Disproportionation and Metallization at Low-Spin to High-Spin Transition in Multiorbital Mott Systems

We study the thermally driven spin state transition in a two-orbital Hubbard model with crystal-field splitting, which provides a minimal description of the physics of ${\mathrm{LaCoO}}_3$. We employ the dynamical mean-field theory with a quantum Monte Carlo impurity solver. At intermediate temperatures we find a spin disproportionated phase characterized by a checkerboard order of sites with small and large spin moments. The high temperature transition from the disproportionated to a homogeneous phase is accompanied by a vanishing of the charge gap. With the increasing crystal-field splitting the temperature range of the disproportionated phase shrinks and eventually disappears completely.

Figure 1

Conceptual phase diagram of the two-band model for $U/J=4$. The size of the charge gap is indicated by color intensity ($\mathrm{\text{white}}=\mathrm{\text{no gap}}$). The parameters of the present study are marked with the cross.

Figure 2

(a) The $T$ dependence of the site-averaged local spin susceptibility (filled circles) for $\Delta$ of 3.40 [gray (red)] and 3.42 (black) eV. The corresponding site-resolved contributions are shown in the inset. The $\Delta =3.40\mathrm{eV}$ data are compared to the uniform susceptibility (diamonds) and the local susceptibility obtained in the homogeneous phase (empty circles). (b) The site-resolved occupancy ${\overline{n}}^a$ (the same color coding as above). (c,d) The spin-spin correlation functions on sites $A$ (c) and $B$ (d) for $\Delta =3.40\mathrm{eV}$ and $T=290\mathrm{K}$. (Note the different intervals on the vertical axis covered in the two graphs.) The column charts show the contributions of the different local eigenstates described in the text.

Figure 3

The $T$ evolution of the one-particle spectra for $\Delta =3.40$. The spectral densities of different orbitals are resolved by color: $a$ (black) and $b$ [gray (red)], while the dashed lines correspond to the $B$ sites and full lines to the $A$ sites.

Figure 4

The uniform susceptibility of the classical model as a function of temperature and the parameter ${\xi }_0$. The inset shows the difference of the HS populations $x_A-x_B$ as a function of temperature and ${\xi }_0$.