| Magnetoelectric effect and multiferroic materials have received great interest for their potential applications in new storage devices and spintronics. Magnetoelectric effect (ME) is defined as the coupling between the electric and magnetic fields in matter. This coupling allows the electric control of magnetic polarization and the magnetic control of electric polarization. In single phase materials, the upper limit of linear magnetoelectric effect is the product of dielectric constant and magnetic susceptibility. Multiferroics, which combine ferroelectricity and magnetism in a single phase, is the most promising single-phase magnetoelectric materials. However, in conventional materials, ferromagnetism and ferroelectricity are mutually exclusive. In conventional perovskite ferroectrics, the occurrence of ferroelectric distortion requires empty d orbitals of ions at B site while magnetic moments come from d electrons. This contradiction leads to the scarcity of multiferroics.Recently, two bismuth-based perovskites, BiFeO3and BiMnO3are found to be multiferroic. The ferroelectricy of these bismuth-based perovskites is induced by the lone pair of Bi:6s2, while the magnetism originates from3d electrons of transition metals. However, none of the two are ideal multiferroics. BiFeO3is antiferromagnetic and the Curie temperature of BiMnO3is very low, which limit their practical applications. To achieve the coexistence of room temperature ferromagnetism and ferroelectricity, some researchers doped transition metals into ferroelectricity. They indeed found room temperature ferromagnetism in these doped ferroelectrics, but the ferroelectricity was broken by the alien atoms.Another route to magnetoelectric coupling is the ferroelectric/ferromagnetic heterostructure. From symmetry consideration, the interface between ferroelectric and ferromagnetic is time-reversal symmetry broken and space-reversal symmetry broken simultaneously, which is the prerequisite of magnetoelectric effect. At the interface, the transition metal ions of the ferromagnet form bonds with the ions of ferroelectric. When the ferroelectric polarization is switched by external electric field, the atomic displacements and bondings at the interface are changed, altering the magnetic moments. A typical ferroelectric/ferromagnetic heterostructure is BaTiO3/Fe, which exhibit0.03μB/Fe change between two electric polarization states. However, in these ferroelectric/ferromagnetic heterostructures, the electric polarization could only slightly change the value of magnetic moments, while the direction of magnetization or spin order have never been changed.First-principles calculation has played an important part in the research of magnetoelectric effect and multiferroics, including the elucidation of magnetic structure and ferroelectric origin of BiFeO3and the prediction of magnetoelectric coupling in BaTiO3/Fe heterostructure. In this dissertation, we use first-principles calculation to explore the magnetization of transitional metal doped ferroelectric BiAlO3and the magnetoelectric effect at the BiFeO3/Fe heterostructure.As one of the bismuth-based perovskite ferroelectrics, the ferroelectricity of BiAlO3is also induced by the lone pair of Bi:6s2. As the B site is the non-magnetic Al ion, we introduce transition metal ions to substitute some of Al ions and expect ferromagnetism can occur. We theoretically investigated the electronic structures and magnetic properties of transition-metal (Cr, Mn and Fe) doped BiAlO3and found that the manganese ions can make the ferroelectric material room-temperature ferromagnetic while keep it insulating. The ferromagnetic coupling is further confirmed by applying DFT+U method and explained by super-exchange interaction between two Mn ions. The dopants tend to form ferromagnetic cluster structure, which will be a guarantee for macroscopical ferromagnetism for the materials. The other transition metals (Cr and Fe) cannot induce ferromagnetism.As the magnetoelectric coupling of the existing ferroelectric/ferromagnetic heterostructure is very weak, we propose a multiferroic/ferromagnetic heterostructure to utilize the spin order coupling at the interface and the prototype is BiFeO3/Fe. Our electronic structure calculations suggest that the reorientation of ferroelectric polarization of BiFeO3can change the spin ordering of the Fe monolayer. When the direction of ferroelectric polarization points to the Fe monolayer, iron atoms are antiferromagnetically coupled, exhibit no net magnetic moments. When the polarization points to the opposite side, iron atoms are ferromagnetically coupled, and the magnetic moment per Fe ion is3.5μB. In this heterostructure, the electric polarization changes the spin order and induces robust magnetoelectric coupling effect.
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