On the depolarization energy of ferroelectrics

This paper examines the depolarization energy of ferroelectrics arising from the polarization distribution, which is nonlocal and involves long range interaction between dipoles. By introducing new testing fields, the depolarization energy can be reformulated into variational frameworks where only local variables are involved, from which the upper and lower bounds on the depolarization energy can be established, and more efficient numerical algorithm can be developed. The concept has been demonstrated in two-dimensional and one-dimensional ferroelectrics where the variational principles are considerably simplified. Ferroelectrics with ellipsoidal symmetry are also discussed and explicit expressions of the depolarization energy are obtained.