Energy-dependent crossover from anisotropic to isotropic magnetic dispersion in lightly doped La_1.96Sr_0.04CuO₄

Inelastic neutron-scattering experiments have been performed on lightly doped La_1.96Sr_0.04CuO₄, 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. 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, cross over to an isotropic, conical dispersion that resembles spin waves in the parent compound La₂CuO₄. The change from twofold to full symmetry on crossing the waist of the hourglass reproduces behavior first identified in studies of underdoped YBa ₂Cu₃O_6+x. We discuss the significance of these results.