Theory of Valence Transition in ${\mathrm{BiNiO}}_3$

Motivated by the colossal negative thermal expansion recently found in ${\mathrm{BiNiO}}_3$, the valence transition accompanied by the charge transfer between the Bi and Ni sites is theoretically studied. We introduce an effective model for $\mathrm{Bi}\text{−}6s$ and $\mathrm{Ni}\text{−}3d$ orbitals taking into account the valence skipping of Bi cations, and investigate the ground-state and finite-temperature phase diagrams within the mean-field approximation. We find that the valence transition is caused by commensurate locking of the electron filling in each orbital associated with charge and magnetic orderings, and the critical temperature and the nature of the transitions are strongly affected by the relative energy between the Bi and Ni levels and the effective electron-electron interaction in the Bi sites. The obtained phase diagram well explains the temperature- and pressure-driven valence transitions in ${\mathrm{BiNiO}}_3$ and the systematic variation of valence states for a series of Bi and Pb perovskite oxides.

Figure 1

(a) Schematic electron configurations for $\mathrm{Bi}\text{−}6s$ and $\mathrm{Ni}\text{−}3d$ $e_g$ orbitals in ${\mathrm{BiNiO}}_3$ and (b) those in the effective model in Eq. (1). CO, PM, AFM, and CT denote charge order, paramagnetic, antiferromagnetic states, and charge transfer, respectively. Schematic pictures of (c) the perovskite structure for ${\mathrm{BiNiO}}_3$ and (d) the projected two-dimensional lattice structure for the effective model. The shaded area represents the mean-field unit cell.

Figure 2

(a) Ground state phase diagram. The solid and broken lines denote the second and first order transitions, respectively. Schematic pictures of charge and spin configurations: (b) uniform-I, (c) $\mathrm{CO}+\mathrm{AFM}$, (d) uniform-II, (e) sub-I, and (f) sub-II. The circles and arrows represent the charge densities and spin moments at each site, respectively.

Figure 3

$\mathrm{\Delta }$ dependences of the charge densities (upper panels) and spin moments (lower panels) at each Bi and Ni site for $t_{\mathrm{B}}=t_{\mathrm{N}}=1$, $t_{\mathrm{BN}}=0.5$, $U_{\mathrm{N}}=3$, and $V_{\mathrm{B}}=0.65$. (a) $U_{\mathrm{B}}=-2$. (b) $U_{\mathrm{B}}=0$. (c) $U_{\mathrm{B}}=2$.

Figure 4

Global phase diagram in the $\mathrm{\Delta }\text{−}{U}_{\mathrm{B}}\text{−}T$ space. The solid and broken lines denote the second and first order transitions, respectively. The thin dotted lines are guides for the eye denoting connections between the CO domes.

Figure 5

$T$ dependences of the charge densities at each Bi and Ni site for $t_{\mathrm{B}}=t_{\mathrm{N}}=1$, $t_{\mathrm{BN}}=0.5$, $U_{\mathrm{N}}=3$, and $V_{\mathrm{B}}=0.65$. (a)–(c) $U_{\mathrm{B}}=-2$ and (d)–(f) $U_{\mathrm{B}}=2$ for the different values of $\mathrm{\Delta }$ (indicated in the figures). Note the difference in the $T$ range for the two choices of $U_{\mathrm{B}}$.