Physics

Dipole

Domain wall (magnetism)

Magnetization

Mathematics

Domain (mathematical analysis)

Magnetic field

Periodic boundary conditions

Mathematical analysis

Boundary value problem

Acoustics

Materials science

Perpendicular

Geometry

Condensed matter physics

Lattice (music)

Quantum mechanics

Electric field

Physical Review Materials

Ferroelastic domains generate polarity near domain walls via the flexoelectric effect. Applied electric fields change the wall dipoles and generate additional dipoles in the bulk. Molecular dynamics simulations show that the thickness of domain walls changes when an electric field is applied to the sample. Fields parallel to the walls lead to expansion of the wall thickness while fields perpendicular to the wall lead to shrinking of the wall thickness. The interactions between polar domain walls expand over more than 45 unit cells, the resulting forces change the wall-wall distances if pinning effects are small. The interaction increases nonlinearly with decreasing wall-wall distances favoring equal wall distances as the consequence of energy minimization under the constraints of a constant number of domain walls. Even for small groups of three walls the sequence of walls is locally periodic: assemblies of three parallel domain walls arrange themselves so that the intermediate domain wall is located exactly in the middle between the two outer walls. The driving force is appreciable if the distance between the outer domain walls is below approximately 30 lattice units. Pairs of domain walls often form needle domains where the shaft of the needle is ca. 3 lattice units wide. The movement of needle domains under applied electric field was simulated. The advancement and retraction of needles is larger in finite samples with charge-free surfaces than under periodic boundary conditions in the bulk. The needle tip moves even more freely when the sample surface is charged.

Electrically driven ferroelastic domain walls, domain wall interactions, and moving needle domains