Thermal Conduction And Electromagnon Excitation In Rare-Earth Manganites

Multiferroics are compounds in which the ferroelectric (or antiferroelectric) and ferromagnetic (or antiferromagnetic) order or ferroelastic order coexist simultaneously in certain temperature range. The system with spiral ferromagnetic order is also included in recent study. The materials with both ferroelectric order and magnetic order structures have been extensively researched. Especially, rare-earth manganite RMnO₃ is a representative of this kind of the multiferroics. For R³⁺ cations with small ionic size, RMnO₃ oxides crystallize in hexagonal polytype structure (space group P63cm). For rare-earth cations with large ionic size, a peroviskite-type structure with orthorhombic symmetry (space group Pbnm) is stable. In the hexagonal phase, the gravity center of the positive and negative electrons deviate from each other and then a spontaneous ferroelectric behavior occurs, which coexists with magnetic order at low temperature and gives rise to the inherent magnetoelectric(ME) coupling effect. This effect is stronger in peroviskite-type manganites. In these compounds with spiral magnetic structure, the magnetic order also breaks inversion symmetry as well as time-reversal symmetry, as the change of the sign of all coordinates inverts the direction of the rotation of spins in the spiral. The presence of electric polarization is allowed by this symmetry and has been discovered in materials like TbMnO₃ and DyMnO₃. In adddition, from the view of technology, ME coupling plays a significant role in electric, magnetic and thermodynamic properties of multiferroics, and promises extensive technological applications in non-volatile memory materials, sensor, spintronics and so on. Consequently,the investigation of inherent ME coupling effect is an important fundamental task now, and rare-earth manganite is one of the candidates in application of ME coupling.In this thesis, we have done the following work about rare-earth manganites:1. Thermal transport in hexagonal rare-earth manganitesThe thermal transport in hexagonal rare-earth manganites has been studied experimentally. However, there are few theoretical works, especially in the effect of ME coupling on thermal conduction due to the complex lattice structure. In our work, we utilize the soft-mode theory and the mean-field theory based on Heisenberg model to investigate ME effect on thermal conductivity, and find that this effect is finally embodied on the modification of Debye temperature. Magnon-phonon resonant interaction is considered as one of the scattering mechanisms that correct relaxation time of phonon. We also find the optical phonon, which was always neglected in the previous study on thermal conduction, plays a key role in full description of heat transport in hexagonal rare-earth magnganites. Finally, we fit the temperature-dependence curve of thermal conductivity for YMnO₃. Our theoretical results are in good agreement with the experimental ones.2. Electromagnon excitations in RMnO₃In some peroviskite-type manganites, the spin reorientation brings about lattice reorientation and then an electric polarization appears, which indicates strong magnetoelectric coupling. Electric polarization also coupled with magnetic dynamically. The coupling between spin oscillations and lattice vibrations produces spin waves that interact with ac electric field,so the magnon is electric dipole active and named electromagnon. In our work, from the relation between static electric polarization and spin (P|-)∝(e|-)_i×((S|-)_i×(S|-)_j), we discuss the possible way of dynamical ME coupling, and obtain the coupling with select rule e‖b‖P which can explain electromagnon in RMnO₃ with ab spiral spin plane besides the well studied one with select rule e‖b⊥P. Furthermore, using second quantization method, we calculate spin wave dispersion relation in spiral phase and obtain the frequency of coupled mode or electromagnon by diagonalizing Hamiltonian with ME coupling. The origin of electromagnon in sinusoidal phase is also explored from a new viewpoint.