低维各向异性海森堡铁磁与反铁磁模型的磁性研究
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摘要
随着磁性合成材料的进步,人们对合成材料的磁性能产生了浓厚的兴趣,这也正是低维量子磁性研究成为热门的研究领域之一的原因。从研究物质磁性及其形成机理出发,探讨提高磁性材料性能的新途径,开拓磁性材料新的应用领域已成为当代磁学的主要研究方法和内容。在研究磁性的过程中,产生了很多研究方法,但是相比而言,格林函数方法能在全温度区域内处理问题,所得到的结果与实验和其它理论结果符合的较好,因此该方法是目前研究物质磁性比较好的方法之一。在本文中,我们就是运用格林函数方法来研究低维各向异性的海森堡铁磁和反铁磁模型。
在运用格林函数方法处理系统模型时,会产生高阶格林函数的运动方程链,这样就需要利用切断近似的手段来对运动链做切断近似处理,从而可以得到自洽的函数方程。本文中,我们利用无规相近似和安德森-卡伦近似来对海森堡铁磁系统做切断近似处理,而对于海森堡反铁磁系统,我们是运用无规相近似来处理得。在这两种系统模型中,我们所得到的结果与其他人的结果符合的比较好。
第一章是绪论。介绍了海森堡铁磁和反铁磁模型研究背景和本文的研究内容,及所采用的格林函数研究方法。
第二章研究有交换和单离子各向异性一维自旋1的海森堡铁磁体的磁性质。我们运用双时格林函数方法对系统的哈密顿量进行处理,得到了高阶的格林函数的运动方程,接着运用无规相近似来对交换各向异性项进行处理,而用安德森-卡伦近似来处理单离子各向异性项,从而得到了自洽的格林函数方程,最后利用谱定理,得到了磁化强度关于温度、外磁场和各向异性参量之间的函数关系式,进而也建立了临界温度和磁化率关于温度、外磁场和各向异性参量之间的函数关系式。在本章的后面,我们也讨论了关联长度与温度和各向异性参数的关系。我们得到的结果与其他理论工作者得到的结果符合的比较好。
第三章研究高温和低温情况下二维自旋1/2的海森堡反铁磁体的磁性质。本章中我们仍然采用格林函数方法来处理海森堡反铁磁的模型,运用无规相近似来对交换各向异性项进行处理。我们主要讨论了高温无外场和高温有外场,以及低温情况下,磁化强度和磁化率随温度、外场和各向异性参数的变化规律。发现在高温零场的情况下,磁化率χ随温度T的增加而变小,随的各向异性参数η的增加,磁化曲线向左移动,在高温有外场的情况下,η一定时,随着温度T的增加,磁化强度m变大,低温有小磁场情况下,在给定各向异性参数η时,磁化强度m随着温度T的增加而变大,随着外场h的增加而使m-t曲线向上移动。我们得到的结果与其他理论工作者得到的结果符合的比较好。
第四章是本文的结论和以后工作的展望。
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.
在运用格林函数方法处理系统模型时,会产生高阶格林函数的运动方程链,这样就需要利用切断近似的手段来对运动链做切断近似处理,从而可以得到自洽的函数方程。本文中,我们利用无规相近似和安德森-卡伦近似来对海森堡铁磁系统做切断近似处理,而对于海森堡反铁磁系统,我们是运用无规相近似来处理得。在这两种系统模型中,我们所得到的结果与其他人的结果符合的比较好。
第一章是绪论。介绍了海森堡铁磁和反铁磁模型研究背景和本文的研究内容,及所采用的格林函数研究方法。
第二章研究有交换和单离子各向异性一维自旋1的海森堡铁磁体的磁性质。我们运用双时格林函数方法对系统的哈密顿量进行处理,得到了高阶的格林函数的运动方程,接着运用无规相近似来对交换各向异性项进行处理,而用安德森-卡伦近似来处理单离子各向异性项,从而得到了自洽的格林函数方程,最后利用谱定理,得到了磁化强度关于温度、外磁场和各向异性参量之间的函数关系式,进而也建立了临界温度和磁化率关于温度、外磁场和各向异性参量之间的函数关系式。在本章的后面,我们也讨论了关联长度与温度和各向异性参数的关系。我们得到的结果与其他理论工作者得到的结果符合的比较好。
第三章研究高温和低温情况下二维自旋1/2的海森堡反铁磁体的磁性质。本章中我们仍然采用格林函数方法来处理海森堡反铁磁的模型,运用无规相近似来对交换各向异性项进行处理。我们主要讨论了高温无外场和高温有外场,以及低温情况下,磁化强度和磁化率随温度、外场和各向异性参数的变化规律。发现在高温零场的情况下,磁化率χ随温度T的增加而变小,随的各向异性参数η的增加,磁化曲线向左移动,在高温有外场的情况下,η一定时,随着温度T的增加,磁化强度m变大,低温有小磁场情况下,在给定各向异性参数η时,磁化强度m随着温度T的增加而变大,随着外场h的增加而使m-t曲线向上移动。我们得到的结果与其他理论工作者得到的结果符合的比较好。
第四章是本文的结论和以后工作的展望。
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.
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