Theoretical Studies On Shallow Donor Impurity In A Spherical Parabolic Quantum Dot With An Electric Field

With the progress in synthesis of new magnetic materials, the magnetic properties of composite materials have received considerable interest.That's why the low-dimensional quantum magnetism becomes one of the hot research fields. Starting from the magnetism and formation mechanism of magnetic materials,discussing new ways to improve magnetic properties and opening up new fields of application of magnetic materials have become major research methods and content in the contemporary magnetism. As magnetic syn-thetic materials are developing, there are many experimental and theoretical methods, which have been employed to investigate the magnetism. Of all these methods,Green's function method is considered to be one of the best methods because it can be applied to all temperature areas,and it can get good results which agree with others results. In this paper, we adopt Green's function to investigate the low-dimensional quantum ferromagnetic and anti-ferromagnetic anisotropic Heisenberg models.When we use Green's function method to deal with the magnetic system, we will obtain the equations of motion of high-order Green's function chain.In order to obtain self-consistency equations,we need to adopt the methods of approximation.In this pa-per,we apply the random phase approximation and the Anderson-Callen approximation for the ferromagnetic Heisenberg model,and the random phase approximation for anti-ferromagnetic Heisenberg model. In these two systems,the results which we get from the above approximations are good agreement with others.In the first chapter,the research background and contents of ferromagnetic and anti-ferromagnetic Heisenberg models have been summarized briefly, and a simply introduction of Green's function method has been given.In the second chapter, the one-dimensional spin-1 ferromagnetic Heisenberg model with the exchange anisotropy and single-ion anisotropy has been investigated by Green's function method.We apply Green's function method to cope with the Hamiltonian of the system, and obtain the equations of motion of high-order Green's function chain. In order to obtain self-consistency equations,we use the random phase approximation for the exchange interaction term and the Anderson-Callen approximation for the single-ion anisotropy term.Through the spectral theorem,the critical temperature, magnetization, and susceptibility are found to be as a function of the temperature, magnetic field and anisotropies.Our results are in agreement with the other theoretical results.In the third chapter, theoretical calculations are carried out on the two-dimensional spin-1/2 anti-ferromagnetic Heisenberg model under high-and low-temperature regions. We also apply Green's function method to cope with the Hamiltonian of the system, and use the random phase approximation for the anisotropic term. In high-and low-temperature regions,we establish the magnetization and susceptibility as a function of the temperature, magnetic field and anisotropy. Through the analysis,we find that in high temperatures and zero external magnetic fields,the susceptibilityχbecome smaller as the temperature T gets bigger. And with increasing of the anisotropyη, the magnetization curve shifts to left.In high temperatures and non-zero external magnetic fields,whenηis given, the magnetization m increases as the temperature raises.In low temperatures and small external magnetic fields,whenηis given,the magnetization m become large with the increasing temperature T. And the curve of m-t shifts to above as the external magnetic field h raises.Our results are in agreement with the other theoretical results.In the last chapter,a brief summary of this paper, including the theories and the results,is given. The shortage and further research are also mentioned.