Non adiabatic dynamics of the ferroelectric soft mode

Abstract

Most microscopic descriptions of structural dynamics assume the Born-Oppenheimer separation, where electrons adjust adiabatically to ionic motion. When this separation breaks down, electronic and lattice degrees of freedom can evolve on different timescales, giving rise to new physical phenomena beyond the adiabatic limit. Here we use time-resolved, phase-sensitive second-harmonic generation and pump-probe reflectivity to reshape the ferroelectric free-energy landscape of SnTe while separately tracking polar order and coherent lattice motion. When photoexcitation transiently suppresses the double-well barrier, polarization dynamics become strongly nonlinear, while the coherent phonon dynamics remain harmonic. This decoupling cannot be described by a single adiabatic coordinate for the electronic polarization and ionic positions. We provide a unifying physical description for the non adiabatic dynamics of the ferroelectric mode and the mixed displacive/order-disorder nature of SnTe based on a separation of scales for the renormalization of the ferroelectric stiffness.

Figures (6)

• Figure 1: (a-d) The SHG intensity as a function of rotation angle of the SnTe (111) surface taken at temperatures of 300K (a)+(c) and 10K (b)+(d) in the parallel (c,d) and perpendicular (a,b) configurations. Orange circles are the datapoints and the solid black line is a fit to the data. Dashed purple lines mark the direction of mirror planes. Illustrations of the SnTe (111) surface above and below the transition are shown at the sides, Sn and Te planes shifts are exaggerated for clarity, mirror planes are marked with dashed lines. Symmetry breaking is exaggerated below the transition. (e) Magnitude of the ferroelectric order parameter $P_{FE}$, as extracted from the fits to the data. Blue circles are data points and the orange curve is a mean field fit. The dashed black line at 71K marks $T_{c}$ as extracted from the fit. Inset shows $\chi_{3fold}^{\perp}$ as a function of the temperature.
• Figure 2: (a) Pump probe reflectivity at a fluence of $\sim4.76 [mJ/cm^2]$ as a function of temperature from 10K to 80K, temperatures are marked below the data, black lines are fits to the data, different traces are vertically shifted for clarity. (b) $\omega^2$ extracted from fitting the data shown in (a) as a function of temperature. The orange line is a linear fit to the data. The dashed line marks $T_{c}$ extracted from the SHG measurements. The inset shows the Fourier transform of the data in (a).
• Figure 3: (a) Time resolved SHG (bottom) and $\Delta R/R$ (top) at a pump fluence of $\sim 5.9[mJ/cm^2]$ and $T=$5K. Dashed lines are guides to the eye for the joint oscillation minima and maxima positions. (b) RA-SHG pattern taken in the absence of the pump. Measurements in (a) and (c) were taken along the mirror plane at $60$°. A dashed purple line marks the mirror plane. (c) SHG intensity as a function of time delay for various pump fluences coded by color, similar to panel (d). All data is shifted for clarity. The top four traces are multiplied by a factor of 6 for clarity. (d) $\Delta R/R$ as a function of time delay for various fluences taken at 5K. Numbers next to data are the respective fluences in $mJ/cm^2$. Black solid lines are fits to the data. (e) Frequency extracted from the pump probe data in (d) as a function of the pump's fluence. (f) Fourier transform for the data in (d), colors mark the same fluences as in (d).
• Figure 4: (a) $P_{FE}$ Normalized to its equilibrium value as a function of pump delay time for a fluence of $\sim35.8 [mJ/cm^2]$ at 5K. Blue dots are the data, orange line is a fit and the blue shading is the fit $1\sigma$ confidence band. Dashed lines mark specific times for which normalized RA-SHG patterns are displayed above the plot. (b) $\chi_{3fold}^{\parallel}$ normalized to its equilibrium value as a function of time delay. (c-e) The double-well potential for the extracted fitting parameters at three specific delay times. Blue curve is the Landau potential, orange dot is the position value of $P_{FE}$ and the black arrow marks the direction and magnitude of the velocity. (c) Before quenching the barrier, (d) after quenching the barrier and (e) when it has partially recovered
• Figure S1: Schematic of the optical setup used in this work. (a) The optical setup used for the pump-probe measurements, and (b) the optical setup for the SHG measurements. Unlabeled components are silver mirrors.