| Multiferroic materials are of renewed interest not only for their fundamental scientific significance but also for their potential applications in data storage and spintronics. The general mesoscopic approaches for multiferroic materials, however, are still lacking because it is challenging to incorporate the traditional computation approaches with the coupling between ferroelectric and antiferromagnetic orderings, commonly existing in multiferroic materials. In this dissertation, we develop a framework of unconventional mesoscopic approaches to study a variety of heterogeneous multiferroic materials including ferromagnetic shape memory alloys (FSMA) and multiferroic bismuth ferrite (BiFeO3). Explicit closed-form expressions of magnetoelectric Green's functions for uniaxial multiferroic materials are first derived to determine the field distribution resulting from magnetoelectric coupling in multiferroics. An unconventional phase field method is then developed to investigate the magneto-elastic microstructure in FSMAs and its evolution under external magneto-mechanical loads. A continuum description at mesoscopic scale is developed for antiferromagnetic ordering, and is then incorporated into the unconventional phase field method to study the coupling among ferroelastic, ferroelectric, and antiferromagnetic orderings in BiFeO3. The mesoscopic model developed offers deep insight into the microstructural evolution and macroscopic properties of a wide range of multiferroic materials with magnetoelectric coupling. |
