Fig. 5: Simulated real-time dynamics in a theoretical model for BiFeO3.

a Temporal profiles of the ferroelectric and antiferrodistortive distortions, QFE (top panel) and QAFD (bottom panel). ΔQX = (QX − QX,0)/QX,0 (X = FE, AFD) represents the relative displacement measured from its equilibrium position QX,0. b Spectrograms of QFE (top) and QAFD (bottom), using their time derivatives to remove the dc (ω = 0) component. The solid and dotted curves illustrate the eigen-energies of the ferroelectric (QFE) and antiferrodistortive (QAFD) modes, respectively, calculated from the instantaneous values of QFE and QAFD in the absence of the couplings to the electrons and the localized spins. c Optical conductivity around the in-gap state (ℏω ≈ 2 h) at different times t.