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

TL;DR

This paper investigates Coulomb correlations, charge disproportionation, and spin ordering in Na(x)CoO2 using LDA+U calculations, revealing critical U values for phase transitions and their dependence on magnetic order and doping levels.

Contribution

It provides a detailed analysis of how Coulomb interactions influence charge and spin orderings in Na(x)CoO2, highlighting the crossover from single-band to multi-band regimes with doping.

Findings

Charge disproportionation occurs above a critical U for both x=1/3 and x=2/3.

Antiferromagnetic coupling is favored in a Co(3+)-Co(4+) ordered state.

Correlation effects are significantly reduced below x=0.5, indicating a crossover in electronic behavior.

Abstract

The strength and effect of Coulomb correlations in the (superconducting when hydrated) x~1/3 and ``enhanced'' x~2/3 regimes of Na(x)CoO2 are evaluated using the correlated band theory LDA+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, (4) in a Co(3+)-Co(4+) ordered state, antiferromagnetic coupling is favored over ferromagnetic, while below U_c ferromagnetism is favored. 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 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/\sqrt(3) ~ W and correlation effects are substantially reduced.