Charge- and Spin-Ordering Tendencies in Na(x)CoO2

The strength and effect of Coulomb correlations in the (superconducting when hydrated) $x\approx$1/3 regime of Na$_x$CoO$_2$ have been evaluated using the correlated band theory LDA+U method. Our results, neglecting quantum fluctuations, are: (1) there is a critical U_c = 3 eV, above which charge ordering occurs at x=1/3, (2) in this charge-ordered state, antiferromagnetic coupling is favored over ferromagnetic, while below U_c, ferromagnetism is favored; and (3) carrier conduction behavior should be very asymmetric for dopings away from x=1/3. For x < 1/3, correlated hopping of parallel spin pairs is favored, suggesting a triplet superconducting phase. The lack of any observed magnetic behavior in this regime is addressed.