The Study Of The Ground State Properties Of The Frustrated Classical Heisenberg Moderl In One Dimensional With Nearest-Neighbor Biquadratic Exchange And Dyaloshinskil-Moriya Interaction

The main symbol of the history in the development of the humen beings is the material. For several decades,driving by the demands of developing technology,all the branches of new materials grew very fast and the breakthrough in searching for new materials never end. The material containing more then two forms of ferroics simultaneously is called multiferroic material.Frustrated spin systems have been of interest for well over half a century, with an increase in activity over the last 10-20 years. One important motivation for recent interest is the role played by complex magnetic order in multiferroics. In this thesis,the historical background and latest developments of multiferroics is introduced briefly, we studied and discussed the ground state properties of the Frustrated Classical Heisenberg model in one dimensional with nearest-neighbor biquadratic exchange and Dzyaloshinskii-Moriya (DM) interaction by theoretical and numerical solution methods.Firstly,based on the study of exact solution for the Frustrated Classical Heisenberg model in one dimensional with nearest-neighbor biquadratic exchange, the original model was rewritten by the Cluster Method. The derivation of the "cluster energy" was numerical solved by Monte Carlo method and got the ground state phase diagram.This phase diagram is as same as the Kaplan's which got by exact solution. The result shows that Kaplan found all the ground solutions without losing. On the other hand, this kind of Monte Carlo Method is available for the solution of this type of nonlinear equations. The phase shows spiral spin state,this result challenge the conclusion that the spiral spin state only emerge in finite temperature. Secondly, we introduce the DM interaction to the original Hamilton,and the new Hamilton was also rewritten by The Cluster Method. The derivation of the "cluster energy" was also numerical solved by the Monte Carlo method due to the difficulty of exact solution.There is a "propagate" problem of the spin configuration because this solving process is based on the Cluster approach. We found that all the spin configuration can propagate in the spin chains. So we obtain the ground state phase diagram in different strength of DM interaction.In the phase diagram,the spiral area expand, some transitional phase emerge in the other areas. With the DM interaction strength enhanced,all the phase areas is shrinking and disappeared at last except the spiral area. The result shows that the important role played by DM Interactionin in the origin of spiral spin order. Finally, the original model and the new model was Minimized by Simulated Annealing—Simplex Method in the free boundary conditions due to practical range of Cluster Method and the "propagates" problem. We got the spin configuration of the original model and the new model in the ground state.We get the phase transition point from the analysis of average magnetization and polarization.This conclusion is as same as the result we got by Monte Carlo Method and the result of kaplan's exact solution. We also found that the spiral phase expand and the other phases disappeared with the DM interaction strength enhanced.This conclusion is as similar as the result we got by Monte Carlo Method.