Enhanced transient negative capacitance during inhomogeneous ferroelectric switching

The reversal of polarization in a ferroelectric material involves overcoming an energy barrier, and has been previously proposed and found to yield transient negative capacitance (NC) in the intermediate states of the switching process. Homogeneous switching was assumed to interpret the experimental results of NC; however, inhomogeneous switching is a more abundant mechanism than homogeneous switching, but its possible effect on NC is basically unknown. Here, we use first-principles-based techniques to investigate the occurrence of NC during these two types of switching processes in the supertetragonal phase of ${\mathrm{BiFeO}}_3$. We find NC in both cases, but with the magnitude of the inverse of the capacitance being drastically larger in the inhomogeneous (nucleation limited) switching, as compared to the homogeneous switching. We further analyze the origin of the different NC effects, and point to the different energetic trajectories between these two representative switching mechanisms.

Figure 1

Negative capacitance (NC) in the switching of T-BFO. (a), (b) $z$ component of the polarization $P_z$ and total energy as a function of simulation time in MD, under a field of 25 MV/cm. (c), (d) Total energy and its second derivative as a function of $D_z$, under a field of 25 MV/ cm. The solid curves are the spline fitting to the data. At this field, the switching mechanism is nucleation limited switching (NLS). (e)–(h) Likewise for a field of 40 MV/cm for homogeneous switching (HS). The time intervals at which NC occurs are highlighted in each panel.

Figure 2

Schematics of the energy landscapes under different $E$ fields. (a) Zero field, no switching. (b) Intermediate field, inhomogeneous switching. The red arrow denotes the initial trajectory of the local dipoles, followed by the green and blue arrows, denoting different trajectories of the dipoles. (c) High field, homogeneous switching.

Figure 3

Comparison of the trajectories of the local dipoles based on the MD simulations. Nine representative local dipoles are chosen for the illustration. (a) NLS switching under a field of 25 MV/cm. (b) HS switching under a field of 40 MV/cm. The time range having NC is highlighted.