Energy-dependent crossover from anisotropic to isotropic magnetic dispersion in lightly-doped La1.96Sr0.04CuO4

Inelastic neutron scattering experiments have been performed on lightly-doped La$_{1.96}$Sr$_{0.04}$CuO$_{4}$, which shows diagonal incommensurate spin correlations at low temperatures. We previously reported that this crystal, with a single orthorhombic domain, exhibits the "hourglass" dispersion at low energies [Phys. Rev. Lett. 101, 197001 (2008)]. In this paper, we investigate in detail the energy evolution of the magnetic excitations up to 65 meV. It is found that the anisotropic excitations at low energies, dispersing only along the spin modulation direction, crossover to an isotropic, conical dispersion that resembles spin waves in the parent compound La$_2$CuO$_{4}$. The change from two-fold to full symmetry on crossing the waist of the hourglass reproduces behavior first identified in studies of underdoped YBa$_2$Cu$_3$O$_{6+x}$. We discuss the significance of these results.