Charge disproportionation and spin ordering tendencies in Na_xCoO₂

The strength and effect of Coulomb correlations in the (superconducting when hydrated) x≈1∕3 and “enhanced” x≈2∕3 regimes of Na_xCoO₂ are evaluated using the correlated band theory LDA+U (local density approximation of Hubbard U) method. Our results, neglecting quantum fluctuations, are (1) allowing only ferromagnetic order, there is a critical U_c=3 eV, above which charge disproportionation occurs for both x=1∕3 and x=2∕3, (2) allowing antiferromagnetic order at x=1∕3, U_c drops to 1 eV for disproportionation, (3) disproportionation and gap opening occur simultaneously, and (4) in a Co³⁺−Co⁴⁺ ordered state, antiferromagnetic coupling is favored over ferromagnetic, while below U_c ferromagnetism is favored. A comparison of the calculated Fermi level density of states compared to reported linear specific heat coefficients indicates enhancement of the order of five for x∼0.7, but negligible enhancement for x∼0.3. This trend is consistent with strong magnetic behavior and local moments (Curie-Weiss susceptibility) for x>0.5 while there is no magnetic behavior or local moments reported for x<0.5. We suggest that the phase diagram is characterized by a crossover from effective single-band character with U⪢W for x>0.5 into a three-band regime for x<0.5, where U→U_eff⩽U∕√3∼W and correlation effects are substantially reduced.