<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>DFT</mml:mi><mml:mo>+</mml:mo><mml:mi>DMFT</mml:mi></mml:mrow></mml:math> study of spin-charge-lattice coupling in covalent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>LaCoO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

Abstract

We study energetics and the nature of both homogeneous and mixed spin (MS) states in ${\mathrm{LaCoO}}_{3}$ incorporating structural changes of the crystal volume expansion and the Co-O bond disproportionation (BD) during the spin-state transition using the density functional theory plus dynamical mean field theory ($\mathrm{DFT}+\mathrm{DMFT}$) method. $\mathrm{DFT}+\mathrm{DMFT}$ predicts that energetics of both excited spin states are almost the same while $\mathrm{DFT}+U$ calculations of the same structures energetically favor the MS states and produce various metastable solutions whose energetics depend sensitively on final spin states. Within $\mathrm{DFT}+\mathrm{DMFT}$, the homogeneous spin state in the expanded crystal volume shows the multiconfigurational nature with non-negligible occupancy probabilities of both high spin (HS) and low spin (LS) states along with ${d}^{6}$ and ${d}^{7}$ charge configurations indicating the dynamically fluctuating nature of spin and charge states due to the Co-O covalency. The nature of the MS state under the BD structure reveals that Co sites with the long Co-O bonds develop a Mott insulating state and favor HS with a ${d}^{6}$ configuration, while more covalent Co sites with the short Co-O bonds occupy more LS states with a ${d}^{7}$ configuration and behave as a band insulator, as a result, charge ordering is induced in the BD structure from the spin-state ordering. We also find that both energetics and electronic structure sensitively depend on the Co-O covalency effect, which can be tuned by changing the double counting potential and the resulting $d$ occupancy (${N}_{d}$), and ${N}_{d}$ close to 6.7 is consistent with the nature of the spin-state transition. Our results show that structural changes during the spin-state transition can play an important role in understanding energetics and electronic structure of ${\mathrm{LaCoO}}_{3}$.

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