The Power of Feedback: From Dielectric to Ferroelectric Systems
H. Kliem and A. Leschhorn
Institute of Electrical Engineering Physics, Saarland University, Germany
Abstract- Dielectric properties can be described using a double well potential model as introduced in dielectric theory by H. Fröhlich. Charges and/or dipoles fluctuate thermally activated between two directions. Their transition probabilities depend on the local field.
For non-interacting double well systems we find the Debye response of relaxation. With increasing dipole density and/or increasing dipole moments an interaction between the dipoles becomes significant. The mutual dipolar fields alter the local fields at the dipoles and change their transition probabilities. We focused on two approximations for this interaction.
Following the ideas of P. Weiss for a macroscopic approach, the mean local field is influenced by the polarization itself. Using this average local field within the transition probabilities of the dipoles we get a feedback loop for the polarization resulting in a second order ferroelectric phase transition. Considering also the piezoeffect we get a first order transition. Furthermore we compute: the hysteresis loops of the polarization, for the first order transition the double hysteresis loops close to the Curie temperature Tc, and the susceptibility for different temperatures and fields. An intrinsic asymmetry of the double well potentials can change the ferroelectric behavior to a relaxor like behavior.
In the microscopic approach we calculate numerically the local field at each dipole. In systems between parallel electrodes the local field is the superposition of the applied field and the sum over the fields of all other charges and dipoles and their images. Here the feedback enters with the sum over all dipole fields into the computation. The orientations of permanent dipoles are calculated using a dynamic Monte Carlo scheme. Simultaneously the induced dipoles in the sample are considered and computed iteratively. We compute domains and nonswitchable dead layers at electrodes and defects. The switching process is calculated to depend at low fields on the formation of a reverted stable nucleus and in high fields on the domain wall propagation speed.
Keywords-Dielectrics, ferroelectrics, relaxor materials, modeling, local electric field