二维范德华磁性材料由于其独特的磁性特征，对研究低维极限磁态、寻找新型磁性材料、制造高性能自旋器件具有重要意义。二维磁性材料的层内和层间耦合存在显著的强度差异且具有不同的磁交换机制。研究发现，层数的堆叠会对晶体的层内、层间磁相互作用产生影响，进而实现磁态的切换和居里温度的调控。本文基于第一性原理密度泛函理论，对于四种二维范德华磁性材料CrI₃、Cr₂Ge₂Te₆、Fe₃GeTe₂和Fe₃GaTe₂的磁交换系数和磁振子谱进行了计算和绘制，通过理论计算的结果对材料的多种磁交换作用进行了分析，并探讨了层数堆叠对磁交换作用和磁振子谱形貌的影响。

对于CrI₃和Cr₂Ge₂Te₆两种材料，都采用能量映射和线性响应两种方法对单层结构进行了计算，考虑到了最近邻、次近邻和次次近邻之间的交换系数。详细讨论了最近邻Cr原子间的超交换作用和直接交换作用的竞争关系；并揭示了Cr原子平面六边形蜂窝状结构与自旋波谱K点附近的Dirac锥具有对应关系。

在此基础上额外讨论了CrI₃的多层结构，发现层内最近邻磁交换作用随堆叠层数的增加而增强，且中间层相较于顶层和底层展现出更强的FM层内最近邻交换作用，与体块CrI₃具有较高居里温度的事实相符。多层结构CrI₃的自旋波谱显示，层内磁交换确定了磁振子谱的基本形貌，层间磁交换作用在层内磁交换作用的基础上进一步改变磁振子谱的形貌，打开了自旋波谱Dirac点的能隙；并且确定不同层间堆叠方式具有不同的层间磁交换机制，进而导致了多层结构CrI₃自旋波谱在Γ点和K点的不同行为，其本质原因可以归于不同层间堆叠方式所对应的不同对称性。

对于导体Fe₃GeTe₂和Fe₃GaTe₂，考虑到其巡游磁性，仅采用了线性响应法对单层结构和体块结构进行了计算。考虑了4对层内作用和3对层间作用，发现层内和层间都同时存在铁磁与反铁磁的交换作用，且都以铁磁占主导。无论是Fe₃GeTe₂还是Fe₃GaTe₂，原子层堆叠所带来的层间磁相互作用远小于层内磁相互作用，且层间堆叠对层内磁交换作用的影响基本可以忽略，因而体块结构的磁振子谱仅相对于单层结构产生微小的劈裂，基本不改变磁振子谱的形貌。Fe₃GaTe₂与Fe₃GeTe₂具有完全不同的Fe离子层层内磁交换作用，这导致了两者在磁振子谱形貌上的显著差异；此外，相比于Fe₃GeTe₂，Fe₃GaTe₂具有更强的Fe离子层层内FM交换作用，这与Fe₃GaTe₂较高的居里温度相吻合，从磁交换机制角度考虑，这与Ga和Ge所起到的介导作用有着密切联系。

Two-dimensional van der Waals magnetic materials are of great significance for the study of magnetic states with low-dimensional limit, the search for new magnetic materials and the manufacture of spin devices with high efficiency, taking advantage of their unique magnetic characteristics. There is a significant difference in the strength of the intralayer and interlayer magnetic coupling, which correspond to different magnetic exchange mechanisms. It is found that the stacking of layers can affect the magnetic interaction between layers and within layers, and thus realize the switching of magnetic states and the control of Curie temperature. In this paper, based on the first principle calculation, we calculate the magnetic exchange constants and plot spin spectrum of four two-dimensional van der Waals magnetic materials CrI₃, Cr₂Ge₂Te₆, Fe₃GeTe₂ and Fe₃GaTe₂. Based on the results of theoretical calculation, the magnetic exchange mechanisms of the materials are analyzed. The effects of layer stacking on magnetic exchange and spin spectrum are also discussed.

For CrI₃ and Cr₂Ge₂Te₆, the monolayer structures are calculated by energy mapping method and linear response method, taking into account of the exchange constants between the nearest neighbor, the second nearest neighbor and the third nearest neighbor. The competition between the superexchange and the direct exchange between the nearest Cr atoms is discussed. Moreover, it is determined that the planar hexagonal honeycomb structure of Cr atom corresponds to the Dirac cone at the K point of the spin spectrum.

On this basis, the multilayer structure of CrI₃ is discussed. It is found that the nearest-neighbor magnetic exchange increases with the number of stacked layers, and the middle layer has stronger FM nearest-neighbor exchange than the top layer and the bottom layer, which is consistent with the fact that bulk CrI₃ has a higher Curie temperature. In terms of the spin spectrum of CrI₃ multilayer structure, it is found that the intralayer magnetic exchange determines the basic morphology of the spin spectrum, and the interlayer magnetic exchange further changes the morphology of the spin spectrum on the basis of the intralayer magnetic exchange, opening the energy gap at the Dirac point. Moreover, it is determined that different stacking modes have different interlayer magnetic exchange mechanisms, which leads to the different behaviors of spin spectra at Γ and K points, attributed to the different symmetries corresponding to different stacking modes.

Considering the itinerant property of Fe₃GeTe₂ and Fe₃GaTe₂, only the linear response method is used to calculate the monolayer structure and bulk structure. Considering 4 pairs of intralayer interaction and 3 pairs of interlayer interaction, it is found that there are both ferromagnetic and antiferromagnetic exchange between layers and within layers, and all are dominated by ferromagnetism. Regardless of Fe₃GeTe₂ or Fe₃GaTe₂, the interlayer magnetic interaction caused by layer stacking is much smaller than the intralayer magnetic interaction, and the influence of stacking on the intralayer magnetic exchange can be almost ignored. In this way, the spin spectrum of the bulk structure only has a slight split compared with that of the monolayer structure, and does not change the morphology of the spin spectrum. Fe₃GaTe₂ and Fe₃GeTe₂ have completely different magnetic exchange within Fe layers, which leads to the difference in spin spectrum morphology. In addition, compared with Fe₃GeTe₂, Fe₃GaTe₂ has stronger FM magnetic exchange within Fe layers, which is consistent with its higher Curie temperature. From the perspective of magnetic exchange mechanism, this is closely related to the mediating effect of Ga and Ge.