The thickness effect in ferroelectric thin films has been theoretically investigated using the LandauKhalatnikov theory. Ferroelectric properties such as the hysteresis loop, and its associated coercive field and the remanent polarization of various film thicknesses have been numerically simulated. In this simulation, the thin film was modeled by the stacking of layers, each of which has unique parameters for the Landau free energy. Due to the interfacial effects near the electrodes, the parameters for the surface layers are different from those for the bulk. The simulated result shows that the coercive field decreases while the remanent polarization increases with thickness. Both of these trends qualitatively agree with experiments.
The presence of oxygen vacancies is considered to be the cause of various phenomena in ferroelectric thin films. In this work, the role of oxygen vacancies is theoretically modeled. Various properties are numerically simulated using the two-dimensional Ising model. In the presence of an oxygen vacancy in a perovskite cell, the octahedral cage formed by oxygen ions is distorted so that the potential energy profile for the displacement of the titanium ion becomes asymmetric. It requires additional energy to move from the lower minimum position to the higher one. Moreover, space charges are also developed by trapping charge carriers into these vacancies. The combination of the pinning effect induced by the distorted octahedral cage and the screening of the electric field in the presence of space charges results in phenomena such as fatigue and imprint.
The role of oxygen vacancy in lead-titanate-zirconate ferroelectric thin film has been numerically simulated using the two-dimensional four-state Potts model. On one hand, the presence of an oxygen vacancy in a perovskite cell strongly influences the displacement of the Ti 4+ ion. Hence the vacancy-dipole coupling must be considered in the switching mechanism. On the other hand, a space charge layer is established by the inhomogeneous distribution of oxygen vacancies through trapping charge carriers. Consequently, the thickness dependence of the coercive field and remanent polarization are reproduced in the presence of this oxygen vacancy distribution. Frequency, temperature, and driving voltage-dependent polarization fatigue behaviors are also simulated.
To understand the collinear-magnetism-driven ferroelectricity in the frustrated Ising spin chain, the fascinating magnetoelectric behavior is investigated by using Monte Carlo simulation based on one dimensional elastic Ising model. Our simulation quantitatively reproduces the experimental results of the complicated electric and magnetic behaviors as functions of temperature observed in Ca 3 CoMnO 6 compound ͓Phys. Rev. Lett. 100, 047601 ͑2008͔͒. Moreover, the short-ranged up-up-down-down magnetic ordering is confirmed to be the origin of electric polarization, and the curves of energy components dependent on temperature provide a reasonable explanation for the unconventional magnetoelectric phase transition revealed in the Ising chain magnet.
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