Role of entropy and structural parameters in the spin-state transition of ${\mathrm{LaCoO}}_3$

The spin-state transition in ${\mathrm{LaCoO}}_3$ has eluded description for decades despite concerted theoretical and experimental effort. In this study, we approach this problem using fully charge self-consistent density functional theory + embedded dynamical mean field theory (DFT+DMFT). We show from first principles that ${\mathrm{LaCoO}}_3$ cannot be described by a single, pure spin state at any temperature. Instead, we observe a gradual change in the population of higher-spin multiplets with increasing temperature, with the high-spin multiplets being excited at the onset of the spin-state transition followed by the intermediate-spin multiplets being excited at the metal-insulator-transition temperature. We explicitly elucidate the critical role of lattice expansion and oxygen octahedral rotations in the spin-state transition. We also reproduce, from first principles, that the spin-state transition and the metal-insulator transition in ${\mathrm{LaCoO}}_3$ occur at different temperature scales. In addition, our results shed light on the importance of electronic entropy in driving the spin-state transition, which has so far been ignored in all first-principles studies of this material.

Figure 1

Unit cell for a perovskite with no octahedral rotations $(a^0{a}^0{a}^0$ structure). In ${\mathrm{LaCoO}}_3$, the green atoms would be La, the red atoms O, and the blue atom Co. The figure also shows the octahedra formed by the oxygen atoms around the Co atom.

Figure 2

A depiction of the pattern of octahedral rotations that is present in ${\mathrm{LaCoO}}_3$. Each of the oxygen octadra rotates in opposite direction to all nearest-neighbor octahedra by the same amount relative to all three Cartesian axes $(a^{-}{a}^{-}{a}^{-}$ structure).

Figure 3

Density of states $(t_{2g},e_g$, and total including all atoms) for all four structures at 116 and 1160 K.

Figure 4

(a) Evolution of $|S_z|$ with temperature for all four structures. (b) Evolution of density of states at Fermi level with temperature for all four structures.

Figure 5

Evolution of occupation probabilities for all the spin states for the four structures with temperature.

Figure 6

Occupancy histogram showing the occupancy probability for the different atomic states for the $d$ orbital of the Co atom for all the four structures at two different temperatures. The different background colors mark the areas reserved for different spin sectors. The lower $x$-axis ticks as well as the color of the histogram bars denote the different occupancies of the $d$ orbital. Note that odd occupancies only allow half-integer values of $|S_z|$ while even ones allow integer values.