Magnetic excitations in L -edge resonant inelastic x-ray scattering from cuprate compounds

We study the magnetic excitation spectra in L-edge resonant inelastic x-ray scattering (RIXS) from undoped cuprates. We analyze the second-order dipole-allowed process that the strong perturbation works through the intermediate state in which the spin degree of freedom is lost at the core-hole site. Within the approximation neglecting the perturbation on the neighboring sites, we derive the spin-flip final state in the scattering channel with changing the polarization, which leads to the RIXS spectra expressed as the dynamical structure factor of the transverse spin components. We assume a spherical form of the spin-conserving final state in the channel without changing the polarization, which leads to the RIXS spectra expressed as the ``exchange''-type multispin correlation function. Evaluating numerically the transition amplitudes to these final states on a finite-size cluster, we obtain a sizable amount of the transition amplitude to the spin-conserving final state in comparison with that to the spin-flip final state. We treat the itinerant magnetic excitations in the final state by means of the $1/S$ expansion method. Evaluating the higher-order correction with $1/S$, we find that the peak arising from the one-magnon excitation is reduced with its weight, and the continuous spectra arising from the three-magnon excitations come out. The interaction between two magnons is treated by summing up the ladder diagrams. On the basis of these results, we analyze the L₃-edge RIXS spectra in Sr₂CuO₂Cl₂ in comparison with the experiment. It is shown that the three-magnon excitations as well as the two-magnon excitations give rise to the intensity in the high-energy side of the one-magnon peak, making the spectral shape asymmetric with wide width, in good agreement with the experiment.