Intrinsic Nucleation Mechanism and Disorder Effects in Polarization Switching on Ferroelectric Surfaces

The temperature dependence of ferroelectric domain nucleation in epitaxial films of ${\mathrm{BiFeO}}_3$ is studied using variable temperature ultrahigh vacuum piezoresponse force spectroscopy in the 50 to 300 K temperature range. The nucleation bias corresponding to the onset of local ferroelectric switching in the volume of an electrostatic field confined by the metal tip was found to change less than 20% across the entire temperature range. A combination of the analytical and phase-field analysis proves that the weak temperature dependence of nucleation bias is a hallmark of an intrinsic nucleation mechanism with minimal contribution of thermal fluctuations. The effect of disorder on the observed distribution of the nucleation bias between vacuum and ambient environments is compared.

Figure 1

Topography, amplitude, and phase of piezoresponse of 50 nm ${\mathrm{BiFeO}}_3(100)$ film used in this study. The panel below shows averages of 50–100 local ferroelectric hysteresis loops obtained with the same physical cantilever in ultrahigh vacuum and after venting the chamber to ambient.

Figure 2

Temperature dependence of local ferroelectric switching. (a) Average hysteresis loops of a 50 nm ${\mathrm{BiFeO}}_3$ film as a function of sample temperature obtained using switching spectroscopy PFM in 100–200 places on the surface for each loop. A step feature around zero-bias is an experimental artifact. (b) Statistical distribution of nucleation bias shown as a Gaussian fit to the measured histograms. The nucleation bias for each local loop was measured as at 3% change of the total piezoresponse signal using a 9-parameter phenomenological fit to the experimental loop. (c) Temperature dependence of the nucleation bias (NNB for negative, PNB for positive) and the width of the distributions from (a) and (b), respectively.

Figure 3

Measured and calculated temperature dependence of the nucleation bias. The y-axis is a nucleation bias normalized to the room temperature values. (a) Comparison of experiment with rigid model; (b) Comparison of experiment with phase-field calculations and the analytical LGD model (see Supplementary information [21]). The values of the nucleation bias obtained from phase-field modeling of local ferroelectric switching on ${\mathrm{BiFeO}}_3(100)$ using a Lorentzian distribution of electric field strength on the surface with a characteristic width of 25 nm. The numerical parameters for the LGD-based values ($T_c=974\mathrm{K}$ and $U_0=-0.0077\mathrm{V}/\mathrm{K}$) were obtained by fitting to phase-field data.

Figure 4

Statistical correlation between positive and negative nucleation bias measured on 200 nm ${\mathrm{BiFeO}}_3$ film in vacuum and ambient environment. (a), (b) 2D-histograms of the nucleation bias values. (c), (d) 2D-Gaussian fits to the histograms in (a), (b), respectively.