Study On The First Principle Of Single - Phase Multi - Iron Body CaMn <7> /

In recent years, with the development of computer technology, first-principles calculations have became an important tool for the investigation of multiferroic materials. In this paper, the crystal and electronic structure, lattice vibrations and spontaneous polarization of the single phase multiferroic material CaMn7O12 are calculated by the first-principles calculation method based on density functional theory.Firstly, we studied the electronic structures of the two inventing magnetic structures, including ferromagnetic order (FM)、ferrimagnetic order (AFMr) and the real magnetic structure (AFMI) of CaMn7O12. The results indicate that there are obvious spin polarization phenomenon, have semi-metallic properties, and the orbital hybridization of the Mn-3d and O-2p also exists in the FM structure. The AFMr structure changes from metallic to an indirect band gap insulator with a gap of 0.4 eV for U=3 eV. Both the Mn-3d and O-2p states make contributions to the top of the valence band and the bottom of the conduction band while the Mn ions have the major contribution. With the increasing of U, we find that the Coulomb repulsion between electrons is enhanced and the splitting of the bandgap becomes larger. The AFMI structure is insulating showing narrow-bandwidth effects as indicated by the electronic structure. The gap is 0.43 eV determined by Mn and O at the Fermi surface. In addition, we also find the p-d hybridization.Then we calculated the Brillouin zone center phonon for the AFMr (U=0,3,5 eV) and FM (U=3 eV) structures. There is no imaginary frequency mode, which indicates the absence of soft-mode effect for two inventing magnetic structures. In the AFMr structure, the frequencies of phonons except three Raman modes (one Ag mode and two Eg modes) increase with the increasing of U. This indicates that the phonons-harden have happened in this structure. For U=3, the IR-active phonon frequencies in the FM and AFMr is sensitive to the magnetic structure, which displays the spin-phonon coupling phenomenon. We also analyze the intrinsic displacements of phonon frequencies with the IR and Raman active.02 ions have large contribution to Raman-active phonon frequency. For the IR-active phonon frequency, O ions have largest contribution, while Mn ions also have little contribution. In addition, there is spin-lattice coupling effect in this structure.Finally, we use the modern polarization theory (Berry Phase) method to calculate the spontaneous polarization in the AFMI structure (148), and the investigation of magnetic structure using the AFMr as the reference structure with or without the spin-orbital coupling interaction. The calculation results agree well with the experimental data. Then we use the Born effective charges to calculate the contribution of each ion to the spontaneous polarization. Detailed analysis shows that the origin of the spontaneous polarization can be attribute to the displacements of the Mn and O ions, which are pushed by the nonlinear Propeller-type magnetic order. Among them, the displacements of 02 ions in the xy plane play a major role in the spontaneous polarization in the z-axis direction. The displacements of the Mnl and Mn2 ions in the z-axis directions also have contrition to it. There are spin-orbital coupling interactions, but the contribution to the polarization is very small.