Spin-state transition and phase separation in a multiorbital Hubbard model

We study the spin-state transition and the phase separation involved in this transition based on the multiorbital Hubbard model. Multiple spin states are realized by changing the energy separation between two orbitals and the on-site Hund coupling. By utilizing the variational Monte-Carlo simulation, we analyze the electronic and magnetic structures in hole doped and undoped states. Electronic phase separation occurs between the low-spin band insulating state and the high-spin ferromagnetic metallic state. The difference in the band widths of the two orbitals is of prime importance for the spin-state transition and the phase separation.

Figure 1

(Color online) Phase diagrams at $x=0$. The ratio of the electron transfers is taken to be $t_B/t_A=1/4$ in (a) and $t_B/t_A=1$ in (b). In (b), the filled squares and open circles show the results obtained by the VMC method and the previous DMFT method in Ref. 21, respectively. The broken curves are guides for the eyes. The stars represent the parameters where the carrier dopings were examined.

Figure 2

(Color online) Hole concentration dependences of the energy expectations for several states at $\left(\Delta /t_A,J/t_A\right)=\left(12.2,4\right)$ in (a), and at $\left(\Delta /t_A,J/t_A\right)=\left(8.25,2.5\right)$ in (b). The broken lines are given by the Maxwell’s construction. The ratio of the electron transfers is taken to be $t_B/t_A=1/4$. The constant parameter $C$ in the definition of $E^{\prime }$ is taken to be 16.4 in (a) and 10.5 in (b).

Figure 3

(Color online) Ratio of LS sites to LS and HS sites in the mixed state, $R_{LS}$, and magnetization $M\left(x\right)$ as functions of the hole concentration $x$. The broken line connecting the data at $M\left(x=0\right)$ and $M\left(x=0.33\right)$ is drawn by Maxwell’s rule. For comparison, we plot the $M\left(x\right)=x/2$ curve expected from the hole doping in the LS-BI phase. The parameters are chosen to be $\left(\Delta /t_A,J/t_A\right)=\left(12.2,4\right)$ and $t_B/t_A=1/4$.

Figure 4

(Color online) Hole concentration dependences of the energy expectations for several states where the electron transfer integrals are chosen to be equal as $t_B/t_A=1$. The other parameters are taken to be $\left(\Delta /t_A,J/t_A\right)=\left(12.2,4\right)$, and the constant parameter $C$ in the definition of $E^{\prime }$ is taken to be 16.

Figure 5

(Color online) Schematic density-of-states in the LS-BI state at $x=0$ and that in the HS-ML state in a high hole-doped region.