Recently, many studies interested in ferroelectricity which stacked perovskite structure in two layers artificially and substituted one another atoms in A-site. The ferroelectrics have some characteristics that without external electric fields, if we gave some electric fields with spontaneous polarization materials, it can change their direction of polarization. Most of the ferroelectric materials are known for having band-gaps that penetrate lights which have energies over the range of visible ray. Furthermore, if the material that can penetrate visible light takes a doping, it is able to be a transparent conducting oxide (TCO). The research of transparent conducting oxide is required by increasing industrial utilization such as touch screen of smart phone, flat panel display, and solar cell.
Based on these social needs and interests, in the first section, we studied structure stacked artificially with the formula of AA'Sn2O6 (A, A' = Ba, Sr, Ca). The tilting effect in AA'Sn2O6 (A, A'= Ba, Sr, Ca) of [001], [110], and [111] cation ordering is studied by using first principles calculations. In AA'Sn2O6 superlattices, the structural phase transition is characterized two octahedral tilting modes. We performed the analysis of tilting mode (a-a-c0 and a0a0c+) in fully optimized phase. In the case of [001] and [111] ordered superlattices, the property of hybrid improper ferroelectric (HIF) property is also analyzed. The layer-by-layer analysis of spontaneous polarization is represented for [001] and [111] ordered superlattices in low-symmetry phases.
We explore the studies to using La, Pr, Nd atom in the A-site of the AGaO₃. Therefore the formula is AA'Ga2O6 (A, A' = La, Pr, Nd) and here also studied the effect of octahedral tilting in the array of [001], [110], and [111] cation ordered superlattices. The similar tendency of octahedral tilting generated in high- and low-symmetry structure to AA'Sn2O6. We found that the coupling of octahedral tilting modes were induced polar property, and produces electric polarizations. So we have explained that the value of spontaneous polarization along the [001] and [111] ordering by analyzing layer-by-layer as well.
Lastly, derived perovskite, fresnoite with the formula of Ba2TiSi2O8 (BTS) and Sr2TiSi2O8 (STS) are comparably studied. In the ground state, we found the fact that both BTS and STS compounds have a low-symmetry phase of P4bm as a polar structure, and there occurs fictitious phase transitions. From the results, we found that phase transitions well related the changes of bond length (Ti-O and Si-O). The structural phase transition will scrutinize in this paper by comparing the bond length to apart between the nonpolar and polar phases. Detaching the polyhedrons significant contributes to the size of spontaneous polarization in polar phase of BTS and STS. BTS and STS is SHG material, so we show the second harmonic generation susceptibilities. Our quantitative studies can explore to full understandings of atomic mechanism in the polar and other nonlinear optical material.