Effect Of The Magnetoelectric Coupling On Magnetic Ferroelectrics

Magnetic ferroelectrics are compounds in which the ferroelectric (or antiferroelectric) and ferromagnetic (or antiferromagnetic) orders coexist simultaneously in a certain temperature range. The coexistence of the two order parameters may result in the inherent magnetoelectric (ME) effect. In detail, the ferroelectric polarization may change the magnetic property by redistributing the spin order, correspondingly, the fluctuation of the spin order may induce the dielectric anomaly or the ferroelectric relaxation through the magnetostrictive effect or electron-phonon interaction. The dielectric anomaly at the magnetic transition temperature observed in experiment is indicative of the inherent magnetoelectric coupling in magnetic ferroelectrics. At present, the magnetoelectric effect mainly exists in perovskite manganites (RMnO₃), BiFeO₃, and EuTiO₃. Therefore, the investigation of magnetoelectric properties in magnetic ferroelectrics and the coupling between ferroelectric and magnetic order parameters can make us forecast the new and meaningful characters in magnetic ferroelectrics about their dielectric and magnetic properties. For instance, making use of the supplement of magnetic (ferroelectric) phase transition or the external magnetic (electric) field can alter the ferroelectric (magnetic) properties in magnetic ferroelectrics. A number of device applications have been suggested for magnetic ferroelectrics, including non-volatile memory materials, gate ferroelectrics in field-effect-transistors and magnetoresistance.In this thesis, we have done the following work about magnetoelectric effect in magnetic ferroelectrics:1. Effect of the quadratic magnetoelectric coupling and Dzyaloshinski-Moriya (DM) interaction on domain walls in hexagonal manganites.In general, the magnetoelectric coupling between ferroelectric order parameter and magnetic order parameter takes place when the magnetic Neel temperature (Tn) is close to the ferroelectric Curie temperature (T_fe). Although in hexagonal manganites (RMnO₃), the magnetic Neel temperature (T_n) is much smaller than the ferroelectric Curie temperature (T_fe), there are a small but distinct dielectric anomaly at the Neel temperature (T_N) and a coupling between ferroelectric domain wall and antiferromagnetic domain wall. It suggests that there exists a magnetoelectric coupling. Taking account of the effect of the quadratic...