晶体中过渡金属离子基态与低激发态零场分裂和g因子性质的理论研究与应用
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摘要
本文从晶体场理论出发,采用完全对角化方法,对三角对称和四角对称下d3离子和d2／8离子掺杂体系的基态和激发态自旋哈密顿参量进行了系统的研究。本文的主要结果和创新点有：
(1)通过对晶场势的分析,说明了晶场参量的概念,并对为计算晶场参量而采用的三种模型进行了比较分析。在晶体场理论的发展过程中,出现了几种不同的晶场符号表示,给后来的研究者对晶场符号的使用造成了混乱。本文对不同晶场符号的物理意义进行了说明,分析了晶场符号之间的关系,澄清了文献中对晶场符号使用的混乱。利用群表示理论推导得到了dN离子在三角对称和四角对称下的光谱精细结构。利用自旋哈密顿理论推导得到了基态和激发态零场分裂和g因子的计算公式。
(2)在中间场耦合图像下建立了过渡金属掺杂离子完全能量矩阵。在磁相互作用中考虑了除自旋与轨道相互作用之外的自旋与自旋相互作用、自旋与另一轨道相互作用以及轨道与轨道相互作用等微小磁相互作用。推导得到了基态和低激发态自旋哈密顿参量的计算公式,并利用VB语言编制了相应的计算程序。
(3)利用本文建立的理论和编制的程序,研究了d3离子激发态对基态自旋哈密顿参量的影响。在三角对称和四角对称下,下列结果是成立的：基态是4F态,除自旋四重态外,自旋二重态对基态的零场分裂也有重要贡献。而对g因子来说,二重态对其基本没有贡献；SS机制和SOO机制对基态零场分裂参量的贡献主要由四重态决定,二重态的贡献很小；SO-SS-SOO联合机制对基态零场分裂参量的贡献主要由四重态决定,二重态也有相当的贡献；SS机制对g因子几乎没有影响,而SOO机制对g因子有一定影响,但这一影响也是由四重态决定,与二重态无关。
(4)研究了三角对称下d2／8离子激发态对基态自旋哈密顿参量的影响。为了考察自旋单态和自旋三重态对基态自旋哈密顿参量的贡献,分别在三种情况下计算了三角对称下d2／8离子基态自旋哈密顿参量。结果说明,SO机制对基态自旋哈密顿参量的贡献是主要的,这其中三重态的贡献是主要的,而单态的贡献相对较小。SS机制和SOO机制以及SO-SS-SOO联合机制对基态零场分裂参量的贡献主要由三重态决定,单态的贡献很小。SS机制对g因子几乎没有影响,而SOO机制对g因子有一定影响,但这一影响也是由三重态决定,与单态无关。但是联合作用机制对g因子的贡献中,单态的贡献是不可忽略的。OO作用对g因子的贡献也是只由三重态决定,与单态无关。
(5)建立了激发态零场分裂理论,研究了三角对称下d3离子激发态零场分裂的性质,指出了文献中的印刷错误。对4T2和4T1a态定义了其零场分裂计算公式,对2T1a和2T2a定义了两个零场分裂表达式。计算结果表明,4T2和4T1a项的零场分裂主要来源于三角晶场作用。在磁相互作用的贡献中,低激发态零场分裂主要来源于旋轨耦合作用,微小磁相互作用对低激发态零场分裂的贡献较小。δ1(2T1a。)和δ1(2T2a)这两个能级间隔来自于磁相互作用,δ2(2T1a)和δ2(2T2a)这两个能级间隔主要来源于三角晶场作用。
(6)对四角对称下d3离子4T2和4T1a态零场分裂微扰公式的收敛性进行了分析。结果表明,在较强晶场的情形下,微扰公式的收敛性较好。
(7)研究了三角对称下d3离子2E态g因子的性质,从理论上解释了Al2O3：Mn4+体系和Al2O3：Cr3+体系的2E态g因子。研究发现磁相互作用间存在联合机制,并对各种机制贡献的相对大小进行了研究。微小磁相互作用对基态零场分裂的贡献是不可忽略的,但对2E态零场分裂是很小的。对g因子来说,来自SS、SOO和OO相互作用对基态和E′(2E)态的g因子贡献也是可观的,但对E″(2E)态g因子的贡献是很小的。解释了ZnAl2O4:Cr3+体系2E态g因子的实验值,并对照文献中对ZnGa2O4：Cr3+体系2E态g因子的计算,指出文献中存在有印刷错误。对MgAl2O4：Cr3+体系2E态g因子进行了理论预测,这些结果有待于相应的实验做进一步的验证。
(8)作为本文理论的应用,研究了Al2O3：V2+体系、Al2O3:Cu3+体系、CsMgX3:V2+(X=Cl、Br、I)体系和LiNbO3：Ni2+体系的微观局域结构,理论计算结果和实验值的符合说明我们采用的模型是合理的。
By using complete diagonalization method (CDM), the spin-Hamiltonian (SH) parameters of ground state and excited states for d3 ions and d2/8 ions at trigonal and tetragonal symmetry are studied, based on crystal field theory. The main contents and innovations are as follows:
Firstly, by analyzing the crystal field potential, the concepts of crystal field parameters are illustrated. The three models adopted to calculate CF parameters are compared and analyzed. In the development of CF theory, various CF notations are used, this result in confusion to researchers. In this thesis, the physical meanings of various CF notations are illustrated, the relations between various CF notations are analyzed, and the confusions are clarified. The spectra fine structure of dN ions at trigonal and tetragonal symmetry are deduced by group theory.
Secondly, in the intermediate crystal field coupling scheme, the complete energy matrices for transition metal (TM) ions are constructed. In addition to general spin-orbit (SO) interactions, the slight magnetic interactions including spin-spin (SS), spin-other-orbit (SOO) and orbit-orbit (OO) interactions are taken into account. Formulas of SH parameters of ground state and excited states are deduced, and the corresponding computer program are developed.
Thirdly, by using the theory and the program developed in this thesis, the contribution to SH parameters of ground state from excited states of d3 ions are investigated. For trigonal and tetragonal symmetry, these results are obtained:(a) The ground state is 4F, contributions from spin doublets are appreciable. For g factors, there are almost no contributions from spin doublets, (b) The contributions from SS and SOO mechanisms mainly depend on spin quartets, and the contributions from spin doublets are appreciable. (c) The contribution to g factors from SS mechanism almost is zero, but the contribution to g factors from SOO mechanism is appreciable, and this contribution depends on spin quartets only.
Fourthly, the influence to SH parameters of ground state of d2/8 ions from excited states at trigonal symmetry are studied. It is shown that, the contribution from SO mechanism is dominant, in which, the contributions from spin triplets are mainly. The contributions to ZFS of ground state from SS, SOO and SO-SS-SOO combined mechanisms are mainly due to spin triplets. The contribution to g factors from SS mechanism almost is zero, but the contribution to g factors from SOO mechanism is appreciable, and this contribution depends on spin triplets only. Contributions to g factors from 00 mechanism are depending on spin triplets only.
Fifthly, the theory of ZFS of excited states have been established. The ZFS of low-lying states for d3 ions at trigonal symmetry have been studied, the misprint in reference are pointed out. The formulas of ZFS of 4T2,4T1a,2T1a and 2T2a have been defined. It is shown that, the ZFS of 4T2 and 4T1a terms are mainly depend on trigonal CF. The contribution to ZFS of low-lying states from spin-orbit mechanism is dominant, and the contributions from other mechanisms are slight. The energy integrals ofδ1(2T1α)andδ1(2T2α) depend on magnetic interactions, and the energy integrals ofδ2(2T1α) andδ2(2T2α)depend on trigonal CF.
Sixthly, the convergence of PTM formulas of 4T2 and 4T1a terms for d3 ions at tetragonal symmetry has been analyzed. The results show that, the convergence of PTM formulas is better in the cases of stronger CF.
Seventhly, the g factors of 2E state of d3 ions at trigonal symmetry have been investigated. The g factors 2E state of Al2O3:Mn4+ and Al2O3:Cr3+ systems have been explained theoretically. It is found that, there exists combined mechanism. And the relative magnitude of various magnetic mechanisms has been studied. The contributions to ZFS of ground state from slight magnetic interactions are considerable. But the contributions to ZFS of 2E state from slight magnetic interactions are small. For g factors, the contributions to g factors of the ground state and E'(2E) state from SS, SOO and 00 magnetic interactions can not be omitted, but are slight to the g factors of E"(2E) state. The experimental values of g factors of 2E state of ZnGa2O4:Cr3+ systems have been explained. The values of g factors of 2E state for MgAl2O4:Cr3+ system have been predicted theoretically.
Eighthly, the local structure of Al2O3:V2+, Al2O3:Cu3+, CsMgX3:V2+(X=Cl,Br,I) systems and LiNbO3:Ni2+ systems have been studied by using ligand plane displacement model, center ions displacement model and double displacement model, respectively. The coincidence between the calculated results and the experimental results shows that the models we adopted are reasonable.
(1)通过对晶场势的分析,说明了晶场参量的概念,并对为计算晶场参量而采用的三种模型进行了比较分析。在晶体场理论的发展过程中,出现了几种不同的晶场符号表示,给后来的研究者对晶场符号的使用造成了混乱。本文对不同晶场符号的物理意义进行了说明,分析了晶场符号之间的关系,澄清了文献中对晶场符号使用的混乱。利用群表示理论推导得到了dN离子在三角对称和四角对称下的光谱精细结构。利用自旋哈密顿理论推导得到了基态和激发态零场分裂和g因子的计算公式。
(2)在中间场耦合图像下建立了过渡金属掺杂离子完全能量矩阵。在磁相互作用中考虑了除自旋与轨道相互作用之外的自旋与自旋相互作用、自旋与另一轨道相互作用以及轨道与轨道相互作用等微小磁相互作用。推导得到了基态和低激发态自旋哈密顿参量的计算公式,并利用VB语言编制了相应的计算程序。
(3)利用本文建立的理论和编制的程序,研究了d3离子激发态对基态自旋哈密顿参量的影响。在三角对称和四角对称下,下列结果是成立的：基态是4F态,除自旋四重态外,自旋二重态对基态的零场分裂也有重要贡献。而对g因子来说,二重态对其基本没有贡献；SS机制和SOO机制对基态零场分裂参量的贡献主要由四重态决定,二重态的贡献很小；SO-SS-SOO联合机制对基态零场分裂参量的贡献主要由四重态决定,二重态也有相当的贡献；SS机制对g因子几乎没有影响,而SOO机制对g因子有一定影响,但这一影响也是由四重态决定,与二重态无关。
(4)研究了三角对称下d2／8离子激发态对基态自旋哈密顿参量的影响。为了考察自旋单态和自旋三重态对基态自旋哈密顿参量的贡献,分别在三种情况下计算了三角对称下d2／8离子基态自旋哈密顿参量。结果说明,SO机制对基态自旋哈密顿参量的贡献是主要的,这其中三重态的贡献是主要的,而单态的贡献相对较小。SS机制和SOO机制以及SO-SS-SOO联合机制对基态零场分裂参量的贡献主要由三重态决定,单态的贡献很小。SS机制对g因子几乎没有影响,而SOO机制对g因子有一定影响,但这一影响也是由三重态决定,与单态无关。但是联合作用机制对g因子的贡献中,单态的贡献是不可忽略的。OO作用对g因子的贡献也是只由三重态决定,与单态无关。
(5)建立了激发态零场分裂理论,研究了三角对称下d3离子激发态零场分裂的性质,指出了文献中的印刷错误。对4T2和4T1a态定义了其零场分裂计算公式,对2T1a和2T2a定义了两个零场分裂表达式。计算结果表明,4T2和4T1a项的零场分裂主要来源于三角晶场作用。在磁相互作用的贡献中,低激发态零场分裂主要来源于旋轨耦合作用,微小磁相互作用对低激发态零场分裂的贡献较小。δ1(2T1a。)和δ1(2T2a)这两个能级间隔来自于磁相互作用,δ2(2T1a)和δ2(2T2a)这两个能级间隔主要来源于三角晶场作用。
(6)对四角对称下d3离子4T2和4T1a态零场分裂微扰公式的收敛性进行了分析。结果表明,在较强晶场的情形下,微扰公式的收敛性较好。
(7)研究了三角对称下d3离子2E态g因子的性质,从理论上解释了Al2O3：Mn4+体系和Al2O3：Cr3+体系的2E态g因子。研究发现磁相互作用间存在联合机制,并对各种机制贡献的相对大小进行了研究。微小磁相互作用对基态零场分裂的贡献是不可忽略的,但对2E态零场分裂是很小的。对g因子来说,来自SS、SOO和OO相互作用对基态和E′(2E)态的g因子贡献也是可观的,但对E″(2E)态g因子的贡献是很小的。解释了ZnAl2O4:Cr3+体系2E态g因子的实验值,并对照文献中对ZnGa2O4：Cr3+体系2E态g因子的计算,指出文献中存在有印刷错误。对MgAl2O4：Cr3+体系2E态g因子进行了理论预测,这些结果有待于相应的实验做进一步的验证。
(8)作为本文理论的应用,研究了Al2O3：V2+体系、Al2O3:Cu3+体系、CsMgX3:V2+(X=Cl、Br、I)体系和LiNbO3：Ni2+体系的微观局域结构,理论计算结果和实验值的符合说明我们采用的模型是合理的。
By using complete diagonalization method (CDM), the spin-Hamiltonian (SH) parameters of ground state and excited states for d3 ions and d2/8 ions at trigonal and tetragonal symmetry are studied, based on crystal field theory. The main contents and innovations are as follows:
Firstly, by analyzing the crystal field potential, the concepts of crystal field parameters are illustrated. The three models adopted to calculate CF parameters are compared and analyzed. In the development of CF theory, various CF notations are used, this result in confusion to researchers. In this thesis, the physical meanings of various CF notations are illustrated, the relations between various CF notations are analyzed, and the confusions are clarified. The spectra fine structure of dN ions at trigonal and tetragonal symmetry are deduced by group theory.
Secondly, in the intermediate crystal field coupling scheme, the complete energy matrices for transition metal (TM) ions are constructed. In addition to general spin-orbit (SO) interactions, the slight magnetic interactions including spin-spin (SS), spin-other-orbit (SOO) and orbit-orbit (OO) interactions are taken into account. Formulas of SH parameters of ground state and excited states are deduced, and the corresponding computer program are developed.
Thirdly, by using the theory and the program developed in this thesis, the contribution to SH parameters of ground state from excited states of d3 ions are investigated. For trigonal and tetragonal symmetry, these results are obtained:(a) The ground state is 4F, contributions from spin doublets are appreciable. For g factors, there are almost no contributions from spin doublets, (b) The contributions from SS and SOO mechanisms mainly depend on spin quartets, and the contributions from spin doublets are appreciable. (c) The contribution to g factors from SS mechanism almost is zero, but the contribution to g factors from SOO mechanism is appreciable, and this contribution depends on spin quartets only.
Fourthly, the influence to SH parameters of ground state of d2/8 ions from excited states at trigonal symmetry are studied. It is shown that, the contribution from SO mechanism is dominant, in which, the contributions from spin triplets are mainly. The contributions to ZFS of ground state from SS, SOO and SO-SS-SOO combined mechanisms are mainly due to spin triplets. The contribution to g factors from SS mechanism almost is zero, but the contribution to g factors from SOO mechanism is appreciable, and this contribution depends on spin triplets only. Contributions to g factors from 00 mechanism are depending on spin triplets only.
Fifthly, the theory of ZFS of excited states have been established. The ZFS of low-lying states for d3 ions at trigonal symmetry have been studied, the misprint in reference are pointed out. The formulas of ZFS of 4T2,4T1a,2T1a and 2T2a have been defined. It is shown that, the ZFS of 4T2 and 4T1a terms are mainly depend on trigonal CF. The contribution to ZFS of low-lying states from spin-orbit mechanism is dominant, and the contributions from other mechanisms are slight. The energy integrals ofδ1(2T1α)andδ1(2T2α) depend on magnetic interactions, and the energy integrals ofδ2(2T1α) andδ2(2T2α)depend on trigonal CF.
Sixthly, the convergence of PTM formulas of 4T2 and 4T1a terms for d3 ions at tetragonal symmetry has been analyzed. The results show that, the convergence of PTM formulas is better in the cases of stronger CF.
Seventhly, the g factors of 2E state of d3 ions at trigonal symmetry have been investigated. The g factors 2E state of Al2O3:Mn4+ and Al2O3:Cr3+ systems have been explained theoretically. It is found that, there exists combined mechanism. And the relative magnitude of various magnetic mechanisms has been studied. The contributions to ZFS of ground state from slight magnetic interactions are considerable. But the contributions to ZFS of 2E state from slight magnetic interactions are small. For g factors, the contributions to g factors of the ground state and E'(2E) state from SS, SOO and 00 magnetic interactions can not be omitted, but are slight to the g factors of E"(2E) state. The experimental values of g factors of 2E state of ZnGa2O4:Cr3+ systems have been explained. The values of g factors of 2E state for MgAl2O4:Cr3+ system have been predicted theoretically.
Eighthly, the local structure of Al2O3:V2+, Al2O3:Cu3+, CsMgX3:V2+(X=Cl,Br,I) systems and LiNbO3:Ni2+ systems have been studied by using ligand plane displacement model, center ions displacement model and double displacement model, respectively. The coincidence between the calculated results and the experimental results shows that the models we adopted are reasonable.
引文
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