由于磁序和拓扑的相互耦合，磁性拓扑材料具有丰富的演生量子效应和广阔的应用前景，因而备受关注。目前实验实现的磁性拓扑材料体系大多具有结构复杂、工作温度低等特点，限制了其在基础研究和器件应用方面的进一步发展。因而优化现有的磁性拓扑材料体系、设计新型高温磁性拓扑材料是该领域的关键科学问题。另一方面，实验上关于磁性拓扑材料的手性和能隙存在许多困惑之处。若能理解其背后的微观物理机制，将有利于指导磁性拓扑材料的物性优化。基于第一性原理计算、对称性分析和低能有效模型分析，本论文系统地研究了磁性拓扑材料中磁性耦合、手性及拓扑能隙的微观机制，并探索了掺杂、异质结工程、电场、应变、静水压等调控手段对材料体系的磁性与拓扑电子性质的影响。为理解实验上关于量子反常霍尔(QAH)绝缘体的手性与能隙的困惑，通过构建第一性原理QAH材料数据库，我们系统地探索了决定QAH材料性质的微观机制，得到了磁交换和自旋轨道耦合共同作用诱导拓扑能隙的一般物理图像。我们发现在经典磁性半导体理论中被忽略的库仑交换作用在一大类磁性拓扑材料中起到主导作用。进一步地，我们提供了用于QAH材料性质预测的简单指标并提出多种材料性能优化策略，如磁性共掺杂、异质结工程、自旋轨道近邻等。目前关于陈绝缘体的研究聚焦于铁磁绝缘体，但是在自然界中反铁磁绝缘体更为常见且可以有较高的磁转变温度。通过对称性分析和第一性原理计算，我们提出通过调控反铁磁材料的对称性破缺来实现高温陈绝缘体的材料设计策略，并预测在SrMnPb薄膜中存在单轴应变诱导的高温、高陈数、易调控的拓扑态。进一步地，基于其应变可控的拓扑性质，我们提出若干基于反铁磁陈绝缘体的拓扑自旋电子器件的设计构想。静水压是调控磁性和拓扑电子性质的一种常见手段。我们系统研究了静水压对MnBi2Te4家族材料的晶体结构、磁性与拓扑电子性质的影响，预测了静水压诱导的一系列的磁性相变和拓扑相变。由于压力导致层内和层间反铁磁作用的增强，其磁基态由A型反铁磁态转变到具有层内反铁磁耦合的不寻常的A型反铁磁态，最终演变到几何阻挫态。进一步地，不同类型的磁性拓扑态，包括A型或G型反铁磁拓扑绝缘体、第一类或第二类磁性外尔半金属和高阶磁性拓扑绝缘体，能够在静水压下该族材料的不同磁性相中实现。
Magnetic topological materials exhibit abundant emergent quantum effects and broad potential applications due to the interplay of magnetism and topology, which have attracted enormous research attention. The current experimentally realized magnetic topological material systems are structurally complex and their working temperatures are ultralow, which limits their further developments in fundamental science and device ap- plications. Thus optimizing the existing magnetic topological materials and designing new high-temperature magnetic topological materials become key research subjects of the field. On the other hand, the microscopic mechanism of chirality and topological gap remains as a puzzle in magnetic topological materials. Understanding the underlying mechanism can contribute to guiding the property optimization of magnetic topological materials. Based on first-principles calculation, symmetry analysis and low-energy effective model analysis, we systematically investigated microscopic mechanisms determining magnetic coupling, chirality and topological gap, and explored the influence of doping, heterostructuring, electric field, strain and hydrostatic pressure on the magnetic and topological electronic properties of the materials.In order to understand the chirality and band gap puzzles of quantum anomalous Hall (QAH) insulators in experiments, based on first-principles calculated QAH material database, we systematically explore microscopic mechanisms determining the QAH material properties, and obtain a general physical picture of topological gap generation induced by the interplay of magnetic exchange and spin-orbit coupling. We find that the Coulomb exchange, which is neglected in the classical theory of magnetic semiconductors, is unexpectedly strong in a large class of QAH materials. Moreover, we provide simple indicators for property evaluation and suggest material design strategies to optimize QAH properties by magnetic codoping, heterostructuring, spin-orbit proximity, etc. Previous studies on Chern insulators mainly focused on ferromagnetic materials, while antiferromagnetic (AFM) insulators are common in nature and their magnetic transition temperatures can be high. Through symmetry analysis and first-principles calculations, we propose to design high-temperature Chern insulators by engineering symmetry breaking of two-dimensional AFM materials. Moreover, we predict uniaxial strain-induced high-temperature, high-Chern-number, easily tunable topological states in SrMnPb thin films. Based on the strain controllable topological properties, we further propose potential topological spintronic device applications of AFM Chern insulators.Hydrostatic pressure is a conventional tool to control magnetic and topological properties. We systematically investigate the influence of hydrostatic pressure on structural, magnetic, and topological electronic properties of MnBi2Te4-family materials and predict a series of magnetic and topological phase transitions induced by hydrostatic pressure. The magnetic ground state transits from normal A-type AFM to unusual A-type AFM with intralayer AFM coupling, and finally to geometrically frustrated states due to enhanced intralayer and interlayer AFM interactions under pressure. Furthermore, distinct magnetic topological states, including A-type or G-type AFM topological insulator, type-I or type-II magnetic Weyl semimetal, and high-order magnetic topological insulator, can be realized in various magnetic phases of these materials under pressure.
