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

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.

4 pages and 4 embedded figures

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