Based on dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, static as well as dynamic spin and charge susceptibilites for the phase diagram of the sodium cobaltate system Na${}_x$CoO${}_2$ are discussed. The approach includes important vertex contributions to the $\mathbf{q}$ dependent two-particle response functions by means of a local approximation to the irreducible vertex function in the particle-hole channel. A single-band Hubbard model suffices to reveal several charge- and spin-instability tendencies in accordance with experiment, including the stabilization of an effective kagome sublattice close to $x=0.67$, without invoking the doping-dependent Na-potential landscape. The in-plane antiferromagnetic-to-ferromagnetic crossover is additionally verified by means of the computed Korringa ratio. Moreover an intricate high-energy mode in the transverse spin susceptiblity is revealed, pointing toward a strong energy dependence of the effective intersite exchange.

• Received 17 January 2011

DOI:https://doi.org/10.1103/PhysRevB.85.115128