过渡金属化合物中的过渡金属原子具有未填满的d轨道，因而属于关联电子体系。在这样的体系中，电子关联效应和自旋、轨道、电荷、晶体场等自由度的耦合会导致体系展现出丰富的物理性质，如复杂的相图、大的介电常数、超导电性以及庞磁阻效应等。对于过渡金属化合物这样的实际材料而言，准确计算其关联电子结构对于理解其展现出的物理性质非常重要。在过往关于铁基超导体，莫特绝缘体，重费米子材料的研究中，密度泛函理论结合动力学平均场理论被证明是处理关联电子体系有效的方法之一。    在本论文中，我们采用密度泛函理论结合动力学平均场理论方法对几种过渡金属化合物的关联电子结构进行了研究。在第一个工作中，我们探究了范德瓦尔斯材料CrI₃的带隙来源和结构相变驱动力。我们的计算得到了和实验一致的结果，包括Cr离子磁矩和带隙。计算结果表明CrI₃不是常见的莫特-哈伯德绝缘体，而是莫特-洪特绝缘体，洪特耦合作用对顺磁态CrI₃带隙的形成起到了决定性作用。通过分析CrI₃低温相和高温相的结构以及密度泛函理论结合动力学平均场理论方法计算得到的高温相和低温相中Cr离子的磁矩大小，我们提出铁磁自旋涨落驱动了CrI₃发生从高温相到低温相的结构相变。除此之外，我们的计算还表明将CrI₃中的I原子替换成另外两种卤族元素得到的化合物即CrCl₃和CrBr₃也是莫特-洪特绝缘体。

在第二个工作中，我们对笼目金属Mn₃Sn进行了系统的研究。计算结果表明顺磁态Mn₃Sn的能带展现出典型的笼目晶格具有的特征，包括平带，有质量的狄拉克点以及鞍点。计算得到的Mn 3d电子的质量重整化系数和费米能级附近能带的带宽压缩系数共同表明顺磁态Mn₃Sn是具有中等电子关联强度的笼目金属。对于非共线反铁磁态Mn₃Sn，理论计算得到了和实验一致的结果，包括Mn离子磁矩和角分辨光电子能谱。密度泛函理论结合动力学平均场理论方法计算得到的动量分辨谱函数相较于密度泛函理论方法计算得到的结果发生了以下两点重要改变：第一，K-M路径上的外尔点从费米能级上方约40meV移动到了费米能级下方约5meV。第二，费米能级附近能带的带宽变窄，并且对于不同的能带，变窄的程度不同。最后，我们还对几种不同的非共线磁结构进行了计算，计算结果表明K-M路径上外尔点的存在与否和具体的磁结构有关，所以可以通过调节外加磁场的方式来控制K-M路径上外尔点的有无，进而对受其影响的物理性质，包括手性反常，负磁阻效应和反常霍尔效应进行调控。
 

  There are transition metal atoms which have partly filled d orbitals in transition metal compounds, and thus belong to the correlated electron system. In such systems, the coupling of the electronic correlation effect with other degrees of freedom such as spin, orbit, charge and crystal field could result in the system exhibiting rich physical properties, such as complex phase diagram, large dielectric constant, superconductivity and colossal magnetoresistance. For real materials including transition metal compounds, it is important to accurately calculate their correlated electronic structures for understanding the physical properties they exhibit. In the previous studies on iron-based superconductors, Mott insulators and heavy fermion materials, density functional theory combined with dynamical mean-field theory has been proved to be one of the effective methods to deal with correlated electron systems.    

  In this dissertation, we have studied the correlated electronic structures of several transition metal compounds by means of density functional theory combined with dynamical mean-field theory. In the first work, we investigated the source of the band gap and the driving force of the structural phase transition of the van der Waals
material CrI₃. Our calculational results are consistent with the experimental results, including the magnetic moment of Cr and band gap. Our results indicate that CrI₃ is not a conventional Mott-Hubbard insulator, but a Mott-Hund’s insulator. Hund’s coupling plays a decisive role in the formation of the band gap of CrI₃ in the paramagnetic state. By analyzing the structure of high-temperature phase and low-temperature phase of CrI₃ and magnetic moments of Cr ions in the two phases calculated by the density functional theory combined with dynamical mean-field theory, we propose that the structural phase transition of CrI₃ from the high-temperature phase to the low-temperature phase is driven by ferromagnetic spin fluctuations. In addition, our results indicate that the compounds obtained by replacing the I atom in CrI₃ with two other halogen elements, namely CrCl₃ and CrBr₃, are also Mott-Hund’s insulators.     In the second work, we systematically studied the kagome metal Mn₃Sn. Our results show that the band structure of Mn₃Sn in the paramagnetic state exhibits typical features of the kagome lattice, including flat bands, massive Dirac points and saddle points. The calculated mass
enhancement of Mn 3d electrons and the bandwidth renormalization factor of the bands near the Fermi energy (E_F) together indicate that paramagnetic Mn₃Sn is a kagome metal with intermediate electronic correlation strength. As for Mn₃Sn in the noncollinear
antiferromagnetic state, our calculational results are consistent with the experimental results, including Mn magnetic moment and angle-resolved photoemission spectroscopy. The momentum-resolved spectral functions obtained by DFT+DMFT method has the following two important changes compared with the results obtained by DFT method: first, the Weyl point along K-M moves from ~40meV above E_F to ~5meV below E_F. Second, the bandwidth narrows differently for different bands near E_F. What’s more, we have calculated the electronic structures of several different magnetic configurations of Mn atoms in Mn₃Sn and found that the existence of the Weyl point along the K-M path are related to specific magnetic configuration. We can therefore control the existence of the Weyl point along the K-M path and related physical properties, including chiral anomaly, negative magnetoresistance effect and anomalous Hall effect by tuning the magnetic fields applied to this material.