Structures and velocities of noisy ferroelectric domain walls

Ferroelectric domain wall motion is fundamental to the switching properties of ferroelectric devices and is influenced by a wide range of factors including spatial disorder within the material and thermal noise. We build a Landau-Ginzburg-Devonshire (LGD) model of ${180}^{\ensuremath{\circ}}$ ferroelectric domain wall motion that explicitly takes into account the presence of both spatial disorder and thermal noise. We demonstrate both creep flow and linear flow regimes of the domain wall dynamics by solving the LGD equations in a Galilean frame moving with the wall velocity $v$. Thermal noise plays a key role in the wall depinning process at small fields $E$. We study the scaling of the velocity $v$ with the applied DC electric field $E$ and show that noise and spatial disorder strongly affect domain wall velocities. We also show that domain walls develop a local, metastable paraelectric region and widen significantly in the presence of thermal noise in materials with ``multiwell'' potentials, representative of ferroelectrics at temperatures $T$ just below a first-order phase transition (Curie) temperature ${T}_{c}$. These calculations point to the potential of noise and disorder to become control factors for the switching properties of ferroelectric materials, for example for advancement of microelectronic applications.