量子自旋系统与磁性氧化物的量子磁性理论研究
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摘要
近年来,随着凝聚态物理学的迅速发展,对磁性物理学的研究也不断的深化。这主要是因为新近发现的磁性材料系统所具有的许多奇异的性质,如巨磁阻效应、磁光活动和磁致伸缩等。特别是研究发现第一代高温铜氧化物超导体和第二代铁基超导体的磁性质可以用海森堡模型给予理论分析和预测。对磁性材料的研究已成为理论和实验技术应用中的热门课题。这方面国际上近来的研究取得了一些引人注目的突破性成果,所取得的发现和成就不但对磁性物理学本身的发展有重要意义,还将对物理学的其它领域和相关学科产生巨大的影响。因此,从研究物质的磁性及其形成机理出发,探讨提高磁性材料性能的新途径,开拓磁性材料的新应用领域已成为当代磁学的主要研究方向和内容。本文从微观交换相互作用和耦合作用哈密顿模型出发,采用格林函数理论方法,在无规相退耦近似和Callen退耦近似下,研究反铁磁系统、铁磁系统和一些磁性化合物的相变温度、磁化强度、磁化率和色散关系等磁性质。
本文包括六章。在第一章中,我们对磁性系统和一些磁性氧化物的研究背景、基本概念及研究进展进行了简单的介绍,同时也简单的介绍本文的研究方法-双时格林函数方法。
在第二章中,研究了自旋量子数为1的三维易轴单粒子各向异性反铁磁体的磁性质。在无规相退耦近似和Callen退耦近似下,我们研究了系统的相变温度、磁化强度和磁化率。在全温度范围内,我们的研究表明:在低温时,其结果与自旋波理论处理的结果一致;对于λ= 1和D = 0,其结果在温度的中间范围和相变温度附近非常接近团簇展开法、比率法和高温展开得到的结果;对于λ= 1和D = 0.5,其结果在温度1.2≤T≤2.75时(对于简单立方晶格)和1.5≤T≤4(对于体心立方晶格)与团簇展开法和比率法得到的结果一致,但是对于伊辛反铁磁模型,其结果与团簇展开法和比率法的结果有较大的偏离。
在第三章中,研究了任意量子数的二维易轴各向异性的反铁磁体磁性质。在无规相退耦近似和Callen退耦近似下,详细地讨论了五种不同自旋磁性材料K_2NiF_4、Rb_2MnF_4、K_2MnF_4、Rb_2MnCl_4和(CH_3NH_3)_2MnCl_4的相变温度、交挫磁化强度和能隙。与实验和其它理论方法的结果比较,我们计算得到的相变温度、能隙和零温磁化强度等磁性物理量的结果非常好。我们的研究还表明:尽管Callen退耦近似的近似程度要高,但在全温度范围内,无规相退耦近似的结果却能更好的描述这些化合物的磁性质,而且也验证了我们对这些二层结构的磁性材料所选取的各向异性的合理性。
在第四章中,我们采用格林函数方法,在无规相近似下,从三维各向同性的混合自旋铁磁海森堡模型出发,研究了稀土锰氧化物La_(1-x)Sr_xMnO_3的磁性质。给出了磁化强度、相变温度、小k自旋波色散波普和自旋波硬度的解析表达式,详细地讨论了相图、磁化强度、小k自旋波色散波普和自旋波硬度与温度和掺杂浓度之间的关系。我们的结果与实验和其它理论结果符合的很好,同时表明我们的微观模型和理论方法得到的结果能够很好的描述镧锶锰氧化合物的铁磁性质。
第五章中研究了横场下的二维混合自旋各向异性海森堡铁磁体的磁性质。通过坐标旋转方法,我们给出了系统相变温度、高温零场磁化率、自旋波速率、自旋波硬度和能隙的解析表达式。且对于hx=0,在低温时,计算得到的[g(0)?g(T)]∝Tα值接近布洛赫定理的3/2幂次规律;对于hx→0的情况,在高温极限下,磁化率χ_s≈Js(s+1)/(3κBT)和χS≈JS(S+1)/(3κBT),其结果满足居里-外斯定理。对于各向同性情况,结果严格遵守Mermin-Wagner定理。通过数值计算,详细的研究了相变温度、再定位温度和再定位磁场与各向异性参数之间的变化系。
第六章中,基于我们对量子磁性系统研究的现有结果和对准备进行的下阶段工作所做的探索性研究,对今后的工作做一个简要的展望。
In recent years, with the rapid development in condensed matter physics, investigations for magnetic physics are also deepening continually. This is because that magnetic system is of many intriguing physical properties such as colossal magnetoresistance effect, magneto-optical effect and magnetostrictive effect etc. Especially, investigations show that the first generation Cu-oxygen high-temperature superconductor and the second generation Fe-base superconductor of magnetic properties can be theoretical analysis and forecasting by means of Heisenberg model. So investigated of magnetic materials has become the theorists and experimentalists technical application of the popular topics. In recent years, the investigations of development about these aspects are very rapid, and these achievements and findings will definitely stimulate the progress of physics other areas and related scientific. So from studying the origin of the magnetic properties,researching a new way to increase magnetism and finding a new application region for magnetic materials become the main investigated contents of the contemporary magnetism. Following this direction,we try to attack some corresponding theoretical problems.
In this thesis, starting from the exchange interaction of microscopic model and coupled interaction of Hamiltonian model, double time Green’s function is used to investigate the antiferromagnets and some magnetic oxide compounds of magnetic properties within the random phase decoupling approximation.
The whole thesis consists of six chapters. The Chapter one aims at a brief overview of the history, basic concept and progress of magnetic system and some magnetic oxide compounds. In addition, the investigation technique (double time Green’s function) of this thesis will also be described.
In Chapter Two, the ordered and disordered phases of spin-1 Heisenberg and Ising antiferromagnets with easy-axis single-ion anisotropy on a three-dimensional lattice are investigated. By using of the double-time Green's function method within the Tyablikov decoupling for the exchange anisotropy and Callen's approximation for the single-ion anisotropy, the Néel temperature, magnetization and susceptibility are investigated. It shows that our results agree well with ones from spin wave theory at low temperature, and compare reasonably well with those obtained by the linked-cluster series expansion method, by the ratio method and using the high temperature series expansion approach at intermediate temperature and in the vicinity of the critical temperature atλ= 1and D=0. Forλ= 1 and D=0.5, our results agree with the linked-cluster series expansion method ones and ratio method ones in the ranges1.2≤T≤2.75(sc) and1.5≤T≤4 (bcc), respectively. But for D=0 and D=0.5, our results deviate from those obtained by the linked-cluster series expansion method and the ratio method.
In Chapter Three, the magnetic properties of two-dimensional quantum Heisenberg antiferromagnet on the square lattice with easy axis exchange anisotropy are investigated by means of Green’s function approach within random phase and Callen’s approximations. The Néel temperature TN , energy gapω0and staggered magnetization m of magnetic materials (CH_ 3 NH_3 )_2 MnCl_4, Rb_2 MnCl_4, Rb_2 MnF_4 , K_ 2 MnF_4 and K_ 2 NiF_4 are discussed in detailed. Comparing our results with other theoretical and experimental works, our investigations exhibit good results for the Néel temperature, energy gap and staggered magnetization. Meanwhile, our investigations show that result being in good agreement with experiment is obtained within RPA over the entire range of temperature, and it is stated that CA, although more complex, gives no further improvement to the RPA results. We conclude that the physical properties of the magnetic compounds are mainly determined by easy-axis anisotropy in the intralay exchange interaction and can be well modeled and described by the two-dimensional quantum Heisenberg antiferromagnet with this anisotropy.
In Chapter Four, it applies the Heisenberg mixed-spin model to investigate the magnetic properties of the manganese oxide compound La_(1-x)Sr_xMnO_3by using the technique of double-time Green’s function. Within the RPA decoupling for higher order Green’s functions, the analytic expressions of the magnetization, the transition temperature, the spin-wave dispersion relation and spin-wave stiffness are obtained. The phase diagram, magnetization, spin-wave dispersion and spin-wave stiffness of La_(1-x)Sr_xMnO_3as a function of the temperature, magnetic field and doping concentration are discussed in detailed. Comparing our results with other theoretical and experimental works, our results are in agreement with other theoretical and experimental results. Meanwhile, it shows that our microscopic model and method can well describe the magnetic properties of the manganese oxide compound La_(1-x)Sr_xMnO_3.
In Chapter Five, the properties of two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field are studied by means of the double-time Green’s function. The analytic expressions of the critical temperature, the high-temperature zero-field susceptibilities, the spin-wave velocity, spin-wave stiffness and spin-wave gap are obtained. For zero field, the relation[ g (0) ? g (T )]∝Tαis obtained for various mixed-spin. Ourαvalue is close to the well-known Bloch exponent at low temperature. For h x→0, in the high temperature limit,χs≈Js ( s + 1) /(3κBT) andχS≈JS ( S + 1) /(3κBT)are in accordance with the Curie-Weiss law. For hx /J and D = 0, our results obey the Mermin-Wagner theorem. The phase diagrams in which the critical temperature, the reorientation temperature and the reorientation magnetic field are shown as a function of single-ion anisotropic parameter are discussed in detailed.
In Chapter Six, based on our existing studies and further explore research in quantum magnetic system, the prospect of our future works is given in brief.
本文包括六章。在第一章中,我们对磁性系统和一些磁性氧化物的研究背景、基本概念及研究进展进行了简单的介绍,同时也简单的介绍本文的研究方法-双时格林函数方法。
在第二章中,研究了自旋量子数为1的三维易轴单粒子各向异性反铁磁体的磁性质。在无规相退耦近似和Callen退耦近似下,我们研究了系统的相变温度、磁化强度和磁化率。在全温度范围内,我们的研究表明:在低温时,其结果与自旋波理论处理的结果一致;对于λ= 1和D = 0,其结果在温度的中间范围和相变温度附近非常接近团簇展开法、比率法和高温展开得到的结果;对于λ= 1和D = 0.5,其结果在温度1.2≤T≤2.75时(对于简单立方晶格)和1.5≤T≤4(对于体心立方晶格)与团簇展开法和比率法得到的结果一致,但是对于伊辛反铁磁模型,其结果与团簇展开法和比率法的结果有较大的偏离。
在第三章中,研究了任意量子数的二维易轴各向异性的反铁磁体磁性质。在无规相退耦近似和Callen退耦近似下,详细地讨论了五种不同自旋磁性材料K_2NiF_4、Rb_2MnF_4、K_2MnF_4、Rb_2MnCl_4和(CH_3NH_3)_2MnCl_4的相变温度、交挫磁化强度和能隙。与实验和其它理论方法的结果比较,我们计算得到的相变温度、能隙和零温磁化强度等磁性物理量的结果非常好。我们的研究还表明:尽管Callen退耦近似的近似程度要高,但在全温度范围内,无规相退耦近似的结果却能更好的描述这些化合物的磁性质,而且也验证了我们对这些二层结构的磁性材料所选取的各向异性的合理性。
在第四章中,我们采用格林函数方法,在无规相近似下,从三维各向同性的混合自旋铁磁海森堡模型出发,研究了稀土锰氧化物La_(1-x)Sr_xMnO_3的磁性质。给出了磁化强度、相变温度、小k自旋波色散波普和自旋波硬度的解析表达式,详细地讨论了相图、磁化强度、小k自旋波色散波普和自旋波硬度与温度和掺杂浓度之间的关系。我们的结果与实验和其它理论结果符合的很好,同时表明我们的微观模型和理论方法得到的结果能够很好的描述镧锶锰氧化合物的铁磁性质。
第五章中研究了横场下的二维混合自旋各向异性海森堡铁磁体的磁性质。通过坐标旋转方法,我们给出了系统相变温度、高温零场磁化率、自旋波速率、自旋波硬度和能隙的解析表达式。且对于hx=0,在低温时,计算得到的[g(0)?g(T)]∝Tα值接近布洛赫定理的3/2幂次规律;对于hx→0的情况,在高温极限下,磁化率χ_s≈Js(s+1)/(3κBT)和χS≈JS(S+1)/(3κBT),其结果满足居里-外斯定理。对于各向同性情况,结果严格遵守Mermin-Wagner定理。通过数值计算,详细的研究了相变温度、再定位温度和再定位磁场与各向异性参数之间的变化系。
第六章中,基于我们对量子磁性系统研究的现有结果和对准备进行的下阶段工作所做的探索性研究,对今后的工作做一个简要的展望。
In recent years, with the rapid development in condensed matter physics, investigations for magnetic physics are also deepening continually. This is because that magnetic system is of many intriguing physical properties such as colossal magnetoresistance effect, magneto-optical effect and magnetostrictive effect etc. Especially, investigations show that the first generation Cu-oxygen high-temperature superconductor and the second generation Fe-base superconductor of magnetic properties can be theoretical analysis and forecasting by means of Heisenberg model. So investigated of magnetic materials has become the theorists and experimentalists technical application of the popular topics. In recent years, the investigations of development about these aspects are very rapid, and these achievements and findings will definitely stimulate the progress of physics other areas and related scientific. So from studying the origin of the magnetic properties,researching a new way to increase magnetism and finding a new application region for magnetic materials become the main investigated contents of the contemporary magnetism. Following this direction,we try to attack some corresponding theoretical problems.
In this thesis, starting from the exchange interaction of microscopic model and coupled interaction of Hamiltonian model, double time Green’s function is used to investigate the antiferromagnets and some magnetic oxide compounds of magnetic properties within the random phase decoupling approximation.
The whole thesis consists of six chapters. The Chapter one aims at a brief overview of the history, basic concept and progress of magnetic system and some magnetic oxide compounds. In addition, the investigation technique (double time Green’s function) of this thesis will also be described.
In Chapter Two, the ordered and disordered phases of spin-1 Heisenberg and Ising antiferromagnets with easy-axis single-ion anisotropy on a three-dimensional lattice are investigated. By using of the double-time Green's function method within the Tyablikov decoupling for the exchange anisotropy and Callen's approximation for the single-ion anisotropy, the Néel temperature, magnetization and susceptibility are investigated. It shows that our results agree well with ones from spin wave theory at low temperature, and compare reasonably well with those obtained by the linked-cluster series expansion method, by the ratio method and using the high temperature series expansion approach at intermediate temperature and in the vicinity of the critical temperature atλ= 1and D=0. Forλ= 1 and D=0.5, our results agree with the linked-cluster series expansion method ones and ratio method ones in the ranges1.2≤T≤2.75(sc) and1.5≤T≤4 (bcc), respectively. But for D=0 and D=0.5, our results deviate from those obtained by the linked-cluster series expansion method and the ratio method.
In Chapter Three, the magnetic properties of two-dimensional quantum Heisenberg antiferromagnet on the square lattice with easy axis exchange anisotropy are investigated by means of Green’s function approach within random phase and Callen’s approximations. The Néel temperature TN , energy gapω0and staggered magnetization m of magnetic materials (CH_ 3 NH_3 )_2 MnCl_4, Rb_2 MnCl_4, Rb_2 MnF_4 , K_ 2 MnF_4 and K_ 2 NiF_4 are discussed in detailed. Comparing our results with other theoretical and experimental works, our investigations exhibit good results for the Néel temperature, energy gap and staggered magnetization. Meanwhile, our investigations show that result being in good agreement with experiment is obtained within RPA over the entire range of temperature, and it is stated that CA, although more complex, gives no further improvement to the RPA results. We conclude that the physical properties of the magnetic compounds are mainly determined by easy-axis anisotropy in the intralay exchange interaction and can be well modeled and described by the two-dimensional quantum Heisenberg antiferromagnet with this anisotropy.
In Chapter Four, it applies the Heisenberg mixed-spin model to investigate the magnetic properties of the manganese oxide compound La_(1-x)Sr_xMnO_3by using the technique of double-time Green’s function. Within the RPA decoupling for higher order Green’s functions, the analytic expressions of the magnetization, the transition temperature, the spin-wave dispersion relation and spin-wave stiffness are obtained. The phase diagram, magnetization, spin-wave dispersion and spin-wave stiffness of La_(1-x)Sr_xMnO_3as a function of the temperature, magnetic field and doping concentration are discussed in detailed. Comparing our results with other theoretical and experimental works, our results are in agreement with other theoretical and experimental results. Meanwhile, it shows that our microscopic model and method can well describe the magnetic properties of the manganese oxide compound La_(1-x)Sr_xMnO_3.
In Chapter Five, the properties of two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field are studied by means of the double-time Green’s function. The analytic expressions of the critical temperature, the high-temperature zero-field susceptibilities, the spin-wave velocity, spin-wave stiffness and spin-wave gap are obtained. For zero field, the relation[ g (0) ? g (T )]∝Tαis obtained for various mixed-spin. Ourαvalue is close to the well-known Bloch exponent at low temperature. For h x→0, in the high temperature limit,χs≈Js ( s + 1) /(3κBT) andχS≈JS ( S + 1) /(3κBT)are in accordance with the Curie-Weiss law. For hx /J and D = 0, our results obey the Mermin-Wagner theorem. The phase diagrams in which the critical temperature, the reorientation temperature and the reorientation magnetic field are shown as a function of single-ion anisotropic parameter are discussed in detailed.
In Chapter Six, based on our existing studies and further explore research in quantum magnetic system, the prospect of our future works is given in brief.
引文
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