Spontaneous Magnetizations Of Ferromagnet,Antiferromagnet And Ferrimagnetic Crystal

Recently, low-dimensional quantum spin system is one of the most activeareas of research in condensed matter physics. There is a significant researchinterest especially in Heisenberg model. Such systems exhibit a variety ofphenomena on the low-temperature condition. The discovery of high-temperaturecuprate superconductors in 1987 has given a tremendous boost to research activityin magnetism. The properties of many practical materials discovered byexperiments can be analyzed and predicted by Heisenberg model. It is helpful toknow the mechanism for high temperature superconductors to study Heisenbergmodel.We know that exchange interaction can give rise to magnetic order below thecritical temperature. There are three major types of magnetic order in some spinsystems: ferromagnetism(FM), antiferromagnetism (AFM) and ferrimagnetism(Fi). For FM order, the n.n spins have a tendency towards parallel alignment, forAFM order, the n.n. spins tend to be anti-parallel whereas for Fi order, the n.n.spins favour anti-parallel alignment but the associated magnetic moments havedifferent magnitudes. In this paper, by using the methods of he spin-wave theorem,Green's function, Holstein-Primakoff transformation and Bogoliubovtansformation, we discussed spontaneous magnetizations in different spin systemsand arrived some important quantities such as magnetization, magneticsusceptibility, spin-waves spectrum and correlation function...etc. We furtherinvestigated three different spin systems: ferromagnet, antiferromagnet andferromagnetic crystal in the presence of external magnetic field and calculatedthe critical magnetic field in ferrimagnetic crystal. The conclusions of this paperare consistent with Anderson's view and Haldane's conjecture.The mechanism for spontaneous magnetization is rarely referred because ofits complication. We try to explain this mechanism from the side of magnetic movement arrangement in this paper. We will further investigate the mechanismfor spontaneous magnetization on the basis of this view in the future.