自旋波是磁性材料中自旋的集体激发，通常将自旋波量子化后的准粒子称为磁振子。自旋波的传播可以不依赖于电荷进行，因此自旋波器件可以自然地避免传统电子器件中因电子能量损失产生焦耳热的问题。对自旋波的研究目标之一就是通过对它的调控实现对信息的传输、储存和处理。研究不同材料体系中的自旋波的性质可以帮助我们更好地理解和运用自旋波。我们在本文中先结合实验合作组的实验结果发现了中心对称的铁磁体中与应变梯度相关的Dzyaloshinskii-Moriya(DM）相互作用，再利用对称性分析方法得到了这种由应变梯度引起的DM相互作用的有效形式以及它对自旋波的传播所带来的影响。除此之外，我们还探究了反铁磁体和亚铁体中偶极相互作用(dipole-dipole interaction)对自旋波性质所带来的影响。具体内容包括：
∙ 我们利用对称性分析的方法得到了具有中心反演对称性的属于-3m点群的铁磁性材料由应变梯度所导致的DM相互作用的有效形式。实验合作组对属于-3m点群的La_0.67Sr_0.33MnO₃薄膜施加了沿z方向的应变梯度E_zz,z，在自旋波垂直和平行于磁化强度传播时都观测到了自旋波频率具有非互易性。我们研究发现这是由于晶体的主轴方向与z方向之间的夹角导致由E_zz,z诱导的DM相互作用同时具有体(bulk)型和界面(interfical)型DM 相互作用的特征，这很好地解释了实验合作组所观察到的实验现象。另外，我们还分析了表面磁各向异性和磁化强度梯度两种因素对自旋波频率非互易性所带来的影响。
∙ 我们研究了单轴反铁磁体中的偶极自旋波，发现体系是一种由偶极相互作用导致的拓扑非平庸的磁振子节线(nodal line)半金属。更有趣的是，存在于体带能隙中的拓扑表面态具有手性-动量锁定的特征，所以在表面传播的拓扑表面态也具有非互易性。我们基于表面态的特性，提出了一种手性磁振子器件。
∙ 我们展示了在层状铁磁体堆叠而成的亚铁磁体中由偶极相互作用所引起同时受外场调控的磁振子拓扑相。对于垂直磁化情形，当沿易轴施加磁场时，系统可以从拓扑平庸的磁振子绝缘相转变到拓扑非平庸的节线环半金属相。当磁场与易轴成一定夹角时，倾斜的自旋构型将破坏磁振子节线环使其变为一对外尔点。此外，我们还展示了连接两个外尔点的两条磁振子弧。而当磁矩沿面内磁化时，无论磁矩是处于共线态还是倾斜态，体系始终处于外尔半金属相。
∙ 我们从理论上研究了单斜构型的范德瓦尔斯反铁磁体双层 CrI₃在考虑了偶极相互作用时的磁振子能谱。通过推导，我们发现这种二维范德瓦尔斯反铁磁体中的偶极相互作用也可以等效为磁振子系统中的自旋-轨道耦合。同时，不止在布里渊区的中心Γ点附近具有线性色散关系，在布里渊边界K和 K'谷附近也具有线性色散关系。通过增加双层CrI₃的层间距离，层间的偶极相互作用减弱，磁振子体系将从半金属态转变为绝缘态。

Spin waves are collective excitations of spins in ordered magnetic materials. The quasiparticles resulting from the quantization of spin waves are called magnons. The propagation of spin waves does not rely on charge transportation, so spin wave devices can naturally avoid the problem of Joule heating caused by electron energy loss in traditional electronic devices. One of goals for studying spin waves is to achieve information transmission, storage and processing by manipulating of spin waves. Studying the properties of spin waves in different materials can help us better understand and utilize them. In this thesis, we first discover, based on experimental results, the Dzyaloshinskii-Moriya interaction (DMI) related to strain gradient in centrosymmetric ferromagnets. Then, using symmetry analysis method, we obtain the effective form of the DMI induced by strain gradient and its impact on the propagation of spin waves. We also investigate the influence of dipole-dipole interaction (DDI) on the properties of spin waves in antiferromagnets and ferrimagnets. Specific contents include:
1. We derive the effective form of DMI induced by strain gradient in ferromagnetic materials belonging to the -3m point group with inversion symmetry. The experimental collaborators applied a strain gradient E_zz,z along the z direction to La_0.67Sr_0.33MnO₃ thin films belonging to the -3m point group, and observed nonreciprocity in spin wave frequencies when the transmissions of spin wave are perpendicular and parallel to the magnetization. We show that frequency nonreciprocities are due to the finite angle between the principal axis of crystal and the z direction, which leads to strain-gradient-driven DMI with both bulk- and interfacial-type components. Our results provide a good explanation for the experimental observations. In addition, we analyze the influence of surface magnetic anisotropy and magnetization gradient on the nonreciprocity of spin wave frequencies.
2. We discuss the dipolar spin waves in uniaxial antiferromagnets and find that the system is a topologically nontrivial magnon nodal-line semimetal caused by DDI. More interestingly, the topological surface states existing in the bulk band gap have the characteristics of chiral-momentum locking, so the topological surface states propagating on the surface are nonreciprocal. Based on the properties of surface states, we propose a chiral magnonic device.
3. We demonstrate the topological phases of magnons induced by DDI and regulated by external fields in ferrimagnets stacked by layered ferromagnet. For the perpendicular magnetized geometry, when a magnetic field is applied along the easy axis, the system can transition from a trivial magnon insulator phase to a topologically nontrivial nodal-loop semimetal phase. When the magnetic field is tilted from the easy axis, the noncollinear spin configuration breaks the magnon nodal loop and brings in a pair of Weyl points. Furthermore, we show the two magnon arcs connecting two projected Weyl points on surface Brillouin zone. However, for the in-plane magnetized geometry, the magnon system is always in the Weyl semimetal phase, regardless of the collinear state or the canted state.
4. We theoretically study the magnon spectrum of a monoclinic stacked van der Waals antiferromagnet bilayer CrI₃ considering DDI. We find that the DDI in this two-dimensional van der Waals system can introduce a spin-orbit coupling in the magnon system. Such a magnon spin-orbit coupling results in linear band crossings not only near the Γ point of the Brillouin zone, but also around the Brillouin boundary K and K' valley. By increasing the interlayer distance between the bilayer CrI₃, the DDI between the two layers is weakened, and the magnon system changes from the semimetal to an insulator.