Magnetic excitations in the one-dimensional cuprate Sr$_{\mathrm{\mathbf{2}}}$\textbf{CuO}$_{\mathrm{\mathbf{3}}}$\textbf{ probed by resonant inelastic x-ray scattering}

We present a resonant inelastic x-ray scattering (RIXS) study of low energy spectra at the oxygen K-edge of Sr$_{\mathrm{2}}$CuO$_{\mathrm{3}}$. The experimental data shows the presence of several low-energy excitations in the quasi-elastic region ($\omega $\textless 0.5 eV), which we associate with magnetic and lattice excitations. We investigate the system using a one dimensional antiferromagnetic Heisenberg chain comprising of copper and oxygen. Using linear spin wave theory, we compute the RIXS cross section in the ultrashort core-hole lifetime approximation to second order and demonstrate the presence of two-magnon excitations in the low-energy region. Phonon and phonon assisted two-magnon excitations are also calculated within our approach. Our analysis establishes that the two-magnon excitations and phonon excitations are present in Sr$_{\mathrm{2}}$CuO$_{\mathrm{3}}$, indicating that this is potentially an ideal system for studying possible spin-lattice coupling.