Research on one particle picture near the localized-delocalized transition in the strongly correlated f-electron system

开发了用FLAPW和LDA+U方法计算强关联电子体系电子结构的程序代码，以处理磁态。得到了CeU_2Si_2的亚磁转变区的电子结构和CeIn_3在压力下的电子结构。结果强烈地依赖于U的大小和外加磁场，因此这种依赖关系需要进一步研究。现在甚至可以用LDA+U方法得到电场梯度(EFG)。结果表明，非对称性参数强烈依赖于多f态的组态，即使是立方对称下的单重态也是如此。这表明EFG直接与NQR频率相比较，获得了确定多f电子构型的重要信息。另一方面，为了解决j-j耦合模型中被晶体电场势能分裂的多个f电子态与LS耦合模型中得到的多个f电子态，甚至在定性上不兼容的问题，建立了j-j耦合方案的有效晶场模型。众所周知，在j-j耦合方案中，f^2态的非Kramers双重态是不能得到的，因为在j=5/2空间中没有出现6阶项。我们已经提出在CEF计算中必须包含1/lambda量级的项，其中lambda是自旋-轨道相互作用的强度，并假定在j-j耦合格式中是无限大的。这意味着在j-j耦合方案中考虑了j=7/2的贡献。结果表明，我们的有效j-j模型的结果与LS耦合格式的结果在数量上是一致的，即使对于填充的Skutterydute中的T_h对称性也是如此。

The program code for electronic structure calculations with an FLAPW and an LDA+U method has been developed for strongly correlated electron systems, to treat the magnetic states. Then electronic structures are obtained for CeRu_2Si_2 in the region of meta magnetic transition, and for CeIn_3 under pressures. It revels that the results strongly depend on the magnitude of U and the applied magnetic field, so such the dependence should be investigated more. Now the electric field gradients(EFG) can be obtained even by the LDA+U method. It has been revealed that the asymmetry parameters strongly depend on the configurations for multi f states even for the singlet state under a cubic symmetry. This indicates that the EFG, directly compared with NQR frequencies, obtains important information to determine the configuration of the multi f electrons. On the other hand, the effective model for the crystalline electric filed (CEF) for the j-j coupling scheme has been developed, to solve the problem that the multi f electron states split by the CEF potential in the j-j coupling model are not compatible, even qualitatively, with those obtained in the LS coupling scheme. As well known, the non-Kramers doublet cannot be obtained for f^2 state in the j-j coupling scheme, because of no 6^<th> order term appearing in j=5/2 space. We have proposed that the term in the order of 1/lambda must be included in the CEF calculations, where lambda is the strength of the spin-orbit interactions, and assumed to be infinite in the j-j coupling scheme. This means that the contributions from j=7/2 are taken into account in the j-j coupling scheme. Then it is shown the results in our effective j-j model quantitatively agree with those in the LS coupling scheme, even for the T_h symmetry in filled skutterydutes.