Phonons reflect dynamic spin-state order in LaCoO${}_3$

Abstract

We investigate lattice dynamics in LaCoO${}_3$ using inelastic neutron and x-ray scattering over $T = 2\mbox{-}650\,\mathrm{K}$, spanning the spin-state crossover at $T_1\approx 100\mathrm{K}$ and the insulator--metal transition at $T_2\approx 550\mathrm{K}$. Comparison with quasi-harmonic $ab-initio$ lattice-dynamical calculations helps reveal anomalous softening of a $\approx 10\mathrm{meV}$ oxygen phonon, confined to the temperature interval $T_1\le T\le T_2$ and localized in momentum space at ${\mathbf{q}}_{\mathrm{SSO}}={\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)}_c$. This wave vector corresponds to the spin-state ordering originally proposed by Goodenough [J. Phys. Chem. Solids 6, 287-297 (1958)]. Our results therefore provide momentum-resolved evidence for dynamic correlations of high-spin and low-spin Co${}^{3+}$ states in LaCoO${}_3$, linking spin-state fluctuations to anomalous phonon renormalization.

13 pages, 5 figures