| Quantum paraelectrics are quite different from the normal ferroelectrics as far as the dielectric susceptibility is concerned. The susceptibility increases with decreasing temperature, following the Curie-Weiss law, which indicates the appearance of the ferroelectric ordering. But at low temperatures it deviates from the Curie-Weiss behavior and saturates at even lower temperatures, which can be attributed to the effect of quantum fluctuation that stabilizes the paraelectric phase and suppresses the ferroelectric phase transition entirely. The crystal structure of the quantum paraelectrics is mainly perovskite type, similar to most of the ferroelectrics, and external factors, e.g. impurity doping, may induce ferroelectric phase. Some cubic perovskites are good cases in point such as SrTiO3 and KTaO3. Experimental results show that when Ba2+ and Li+ are doped into the above materials respectively and at the same time the impurity content is higher than their critical concentration, the impurity induced ferroelectric phase transition occurs. EuTiO3 is another special quantum paraelectric. It is at the same time a type-G antiferromagnet. So we call it quantum paraelectric-antiferromagnet. Experimental data shows that there exists coupling between the magnetism and dielectric properties, which leads to the dielectric anomaly near its Neel temperature. A great deal of studies have been proceeded on coupling between the magnetism and dielectric properties, which actually exists in the ferroelectromagnets. The ferroelectromagnets, in which ferroelectric ordering and magnetic spin ordering coexist spontaneously at low temperature, have been the object of intensive theoretical and experimental studies from the 60-70's last century for its connection with the finding out this kind of material and theirs some special properties of physics own to magnetoelectric coupling. By magnetoelectric coupling, the application of an electric field or ferroelectric polarization can change one or more of the parameters governing the magnetic behavior of the system. Correspondingly, being possible magnetostrictive effect or electron-phonon interaction, the fluctuation of spin ordering maylead to a dielectric anomaly and ferroelectric relaxation.There exists magnetoelectric effects in two type of material, one of them is spin-order material called magnetoelectrics that may exhibits an induced linear magnetoelectric effect by external field. This effect is named as the electrically induced magnetoelectric effect (ME) E or magnetically induced magnetoelectric effect (ME) H A ferroelectromagnet, however, differs from the magnetoelectrics in that it shows spontaneous magnetoelectric effects in addition to the (ME) E, H effects induced by external fields. They are caused by the coexistence in the crystal of spontaneous ferroelectric and magnetic moments. An anomalies in the dielectric constants and loss tangent have been observed experimentally in the ferroelectromagnet near the antiferromagnetic transition temperature, indicative of a coupling between the ferroelectric and magnetic ordering, but the nature of the mechanism of magnetoelectric coupling and the form of interaction is still an important and debated issue. Although ferroelectric ordering does not appear within the whole temperature range in EuTiO3, coupling of a certain form between the ordering parameters in electrical and magnetic subsystems causes the dielectric anomaly near its Neel temperature.In this paper, we first investigate the impurity effect (Ba2+) on the dielectric and phase transition properties in SrTiO3 within the framework of the transverse-field Ising model (TIM). Then a possible coupling mechanism between the magnetism and dielectric properties in EuTiO3 is discussed and the magnetic influence on the frequency of the soft-phonon mode is investigated via the Heisenberg model, soft-mode theory under the mean field approximation, the second quantization theory and the perturbation theory. And we proceed further investigation on Eu1-xBaxTiO3 of...
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