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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 modelcalculations with full multiplets. We show Na$_x$Ca$_{1-x}$Cr$_2$O$_4$ taking anovel mixed-valence electronic state in which the positive charge-transfer (CT)and the negative self-doped states coexist. While CaCr$_2$O$_4$ (one endmember) exhibits a typical CT nature with strong covalent character, Nasubstitution 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 withequal weight. This unusual electronic state is in sharp contrast to theconventional mixed-valence description, in which the ground state can bedescribed by the mixture of Cr$^{3+}$ ($3d^3$) and Cr$^{4+}$ ($3d^2$).

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