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

We have investigated the electronic structure of ${\mathrm{Na}}_x{\mathrm{Ca}}_{1-x}{\mathrm{Cr}}_2{\mathrm{O}}_4$ using x-ray absorption spectroscopy together with Anderson impurity model calculations. We show ${\mathrm{Na}}_x{\mathrm{Ca}}_{1-x}{\mathrm{Cr}}_2{\mathrm{O}}_4$ takes an unusual mixed-valence electronic state in which the positive charge-transfer (CT) and the negative CT states coexist. While ${\mathrm{CaCr}}_2{\mathrm{O}}_4$ (one end member) exhibits a typical CT nature with strong covalent character, Na substitution causes a negative CT state with an oxygen hole. In ${\mathrm{NaCr}}_2{\mathrm{O}}_4$ (the other end member), positive CT and negative CT 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 ${\mathrm{Cr}}^{3+}$ ($3d^3$) and ${\mathrm{Cr}}^{4+}$ ($3d^2$).

Figure 1

(a) Revised Zaanen-Sawatzky-Allen diagram. (b) Crystal structure of ${\mathrm{NaCr}}_2{\mathrm{O}}_4$, characterized by two inequivalent ${\mathrm{Cr}}^{3+}$ sites with slightly different oxygen coordination. (c) Focusing only on Cr sites, the geometrically frustrated double-chain structure can be seen. The magnetic moment exists on these Cr sites.

Figure 2

Measured evolution of XAS spectra for ${\mathrm{Na}}_x{\mathrm{Ca}}_{1-x}{\mathrm{Cr}}_2{\mathrm{O}}_4$, together with the experimental spectra of the ${\mathrm{Cr}}_2{\mathrm{O}}_3$. (a) Na doping dependence of the experimental Cr $2p$ XAS spectra measured at room temperature. Areas under spectral curves in all spectra were normalized to the same value. (b) Na doping dependence of the experimental O $1s$ XAS spectra measured at room temperature.

Figure 3

(a) Comparison between a calculated Cr $2p$ XAS spectrum for ${\mathrm{CaCr}}_2{\mathrm{O}}_4$ (green line) and experimental spectrum (light blue line). (b) To clarify the effect of Na-doping-induced changes in Cr $2p$ XAS spectra, the observed Cr $2p$ XAS spectrum for a Na $60\%$ doped sample is compared with one for ${\mathrm{CaCr}}_2{\mathrm{O}}_4$ (upper panel). The spectra are normalized by maximum intensity. The calculated XAS spectra for Na $60\%$ doped sample are shown in the lower panel (red line). (c) Upper panel: Comparison between the best-fit Cr $2p$ XAS calculated spectrum for ${\mathrm{NaCr}}_2{\mathrm{O}}_4$ (blue line) and experimental spectra (red line). Lower panel: Calculated spectrum for ${\mathrm{NaCr}}_2{\mathrm{O}}_4$ just by changing the sign of the $\mathrm{\Delta }$ values of the tetravalent site. The other parameter values are fixed to the values in Table 2.

Figure 4

Simulated evolution of XAS spectra for ${\mathrm{Na}}_x{\mathrm{Ca}}_{1-x}{\mathrm{Cr}}_2{\mathrm{O}}_4$ as a function of Na doping level. The doping dependence of the total spectrum was obtained by making a superposition of two calculated spectra in accordance with Na doping level.

Figure 5

Illustration of hole-induced behavior of charge frustration. The $3d^3$ and $3d^3\underline{L}$ states are represented by the same purple balls. Because Cr $3d$ has the same electron number in either state, hole doping in the Cr site leads to the formation of charge frustration or charge ordering. On the other hand, there is no charge frustration at Cr sites by doping the hole to the oxygen octahedron.