ABSTRACT Multiferroics are novel classes of materials that exhibit cross-coupling of mutually excluding phenomena, i.e. magnetism and ferroelectricity. In recent years, the coexistence of ferroelectricity and magnetic orderings has become a hot issue and drawn considerable attentions due to the promising applications to these days technology and the fundamental science involved in these classes of materials. The microscopic origins of magnetism and ferroelectricity differ fundamentally, while the real mechanism of ferroelectricity is still under debate. In the present work, we have started from a simple method Heisengerg hamiltonian and an interaction term resulting from electric field coupling with the magnetic spins with anisotropic limit, demonstrated that magnetization can be manipulated by electric field and anisotropic field in agreement with results experimentally observed. In the multiferroic thin film system the magnetic field tends to play a role in stabilizing the spins in preferred orientations and induces a coupling of magnetism and ferroelectricity that opens a route to switch magnetization with electric polarazation and vice-versa.
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