Influence of Multi-Body and Non-Nearest Interactions on the Shape of Hysteresis Loop and Domain Patterns

Abstract

The shape of hysteresis loop as well as domain pattern of ferroelectric during polarization reversal process has been simulated using Monte Carlo method on Ising model. Apart from the nearest-neighboring exchange interaction in the Ising model, we take into the contributions of the third-neighboring interactions and the four-body couplings. The simulation is carried out on a two-dimension square 200 × 200 lattice with Metropolis sampling. A sinusoidal electric field is applied to reverse the polarization to get the hysteresis loop and domain patterns. At low temperature, the hysteresis loop shows a typical ferroelectric feature. When the temperature increases, pinched hysteresis loops have been obtained. By checking the domain patterns during the reversal process, we found that the domain pattern is firstly switched from a ferroelectric state into a mixed ferroelectric and antiferroelectric states, then to the ferroelectric phase at last. The interesting point in this model is that there is no conventional negative interaction in the Hamiltonian, but a combination of positive non-nearest-neighboring coupling and multi-body coupling. Also this kind of hysteresis loop is quite similar to that observed in sodium bismuth titanate systems experimentally.