}$, the response is strongest near $\mathbf{q}=(1/2,0)$ and related positions.

Figure 2

$\mathbf{q}$ dependence of the magnetic excitations in ${\mathrm{La}}_2{\mathrm{CuO}}_4$. (a) One-magnon dispersion ($T=10\mathrm{K}$) along lines in (c, inset). Symbols indicate $E_i$: 160 meV (□), 240 meV (△), and 450 meV (○). The solid line is a SWT fit based on Eq. (1). (b) Measured ${\chi }^{\prime \prime }(\mathbf{q},\omega )$. Dashed circle highlights the anomalous scattering near $(1/2,0)$. An $\hslash \omega$-dependent background determined near $(1,0)$ has been subtracted. (c) One-magnon intensity. Line is a fit to SWT with renormalization factor $Z_d=0.4\pm 0.04$. (d) One-magnon intensity divided by SWT prediction. (e) SWT dispersion (color indicates SW intensity).

Figure 3

Magnetic excitation spectra in ${\mathrm{La}}_2{\mathrm{CuO}}_4$. (a) $(1/2,1/2)$ position showing the two-magnon continuum. (b) $(1/4,1/4)$ position. (c) $(1/2,0)$ position where the SW pole is strongly damped. Lines show resolution-convolved fits to a spin-wave theory one- plus two-magnon cross section [$\mathrm{SWT}(1+2\mathrm{M})$], quantum Monte Carlo simulation (QMC), and a generic power-law line shape [Eq. (2)]. Data are averaged over equivalent points for $h,k\le 1$ and a background at $(1,0)$ has been subtracted.

Figure 4

Spin-wave and continuum (two-magnon) scattering in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ for energy transfers (a) $\hslash \omega =280$ and (b) 232.5 meV and integration ranges shown. The dotted line is a fit of SWT (one-magnon only) convolved with the instrumental resolution plus a quadratic background. The solid line is one-magnon plus two-magnon model. Right panels are magnified.