Theoretical Studies On Nonlinear Localized Modes In Two-Dimensional Ferromagnets With Different Lattice Structures

Due to the various nonlinear effects in ferromagnets,which play an important role in the applications of magnetic logic devices,magnetic storage devices and magnetic communication technology,the nonlinear effects in ferromagnets have attracted extensive research interest in the past two decades.The theoretical studies of nonlinear localized mode in ferromagnets is helpful to analyze the nonlinear effect in ferromagnetic materials and has a certain theoretical guiding role in the practical application of ferromagnetic materials.In this thesis,the research progress of nonlinear localized modes in ferromagnets at home and abroad is summarized,and the research methods used in this thesis are briefly introduced.Then,the nonlinear localized modes in two-dimensional ferromagnets with hexagonal lattice structure and honeycomb lattice structure and checkerboard lattice structure are studied theoretically.The main contents as follows:In chapter 3,the nonlinear localized modes in ferromagnets with hexagonal lattice structure are studied theoretically.The two-magnon bound states of the system are calculated in the full quantum case and it is found that the existence of anisotropy has a significant effect on the number and energy of the two-magnon bound states.In the semi-classical case,the analytical form of bright two-dimensional discrete breathers with linear localized structure is constructed.It is found that the anisotropy plays an important role in the existence of discrete breathers.Finally,the effect of anisotropy on the localization of discrete breathers is studied.In chapter 4,the nonlinear localized modes in ferromagnets with honeycomb lattice structure are studied theoretically.Firstly,the bright and dark soliton solutions of the two-dimensional nonlinear Schrodinger(2D NLS)equation are obtained by using the Hirota bilinear method.We find that in the center of the Brillouin zone,the acoustic mode supports a bright two-dimensional discrete breather,and its eigenfrequency is below the bottom of magnon acoustic frequency band,while the optical mode supports a resonant two-dimensional discrete breather.In the vicinity of Dirac point,two-dimensional band gap solitons can exist under certain conditions due to the DM interaction,and the motion direction of band gap solitons can be determined by the expression of magnon group velocity.In chapter 5,the nonlinear localized modes in ferromagnets with checkerboard lattice structure are studied theoretically,and the analytical forms of the nonlinear localized modes in the center of Brillouin zone and Brillouin corner are obtained by using the same method as in Chapter 4.In the center of Brillouin region,the acoustic mode supports the bright two-dimensional discrete breather and the optical mode supports the dark two-dimensional discrete breather.At the corner of the Brillouin zone,there is a competition between the Dzyaloshinskii-Moriya(DM)interaction and the Heisenberg next-neighbor exchange,which leads to acoustic support for different types of two-dimensional discrete breathers.The optical mode only supports dark two-dimensional discrete breathers,and when DM interaction meets certain conditions,the frequency of the discrete breathers is in the band gap of the magnon band.