\textit{In Situ} Studies of Domain Dynamics and Wall Pinning Using Scanning Transmission Electron Microscopy*

The mechanism of ferroelectric domain nucleation and growth is studied using in-situ Scanning Tunneling Microscopy (STM) -- Scanning Transmission Electron Microscopy (STEM). A 300 nm multiferroic BiFeO$_{3}$ thin film is grown on DyScO$_{3}$ and has a large density of 71$^{\circ}$ domain walls. A local electrical field is applied using a W tip inside the STEM. Domain formation can be detected from the strain contrast associated with the newly formed ferroelastic domain wall. A step-wise increase of probe bias reveals the critical voltage for the formation of a new domain as 800 mV. This critical domain nucleation bias is much lower than the value observed by Piezoresponse Force Microscopy, which is of the order of 2-5 V. Notably, it also depends on the sample thickness along the beam direction. Repeated switching experiments in the vicinity of a pre-existing 71 $^{\circ}$ domain wall reveal that the acute angle region between the domain wall and the surface is a preferential nucleation site. A strong asymmetry of domain wall pinning is observed during domain growth. The dependence of domain nucleation and growth kinetics on applied bias will also be discussed.