Interplay of spin and charge order in the electron-doped cuprates

We study magnetic and charge order in the electron-doped high-$T_c$ cuprates based on the one-band Hubbard model with onsite ($U$) and nearest-neighbor $(V)$ interactions. To investigate the interplay between the orders, we employ the Kotliar-Ruckenstein slave-boson method and analyze fluctuations descending from an antiferromagnetic parent state. Our analysis reveals incommensurate charge order whose ordering vector matches the doping-dependence of resonant inelastic x-ray scattering (RIXS) measurements in Nd${}_{2-x}$Ce${}_x$CuO${}_4$ (NCCO). From our calculations of paramagnon dispersion as well as dynamical charge and spin structure factors, we reproduce all qualitative features of the RIXS signal.