Disproportionation Transition at Critical Interaction Strength: Na$_{1/2}$CoO$_2$

TL;DR

This study investigates the charge disproportionation transition in Na$_{1/2}$CoO$_2$, revealing a first-order transition linked to spin states and energy changes, with implications for understanding its charge-ordered insulating phase.

Contribution

It demonstrates a first-order charge disproportionation transition in Na$_{1/2}$CoO$_2$ and connects ionic identities more to spin than charge, providing insights into the material's electronic behavior.

Findings

Disproportionation transition is first order with energy discontinuities.

Charge disproportionation is linked more to spin states than charge.

Coulomb repulsion U is concentration-dependent, around 3.5 eV at x=1/2.

Abstract

Charge disproportionation (CD) and spin differentiation in Na$_{1/2}$CoO$_2$ are studied using the correlated band theory approach. The simultaneous CD and gap opening seen previously is followed through a first order charge disproportionation transition 2Co$^{3.5+} \to$ Co$^{3+}$+Co$^{4+}$, whose ionic identities are connected more closely to spin (S=0, S=1/2 respectively) than to real charge. Disproportionation in the Co $a_g$ orbital is compensated by opposing charge rearrangement in other 3d orbitals. At the transition large and opposing discontinuities in the (all-electron) kinetic and potential energies are slightly more than balanced by a gain in correlation energy. The CD state is compared to characteristics of the observed charge-ordered insulating phase in Na$_{1/2}$CoO$_2$, suggesting the Coulomb repulsion value $U$ is concentration-dependent, with $U(x=1/2)\simeq$3.5 eV.