| Multiferroic materials are defined as a kind of system, in which ferromagnetic ordering and ferroelectric ordering or ferroelastic ordering coexist spontaneously below a certain temperature. In recent years, because of some new functions such as magnetoelectric effect, magnetodielectric phenomena induced by strong coupling between two order parameters, implicate coupling mechanisms, as well as their wide and potential applications, multiferroic materials attract more and more attentions both in academic and engineering societies. In this thesis, using the first-principle based on density functional theory with noncollinear magnetic structure calculations and combining Landau-Devonshire thermody- namic theory with magnetostrictive thoery, we investigated in detail the magnetoelectric coupling mechanism of single phase multiferroic material YMnO3, and magnetoelectric effects of the 1-3 type nanocomposite thin films and epitaxial quasi 2-2 type hetero- structures including the magnetic field induced ferroelectric polarization (MIP), the electric field induced magnetization (EIP) reveral and magnetolectric enhancement and so on, respectively. The main results of our study are listed as follows:1.The first-principles study on magnetoelectric couplings of hexagonal perovskite manganite YMnO3Based on the collinear magnetic structure of the first-principles calculations, the comparatively overall research has been carried on the magnetoelectric coupling effects of hexagonal perovskite YMnO3, however, the results are obviously inconsistent with the X-ray diffraction ones. In first section of this thesis, we applied firstly and performed fully the noncollinear magnetic structure calculations of the first-principles based on density functional theory with generalied gradient approximation for hexagonal perovskite YMnO3. By comparing the cases calculated in different magnetic configurations, we investigated systematically the effects of the frustrated triangular spin of Mn3+ ions, spin-orbit coupling on the energy gap, magnetic moments, electronic structure, orbit hybridization and Born effective charges of YMnO3. Our conclusion provides a first-principle profound understanding of multiferroic origin in YMnO3, and the calculated results are in good agreement with the related experimental ones. We are surprised that, due to triangular spin frustration and spin-orbit coupling, the total energy of the supercell is reduced to the lowest, the energy gap is opened to the largest, the every ionic position and magnetic moment of Mn ions are most close to the experimental values. The interaction between the Y 4d and O(3,4) 2p orbits is obviusly increased, while ones between the Mn 3d and O(1,2) 2p states relatively decreased. The large anomalies in Born effective charges on off-centering Y and O ions manifest that the Y 4d0-ness with rehybridization is the driving force for the ferroeleectric of the YMnO3 along the c direction. We have also estimated the spin exchange integrals values of Mn3+ ions by mapping the calculated total energies of different spins configurations onto the Heisenberg spin model. It reveals a rather strong antiferromagnetic coupling exists between two nearest neighbor Mn ions spins, which leads to the spins frustration with 2Ï€/3 angles between spins in plane triangular lattice, and a weaker antiferromagnetic coupling between nearest neighbor interplane. In addition, considering the strong electronic correction interaction, we also found that because of triangular spin frustration, the distributions of states densities are more localized below the Fermi level, the hybridization between Mn 3d and O 2p states is declined, the band-gap of ground state becomes wider, and the magnetic moment of Mn3+ ion increases.2.Magnetoelectric effects in 1-3 type multiferroic nanocomposite thin fimsAlthough considerable research have been done through experimental and theoretical approaches on the MIP and the EIM in 1-3 type multiferroic nanocomposite thin fims, the polarization induced by appling different direction magnetic fields, the EIP reveral and so on have not been explained systematically in theory. In second section of this thesis, we investigated them by combining the Landau-Devonshire thermodynamic theory with magnetostrictive theory for ferroelectric and ferromagnetic phases, respectively. We divided each of strains from film/substrate and FE/FM interfaces into lattice mismatch strain and magnetostrictive strain, and considered film thickness dependence of epitaxial strains due to relaxation by misfit dislocation during film deposition as well as the coefficients modification of piezoelectric films due to interface constraint to study static dielectric, piezoelectric properties and MIP of thin films. Particularly, the MIP has also been mainly studied by appling the transversal and longitudinal external magnetic fields to the magnetostrictive phase, the results indicated the MIP is strong dependent on anisotropy magnetostriction of thin films and the interface coupling between two phases. On the other hands, in order to investigate the EIM reversal and the correlation between magnetization and polarization reversal, we applied Landau-Devonshire thermodynamic theory to ferroelectric and magnetic phases. After considering the mechanical boundary condition of the films/substrate and introducing the lattice compatible condition combined with the mechanical equation of equilibrium state at interface of two phases, we renormalized the dielectric and magnetic coefficients twice and obtained firstly quasi-intrinsic magneto- electric coupling in Landau free energy function of this multiferroic system. By comparing the electric hysteresis loops and EIM of thin films with different thickness and different temperature, we found that an applied electric field can result in the reversal of magnetization in step with switching of the electric polarization due to the out-of-plane elastic coupling between the interfaces of FE and FM phases. All those can excellently explained EIM reversal deeds obversed in the experiments. At the same time, we also find qualitatively that dislocation induced linear defect leads a large residual stress in thin films. Although this is beneficial to spontaneous polarization and magnetization of thin films, the MIP is depressed, that is, the existence of defect will depress the enhancement of the ME coupling in thin fims.3.Magnetoelectric effects in epitaxial quasi 2-2 type heterostructure thin filmsThe properties of epitaxial heterostructure thin films are different from those of bulk, which mainly depend on the stress states in thin films. Due to the interface coupling of films/substrate, the applied magnetic field not only induces the strain of substrate but also controlls the dielectric, piezoelectric and polarization properties of thin films by adjusting the stress (strain). In this section, we introduced the effective residual strain and interface scale factor and combined the modified constitutive equations with the Landau- Ginsberg-Devonshine thermodynamic theory to investigate the MIP of the quasi 2-2 type heterostructure thin films. We analyzed the total electric polarization and MIP of this thin films by self-consistent calculation for polarization, piezoelectric and dielectric coefficients. The calculated results show that transverse magnetic-field-induced electric polarization of the multiferroic films increases nonlinearly with increasing external magnetic field. When the magnetostriction reaches its saturation at the higher magnetic field, the MIP begins to approach saturation, indicating large MIP could be produced in ferroelectric film due to a gigantic magnetically induced in-plane constraint. Moreover, because the magnetostriction of magnetic phase reaches a maximum at the magnetic transition temperature, the MIP will also get to a maximum value, further showing that the ME coupling is related to the magnetostriction. Next, we calculated the temperature dependence of magnetoelectric output voltage when the magnetostraction of magnetic phase was saturated. We chose the static, alternative magnetic field and the thickness of thin films comparable to experimental values and assumed the interface scale factor is 1, we found that the ME effect peaks at the ferromagnetic transition temperature of the manganite. Comparison with experimental data of multilayered samples reveals a good interface coupling of the films/substrate and a great magnetostriction of magnetic phase result in a large ME effect in this type of thin films.
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