Fig. 2 | Nature Communications

Fig. 2

From: Momentum-resolved observations of the phonon instability driving geometric improper ferroelectricity in yttrium manganite

Fig. 2

Dynamics and condensation of the K3 distortion across T FE. Phonon dispersions along [H, 0,10] direction measured at T = a 1423, b 1753, d 612, and e 300 K are compared with intensity calculated from DFT model, χ″(Q, E), for c 1500 K and f 0 K DFT simulations (white lines in c, f are the calculated phonon dispersions along the [H, 0, 10]). The (1, 0, 10) and (2, 0, 10) Bragg peaks at 612 and 300 K are due to the trimerization of the unit cell. In e, the phonon dispersion obtained by fitting the scattering intensity is shown as black markers with error bars (one standard deviation on either side of the peak value). The INS signal was integrated over a range −0.2 ≤ Q ⊥ ≤ 0.2 rlu for directions perpendicular to [H, 0, 10]. The high symmetry points (Γ and K) denoting the path above panels refer to the PE phase setting (K becomes Γ in the FE phase). The small difference between the measurements and simulations of phonon intensity near (2, 0, 10) is due to slightly different theoretical atomic coordinates (and consequently structure factor), and possible effects of sample rotation in the beam. The data in a, b and d, e were measured on HYSPEC (phonon annihilation) and ARCS (phonon creation) spectrometers, respectively

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