Address:School of Physical Science and Technology,Lanzhou UniversityMultiferroics, defined for those multifunctional materials in which two or more kinds of fundamental ferroicities coexist(such as ferroelectricity, ferromagnetism and ferroelas-ticity), have become one of the hottest topics of materials science and condensed matter physics in recent years.The significant cross-coupling effects in the newly found materials have invigorated research in multiferroics as they offer a new route toward fundamental understanding of how the spin and lattice degrees of freedom interact to produce macro-scopic phenomena.Furthermore, the emergence of multiple functional properties in those materials has stimulated the application in next generations of novel devices in which polarization can be controlled by a magnetic field or vice versa.In some multiferroics, the ferroelectricity is induced by a fundamental new mechanism, by which magnetic or-ders with broken symmetry result in ferroelectric distortion.This dissertation focuses on the study of the magnetoelectric phase transition by the control of non-magnetic field in multiferroics.In the first chapter, we make a brief overview of the research progress of magne-toelectric effects and multiferroics.In chapter 2, we study three major mechanisms of ferroelectricity of spin origin.In chapter 3, we describe the J1 - J2 model and Monte Carlo simulations which the method we used to calculate is. In chapter 4,we investigate that the thermodynamic properties of Multiferroic Chains are affected by thermal fluctuations and by an electric field theoretically. Furthermore,we extend our investigation of the static and dynamical magnetoelectric effects to a two-dimensional spin structure. |