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Theoretical Study of $L$-edge Resonant Inelastic X-ray Scattering in La$_2$CuO$_4$ on the Basis of Detailed Electronic Band Structure

We study theoretically resonant inelastic x-ray scattering (RIXS) at the Cu $L_3$-edge in a typical parent compound of high-$T_c$ cuprate superconductors La$_2$CuO$_4$ on the basis of a detailed electronic band structure. We construct a realistic and precise tight-binding model by employing the maximally-localized Wannier functions derived from a first-principles electronic structure calculation, and then take account of the Coulomb repulsion between d electrons at each Cu site. The antiferromagnetic ground state is described within the Hartree-Fock approximation, and take account of electron correlations in the intermediate states of RIXS within the random-phase approximation (RPA). Calculated RIXS spectra agree well with the experimentally observed features including low-energy magnon excitation, $d$-$d$ excitations, and charge-transfer excitations, over a wide excitation-energy range. In particular, we stress the importance of photon polarization dependence: the intensity of magnon excitation and the spectral structure of $d$-$d$ excitations depend significantly not only on the polarization direction of incident incoming photons but also that of outgoing photons. It is demonstrated that the single-magnon excitation intensity is maximized when the polarization directions of incoming and outgoing photons are perpendicular to each other.