# Unusual coexistence of negative/positive charge-transfer in mixed-valence Na$_x$Ca$_{1-x}$Cr$_2$O$_4$

## TL;DR

This study reveals a novel mixed-valence electronic state in Na$_x$Ca$_{1-x}$Cr$_2$O$_4$ where positive charge-transfer and negative self-doped states coexist, contrasting with traditional mixed-valence models.

## Contribution

It demonstrates the coexistence of positive charge-transfer and negative self-doped states in Na$_x$Ca$_{1-x}$Cr$_2$O$_4$, challenging conventional mixed-valence understanding.

## Key findings

- Na substitution induces a self-doped state with oxygen holes.
- Na$_x$Ca$_{1-x}$Cr$_2$O$_4$ exhibits coexistence of positive CT and negative states.
- Contrasts with the typical Cr$^{3+}$/Cr$^{4+}$ mixed-valence model.

## Abstract

We have investigated the electronic structure of Na$_x$Ca$_{1-x}$Cr$_2$O$_4$ using x-ray absorption spectroscopy together with Anderson impurity model calculations with full multiplets. We show Na$_x$Ca$_{1-x}$Cr$_2$O$_4$ taking a novel mixed-valence electronic state in which the positive charge-transfer (CT) and the negative self-doped states coexist. While CaCr$_2$O$_4$ (one end member) exhibits a typical CT nature with strong covalent character, Na substitution causes a self-doped state with an oxygen hole. In NaCr$_2$O$_4$ (the other end member), positive CT and negative self-doped states coexist with equal weight. This unusual electronic state is in sharp contrast to the conventional mixed-valence description, in which the ground state can be described by the mixture of Cr$^{3+}$ ($3d^3$) and Cr$^{4+}$ ($3d^2$).