The ground state of ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ ($0.0<x<1.0$) is studied by the local density approximation plus the Gutzwiller approach, where charge transfer and orbital fluctuations are all self-consistently treated ab initio. In contrast to previous studies, which are parameter-dependent, we characterized the phase diagram as (1) Stoner magnetic metal for $x>0.6$ due to $a_{1g}$ van Hove singularity near the band top, (2) correlated nonmagnetic metal without $e_g^{\prime }$ pockets for $0.3<x<0.6$, and (3) $e_g^{\prime }$ pockets appear for $x<0.3$, and additional magnetic instability is revealed. Experimental quasiparticle properties are well explained, and the $a_{1g}\mathrm{\text{−}}{e}_g^{\prime }$ anticrossing is attributed to spin-orbital coupling.

• Received 30 January 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.066403