Correlation Effects and Magnetism in Na$_x$CoO$_2$

Correlation effects are known to be important for the electronic structure and the Fermi surface topology of Na$_x$CoO$_2$ [ref to prl of Zhou et al.]. Here we study magnetic properties of Na$_x$CoO$_2$ based on the multi-orbital Hubbard model for the cobalt $t_{2g}$ electrons in weak and strong coupling limits using Hartree-Fock and Gutzwiller approximations. Both commensurate and incommensurate magnetic order is considered. We present the phase diagram in the parameter space of local Coulomb repulsion and Hund’s rule coupling for different sodium doping concentrations. The interplay between the correlation effects and Fermi surface nesting on the magnetic properties will be discussed.