The Spin-wave Excitations Of The Collinear Antiferromagnetic Phase In Iron Pnictides

The discovery of a new class of high temperature superconductors, the layered compounds based on iron pnictides, has attracted a tremendous interest of scientists. One of the most remarkable character of these materials is that the parent compounds have a structure transition and a antiferromagnetic transition at low temperatures. Doping with electrons or holes in the parent compounds leads to suppression of both transitions, and induces the high temperature superconductivity. It is widely expected that the superconductivity should be intrinsically connected to the frustrated magnetic correlations which presumably cause both structure and antiferromagnetic transitions. In this paper, we will study the spin-wave excitations below the antiferromagnetic transition where the collinear antiferromagnetic long-range ordered phase is observed experimentally.In Chapter One, we review the history of the high temperature super-conductors, focusing mainly on the recent progress of iron-based materials.In Chapter Two, we introduce the general classes of the iron pnictide as well as their structures and characteristics. We mainly focus on the similarities and differences between cuprate and iron ponictide superconductors.In Chapter Three, we study the properties of low-energy magnetic excitations of the two-dimensional collinear antiferro-magnet, based on the frustrated two-dimensional Heisenberg J1-J2 model. We also discuss the phase diagram, the stripe antiferro-magnetic state and the spin fluctuations in this system.Chapter Four is the main part of this thesis. In this Chapter, we study a variety of extend J1-J2 models, including anisotropic J1-J2 model and the J1-J2 matrix model. We analyse the change of the phase diagram, the ground state energy and the spin wave dispersions.The summary and concluding remarks are given in Chapter Five.