自旋/轨道有序体系电子结构与磁特性的第一原理研究
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摘要
复杂物质体系中自旋/电荷/轨道的有序、耦合及其相互作用机制的研究为近年来凝聚态物理学中极其活跃的重要领域，特别是随着自旋电子学的蓬勃发展，更促使人们对自旋/电荷/轨道有序体系的一些基础性物理问题的探索。在这一研究中，电荷、自旋、轨道以及晶格自由度之间强烈的耦合使其表现出丰富多彩的物理性质，从而使其在磁记录、磁传感器等方面有广阔的应用前景。本论文利用第一性原理方法系统研究了自旋/轨道有序典型体系的电子结构和磁特性，其主要内容如下：
第一章综述了近年来人们所关注的一些典型凝聚态体系中的有序现象，包括过渡金属氧化物中的轨道物理学以及与轨道物理有关的氧化物相变的研究背景，强关联电子系统的基础性前沿问题，以及金属团簇的理论基础，过渡金属团簇中的自旋有序和自旋/轨道相互作用研究等等，提出了本论文工作的出发点和主要研究内容。
第二章简要介绍了本文工作的相关理论方法，包括能带理论的三个近似以及密度泛函理论，势的构建与波函数的具体处理方法，如平面波方法和赝势法等等。
第三章给出了立方钙钛矿BaRu_(1-x)Fe_xO_3(x=0,0.25,0.50,0.625,0.75,1)体系电子结构及磁性质的第一原理研究结果。发现在BaFeO3体系中，存在着较大的交换劈裂和相对小的晶场劈裂，而相反的情况出现在BaRuO_3中，其原因主要是因为Ru原子具有比较扩展的4d轨道。对BaRuO_3的计算得到的Ru~(4+)离子的磁矩是0.628μB，远远低于依据t_(2g)3↑t_(2g)1↓的电子结构得到的理想值2μB，产生这种差异的原因应该是BaRuO_3中相对小的交换劈裂以及扩展的4d轨道。进一步的研究表明，如果用Fe替代Ru原子，Ru4d轨道的带宽将被压制，导致BaRu_(1-x)Fe_xO_3在x=0.625和x=0.75的时候，体系出现半金属性。同时，BaRu_(0.375)Fe_(0.625)O_3中不同Ru~(4+)离子的轨道特征也被展示，这些不同的轨道特征可以被看做Fe杂质对Ru4d轨道压制的直接证据。
第四章我们利用第一原理计算，研究了自旋轨道耦合(SOC)效应对二元合金M@Pb_(12)(这里M代表3d和4d过渡金属元素)体系几何结构和磁性质的影响。结果发现，考虑SOC后，体系几何结构的对称性会增强，SOC引起的离域电子数目的增加应该是对称性增强的主要原因。对磁性的研究表明，SOC对3d杂质原子的局域自旋磁矩有轻微的影响，但对4d系列，考虑SOC后，杂质原子的局域自旋磁矩将会显著降低，M3d-Pb6p和M4d-Pb6p之间不同的杂化强度是产生这种差异的主要原因。进一步研究发现，考虑SOC后，一定的轨道磁矩将会出现，对于掺杂的Ti, V, Co和Ru原子，其轨道磁矩可以超过0.8μB，表明SOC在M@Pb_(12)体系中是不能被忽略的。最后，对3d和4d掺杂M原子轨道磁矩的变化规律，我们用Hund定则给出了较为满意的自洽解释。
第五章利用第一原理通过对Ih结构的二元过渡金属团簇Ti_nMn_(13-n)(n=1-12)的研究，我们发现对于最稳定的结构，其中心位置被Mn原子所占据。体系的总磁矩随着Ti原子数的增加起初降低，在Ti11Mn2减小到0μB，随后又重新增加至3μB。总磁矩的变化可以通过Mn原子被Ti原子的替代以及电荷从Ti原子向Mn原子上的转移两方面原因做出解释。对于局域磁矩，同一种类的原子之间是铁磁耦合，而Ti原子和Mn原子之间形成的是反铁磁序。结合能随着Ti原子数的增加而增加，表明拥有较多Ti原子的团簇比拥有较多Mn原子的团簇更稳定。最后，对垂直离子势的讨论表明，较小的交换劈裂也会导致较大的垂直离子势。
第六章是对本文的一个简要总结，以及对未来工作的展望。
One of the important research fields in condensed matter physics is to study thephysical mechanism of spin/charge/orbital ordering, coupling, and its interactionstogether in the systems of complex materials. Especially in recent years, the rapiddevelopment of spintronics can also improve the development of the studies infoundational problems of spin/charge/orbital ordering systems. Among those, charge,spin, orbital and the lattice degree of freedom are coupled to each other, thecomplicated interactions give rise to some interesting phenomena and have thepotential technological applications in such as magnetic memory and magneticsensors, etc. In this dissertation, based on the first-principles calculations, weinvestigated the electronic structure and magnetic characteristics in some typicalspin/orbital ordering systems. There are six chapters in this thesis.
In the first chapter, some ordering phenomena in condensed matter physics areintroduced. For example, the background of the orbital physics and phase transitionrelated to orbital degree of freedom (ODF) in oxides is reviewed, and the electroncorrelation effects are also introduced. The basic theory of metal clusters and the spinordering as well as spin-orbital interaction of transition-metal clusters are brieflymentioned. At the end of this chapter, the motivation and the main research contentsof this dissertation are given.
In the second chapter, the theoretical methods used in this thesis are introduced.The three approximations of energy band theory and density-functional theory (DFT)are introduced first. In the following, we introduced the disposal method of potentialand wavefunctions, for example, plane-wave method and pseudopotential approximation, etc.
In the third chapter, the electronic structures of the Fe-doped perovskiteruthenates BaRu_(1-x)Fe_xO_3with x=0,0.25,0.50,0.625,0.75, and1are investigatedthrough density-functional calculations. Large exchange splitting and small crystalfield splitting are found in BaFeO3, and contrary scenario can take place for BaRuO_3as expected since Ru atom has highly extended4d orbital. The small exchangesplitting and extended4d states are the reasons that the obtained spin magneticmoment (0.628μB) is significantly lower than the spin only value (2μB) for thet_(2g)3↑t_(2g)1↓electronic configuration for Ru~(4+)ion. The further investigations suggest thatFe substitution at the Ru sites can suppress the bandwidths of Ru4d orbital, leading tothe half-metallic behavior in BaRu_(1-x)Fe_xO_3with x=0.625and x=0.75. The differentorbital feature of the Ru~(4+)ions in BaRu_(0.375)Fe_(0.625)O_3is presented, which reflects theinfluence of Fe dopant on Ru4d orbitals.
In the fourth chapter, the effect of spin-orbit coupling (SOC) on geometricalstructure and magnetism of M@Pb_(12)clusters (M=3d and4d atoms) were studied. Wefound that SOC may enhance the symmetry of geometrical configurations for someclusters, which can be ascribed to the increase of the numbers of delocalized electronsafter SOC is considered. The SOC marginally affects the local spin magneticmoments of3d atoms, whereas it can cause large influence on spin magnetism ofimpurities for most4d series, which can be explained based on the differenthybridization strength between M3d-Pb6p and M4d-Pb6p. The considerable orbitalmagnetic moments are produced by SOC, and the local orbital moments of Ti, V, Co,and Ru even exceed0.8μB. The variation trends of the local orbital magnetism of Matoms encapsulated in the Pb12cages for3d and4d series can well be comprehended from Hund’s rule.
In the fifth chapter, we studied the properties of icosahedral bimetallic Ti_nMn_(13-n)(n=1-12) clusters. We found that for the most stable structures, the central position isoccupied by a manganese atom. The total magnetic moment (TMM) decreases withthe increase of Ti atoms and it reaches0μBat the cluster of Ti_(11)Mn_2, and thenincreases to3μBagain. The substitution of Mn atoms by Ti atoms and the chargetransfer from Ti to Mn atoms are mainly responsible for the variation of TMM. Forlocal magnetic moment (LMM), all Ti atoms and most Mn atoms presentferromagnetic ordering, while the spins on Ti atoms are anti-parallel to those on Mnatoms except for Ti_(12)Mn_1, forming antiferromagnetic magnetic structure. The bindingenergy increases monotonically with the increase of Ti atoms, indicating the clusterwith more Ti atoms are more stable than those with more Mn atoms. At last, thevertical ionization potential (VIP) of the lowest energy structure is discussed and theresults show that the little exchange splitting will lead to a relatively larger VIP forTi_(11)Mn_2and Ti_(12)Mn_1.
In the sixth chapter, we give a brief summary and outlook about the followingwork.
第一章综述了近年来人们所关注的一些典型凝聚态体系中的有序现象，包括过渡金属氧化物中的轨道物理学以及与轨道物理有关的氧化物相变的研究背景，强关联电子系统的基础性前沿问题，以及金属团簇的理论基础，过渡金属团簇中的自旋有序和自旋/轨道相互作用研究等等，提出了本论文工作的出发点和主要研究内容。
第二章简要介绍了本文工作的相关理论方法，包括能带理论的三个近似以及密度泛函理论，势的构建与波函数的具体处理方法，如平面波方法和赝势法等等。
第三章给出了立方钙钛矿BaRu_(1-x)Fe_xO_3(x=0,0.25,0.50,0.625,0.75,1)体系电子结构及磁性质的第一原理研究结果。发现在BaFeO3体系中，存在着较大的交换劈裂和相对小的晶场劈裂，而相反的情况出现在BaRuO_3中，其原因主要是因为Ru原子具有比较扩展的4d轨道。对BaRuO_3的计算得到的Ru~(4+)离子的磁矩是0.628μB，远远低于依据t_(2g)3↑t_(2g)1↓的电子结构得到的理想值2μB，产生这种差异的原因应该是BaRuO_3中相对小的交换劈裂以及扩展的4d轨道。进一步的研究表明，如果用Fe替代Ru原子，Ru4d轨道的带宽将被压制，导致BaRu_(1-x)Fe_xO_3在x=0.625和x=0.75的时候，体系出现半金属性。同时，BaRu_(0.375)Fe_(0.625)O_3中不同Ru~(4+)离子的轨道特征也被展示，这些不同的轨道特征可以被看做Fe杂质对Ru4d轨道压制的直接证据。
第四章我们利用第一原理计算，研究了自旋轨道耦合(SOC)效应对二元合金M@Pb_(12)(这里M代表3d和4d过渡金属元素)体系几何结构和磁性质的影响。结果发现，考虑SOC后，体系几何结构的对称性会增强，SOC引起的离域电子数目的增加应该是对称性增强的主要原因。对磁性的研究表明，SOC对3d杂质原子的局域自旋磁矩有轻微的影响，但对4d系列，考虑SOC后，杂质原子的局域自旋磁矩将会显著降低，M3d-Pb6p和M4d-Pb6p之间不同的杂化强度是产生这种差异的主要原因。进一步研究发现，考虑SOC后，一定的轨道磁矩将会出现，对于掺杂的Ti, V, Co和Ru原子，其轨道磁矩可以超过0.8μB，表明SOC在M@Pb_(12)体系中是不能被忽略的。最后，对3d和4d掺杂M原子轨道磁矩的变化规律，我们用Hund定则给出了较为满意的自洽解释。
第五章利用第一原理通过对Ih结构的二元过渡金属团簇Ti_nMn_(13-n)(n=1-12)的研究，我们发现对于最稳定的结构，其中心位置被Mn原子所占据。体系的总磁矩随着Ti原子数的增加起初降低，在Ti11Mn2减小到0μB，随后又重新增加至3μB。总磁矩的变化可以通过Mn原子被Ti原子的替代以及电荷从Ti原子向Mn原子上的转移两方面原因做出解释。对于局域磁矩，同一种类的原子之间是铁磁耦合，而Ti原子和Mn原子之间形成的是反铁磁序。结合能随着Ti原子数的增加而增加，表明拥有较多Ti原子的团簇比拥有较多Mn原子的团簇更稳定。最后，对垂直离子势的讨论表明，较小的交换劈裂也会导致较大的垂直离子势。
第六章是对本文的一个简要总结，以及对未来工作的展望。
One of the important research fields in condensed matter physics is to study thephysical mechanism of spin/charge/orbital ordering, coupling, and its interactionstogether in the systems of complex materials. Especially in recent years, the rapiddevelopment of spintronics can also improve the development of the studies infoundational problems of spin/charge/orbital ordering systems. Among those, charge,spin, orbital and the lattice degree of freedom are coupled to each other, thecomplicated interactions give rise to some interesting phenomena and have thepotential technological applications in such as magnetic memory and magneticsensors, etc. In this dissertation, based on the first-principles calculations, weinvestigated the electronic structure and magnetic characteristics in some typicalspin/orbital ordering systems. There are six chapters in this thesis.
In the first chapter, some ordering phenomena in condensed matter physics areintroduced. For example, the background of the orbital physics and phase transitionrelated to orbital degree of freedom (ODF) in oxides is reviewed, and the electroncorrelation effects are also introduced. The basic theory of metal clusters and the spinordering as well as spin-orbital interaction of transition-metal clusters are brieflymentioned. At the end of this chapter, the motivation and the main research contentsof this dissertation are given.
In the second chapter, the theoretical methods used in this thesis are introduced.The three approximations of energy band theory and density-functional theory (DFT)are introduced first. In the following, we introduced the disposal method of potentialand wavefunctions, for example, plane-wave method and pseudopotential approximation, etc.
In the third chapter, the electronic structures of the Fe-doped perovskiteruthenates BaRu_(1-x)Fe_xO_3with x=0,0.25,0.50,0.625,0.75, and1are investigatedthrough density-functional calculations. Large exchange splitting and small crystalfield splitting are found in BaFeO3, and contrary scenario can take place for BaRuO_3as expected since Ru atom has highly extended4d orbital. The small exchangesplitting and extended4d states are the reasons that the obtained spin magneticmoment (0.628μB) is significantly lower than the spin only value (2μB) for thet_(2g)3↑t_(2g)1↓electronic configuration for Ru~(4+)ion. The further investigations suggest thatFe substitution at the Ru sites can suppress the bandwidths of Ru4d orbital, leading tothe half-metallic behavior in BaRu_(1-x)Fe_xO_3with x=0.625and x=0.75. The differentorbital feature of the Ru~(4+)ions in BaRu_(0.375)Fe_(0.625)O_3is presented, which reflects theinfluence of Fe dopant on Ru4d orbitals.
In the fourth chapter, the effect of spin-orbit coupling (SOC) on geometricalstructure and magnetism of M@Pb_(12)clusters (M=3d and4d atoms) were studied. Wefound that SOC may enhance the symmetry of geometrical configurations for someclusters, which can be ascribed to the increase of the numbers of delocalized electronsafter SOC is considered. The SOC marginally affects the local spin magneticmoments of3d atoms, whereas it can cause large influence on spin magnetism ofimpurities for most4d series, which can be explained based on the differenthybridization strength between M3d-Pb6p and M4d-Pb6p. The considerable orbitalmagnetic moments are produced by SOC, and the local orbital moments of Ti, V, Co,and Ru even exceed0.8μB. The variation trends of the local orbital magnetism of Matoms encapsulated in the Pb12cages for3d and4d series can well be comprehended from Hund’s rule.
In the fifth chapter, we studied the properties of icosahedral bimetallic Ti_nMn_(13-n)(n=1-12) clusters. We found that for the most stable structures, the central position isoccupied by a manganese atom. The total magnetic moment (TMM) decreases withthe increase of Ti atoms and it reaches0μBat the cluster of Ti_(11)Mn_2, and thenincreases to3μBagain. The substitution of Mn atoms by Ti atoms and the chargetransfer from Ti to Mn atoms are mainly responsible for the variation of TMM. Forlocal magnetic moment (LMM), all Ti atoms and most Mn atoms presentferromagnetic ordering, while the spins on Ti atoms are anti-parallel to those on Mnatoms except for Ti_(12)Mn_1, forming antiferromagnetic magnetic structure. The bindingenergy increases monotonically with the increase of Ti atoms, indicating the clusterwith more Ti atoms are more stable than those with more Mn atoms. At last, thevertical ionization potential (VIP) of the lowest energy structure is discussed and theresults show that the little exchange splitting will lead to a relatively larger VIP forTi_(11)Mn_2and Ti_(12)Mn_1.
In the sixth chapter, we give a brief summary and outlook about the followingwork.
引文
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