The Thoery Of Transverse Ising Model Of Ferroelectric Superlattice And The Simulant Calculation

In this thesis, we make use of the transverse Ising model (abbr. TIM) to investigate the relations between the ferroelectric superlattice period and polarization, Curie temperature & dielectric susceptibility in the ferroelectric superlattice by considering the four-body interaction term and coupling effect in the interface. And we draw a set of conclusions that the ferroelectric superlattice can have a notable size-driven effect on polarization, Curie temperature & dielectric susceptibility when ferroelectric superlattice period changing. The Curie temperature of ferroelectric superlattice will increase when two kinds of materials form the ferroelectric superlattice. The main conclusions obtained from above-mentioned work with innovation significance are as follows: 1. By utilizing the transverse Ising model and getting the form of the Hamiltonian considering the interaction on the interface, a theoretic TIM model of the ferroelectric superlattice was established. And a four-body interaction term and coupling effect in the nearest-neighbor pseudospin must be taken into consideration in the transverse Ising model. 2. We get the relations between macro-thermodynamics and microcosmic parameter. Minimizing the free energy F, we obtain the two coupled Euler-Lagrange equations. With boundary conditions, numerical calculations can be carried out by using a finite-difference scheme such as four-order Runge-Kutta method or Euler evaluating-revise method. We simulate the relation between the ferroelectric superlattice period and polarization, Curie temperature & dielectric susceptibility. 3. It was found that with the increment of both thickness of superlattice of BaTiO₃/SrTiO₃, the polarization intensity in BaTiO₃ part is always larger than that in SrTiO₃ part. It is clear that the component of BaTiO₃ is the main contribution of polarization in total BaTiO3/SrTiO3 superlattice. 4. It was found that with the increment of both thickness of superlattice of BaTiO3/SrTiO3, the two peaks of dielectric susceptibility were observed in the dielectric spectra of BaTiO3/SrTiO3 ferroelectric superlattice. This indicates that the different components of ferroelectric superlattice have the different critical size. 5. On the base of theoretic TIM model, it was considered for the long-range coupling interaction in ferroelectric superlattice. And by comparing the different Curie temperature result, it was found that the correct exponent decaying factor is from 3 to 6. 6. Considering Debye relaxation and Maxwell-Wagner effect, the dielectric mechanism on different period of BTO/LAO superlattice was studied. It was found the non-Debye relaxation have an important effect on the dielectric susceptibility of BTO/LAO superlattice. 7. It was simulated for the dielectric susceptibility of different structures of stack periodicitie of BTO/LAO superlattice. It was found that from a certain frequency range, the dielectric constant of 16?/16? of BTO/LAO superlattice is the largest, the 8?/8? is the next largest. As for BTO/LAO superlattice associated with 8?/8?～16? /16? layer(2⁴ crystal cell thickness layer),their stack periodicities may not only ensure to provide enough bondage charge for participating in the relation process , but also avoid permittivity loss caused by the interface dispersion. This makes them have a good permittivity performance. However when thickness of superlattice increases more, Maxwell-Wagner effect come to weakness, bondage charge is mainly dispersed by crystal cell .So the dielectric susceptibility makes approaches to bulk material.