摘要：

We probe the collective magnetic modes of ${\\mathrm{La}}_{2}{\\mathrm{CuO}}_{4}$ and underdoped ${\\mathrm{La}}_{2\\ensuremath{-}x}{\\mathrm{Sr}}_{x}{\\mathrm{CuO}}_{4}$ (LSCO) by momentum resolved resonant inelastic x-ray scattering (RIXS) at the Cu ${L}_{3}$ edge. For the undoped antiferromagnetic sample, we show that the single magnon dispersion measured with RIXS coincides with the one determined by inelastic neutron scattering, thus demonstrating that x rays are an alternative to neutrons in this field. In the spin dynamics of LSCO, we find a branch dispersing up to $\\ensuremath{\\sim}400ext{ }ext{ }\\mathrm{meV}$ coexisting with one at lower energy. The high-energy branch has never been seen before. It indicates that underdoped LSCO is in a dynamic inhomogeneous spin state.

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