Self-consistent Mean Field Theory In A Ferrimagnetic Chain

Recently, because of many exotic physical phenomenons in low-dimensional magnetic systems, the low-dimensional magnetic systems caused wide concern. Discuss the physical phenomenons of the spin chain consist of different spin, especially the one-dimensional Heisenberg ferrimagnetic spin chain with two different spin SA=1, SB=1/2 is one of the most concern area. Now there are many ways used to study the ferrimagnetic chain, such as spin wave theory, Schwinger Boson mean field theory, modified spin wave theory, Green function theory et al.The results of these theories are agree well with the experimental results. In this article, we use the self-consistent mean field theory to establish a self-consistent order parameter equation, and based on this, we discuss the different properties of the one-dimensional Heisenberg ferrimagnetic spin chain.The first task is use self-consistent mean field theory to study the properties of one-dimensional anisotropic ferrimagnetic chains. This article discuss the ground-state energy, energy gaps, length of correlation, spin deviation from the average operator via the Ising anisotropy parameter when given the single-ion anisotropy, and when the anisotropy parameters D is zero, the results compare with quantum Monte Carlo approaches and fourth-order perturbation approaches quit well.The second task is use the self-consistent mean field theory to investigate the thermodynamic properties of the one-dimensional Heisenberg ferrimagnetic spin chain with non-zero magnetic field. By applying the mean-field approach to the Hamiltonian of the one-dimensional Heisenberg ferrimagnetic chain with magnetic field, we study the specific heat via the temperature and found that at low temperatures the specific heat will have double peaks phenomenon and as the temperature increases the two peaks gradually become a single peak. Ferrimagnetic spin chain has two excitation spectrum, one of the excitation spectrum is gapless and reduce magnetization of the system, while the gapped branch is the anti-ferromagnetic excitation spectrum, excitation spectrum of such a composition has led to a specific heat is proportional with the T1/2 at low-temperature. We also study the relationship between magnetization and temperature and found there is a plateaux when magnetization is 0.5, the results of our work are agree with the results of experiments.