The Study Of Magnetism In Frustrated And Multiferromagnetic Materials RMnO₃（R=Rare Earth）

The multiferroic material has been subject to intensive studies in the field of thecondensed matter physics and structural chemistry due to its important role in themultifunction materials and small-sized electronic devices. The materials RMnO3(R=Dy, Sm, Eu) studied belong to the rare earth manganate compound, and have differentstable lattice structures such as cubic, orthorhombic and hexagonal phase dependingon their preparation conditions. Most studies of RMnO3currently focus on the orbitalelectron distribution of the3d-transition metal Mn, the spiral frustration of rare earthionic, and the magnetic ordering under the condition of strong fields. In constrast,theoretical studies are rare and many issues still remain unresolved.In this thesis the first principles method based on the density functional theorycombined with the projector augmented wave (PAW) are used to investigate theelectronic structure, the density of states and magnetic ordering of RMnO3multiferroic materials. The results show that all the materials studied exhibit theindirect energy gap and antiferromagnetism, and the orthorhombic DyMnO3andSmMnO3have the A-type antiferromagnetic order, and the orthorhombic EuMnO3hasthe G-type antiferromangetic order. The calculated results from the Monte Carlomethod show that Mn magnetic order depends on the next-nearest neighborsuperexchange interactions between Mn atoms as well as the nearest neighborsuperexchange interactions. And the moments and electronic structure of theexpending material DyMn2O5are also studied.In addition, the lattice distortion in these rare-earth manganites can be attributedto the orbital hybridization between Mn-3d and O-2p electrons, which is agreementwith the previous studies. The rare earth ions also have an effect on the degree of thelattice distortion, and the strength of magnetism for different materials has anincreasing tendency with the magnetism of the rare earth ions.