  We introduce and analyze an extended Hubbard model, in which intersite
Coulomb interaction as well as a staggered local potential (SLP) are
considered, on the square lattice at half band filling, in the thermodynamic
limit. Using both Hartree-Fock approximation and Kotliar and Ruckenstein slave
boson formalism, we show that the model harbors charge order (CO) as well as
joint spin and charge modulations (SCO) at finite values of the SLP, while the
spin density wave (SDW) is stabilized for vanishing SLP, only. We determine
their phase boundaries and the variations of the order parameters in dependence
on the SLP, as well as on the on-site and nearest-neighbor interactions.
Domains of coexistence of CO and SCO phases, suitable for resistive switching
experiments, are unraveled. We show that the novel SCO systematically turns
into the more conventional SDW phase when the zero-SLP limit is taken. We also
discuss the nature of the different phase transitions, both at zero and finite
temperature. In the former case, no continuous CO to SDW (or SCO) phase
transition occurs. In contrast, a paramagnetic phase (PM), which is accompanied
with continuous phase transitions towards both spin or charge ordered phases,
sets in at finite temperature. A good quantitative agreement with numerical
simulations is demonstrated, and a comparison between the two used approaches
is performed.
