This article reviews the past works on topological Hall effects of magnons in insulating magnets with a particular focus on ferrimagnets. First, we discuss the magnonic quantum Hall effect in ferromagnets induced by the Aharonov–Casher effect. Specifically, starting from the classical Hall effect of magnons proposed by Meier and Loss [Phys. Rev. Lett. 90, 167204 (2003)], we establish the Landau quantization of magnons with suitable electric-field configuration through the Aharonov–Casher effect in ferromagnets. Magnons are shown to form the Landau levels, giving rise to chiral edge magnon states. Second, by making use of the Néel magnetic order of insulating antiferromagnets, we show that a bosonic counterpart of electronic topological insulators can be established by the electric field gradient via the Aharonov–Casher effect, extending the notion of symmetry protected topological phases to antiferromagnetic insulators. Using magnons with opposite magnetic dipole moments associated with the Néel order, we establish a magnonic analog of the quantum spin Hall effect characterized by helical edge magnon states. We generalize this known result for antiferromagnets to ferrimagnets, leading to the discussion of the topological Hall effect of magnons in the bulk of ferrimagnets. Third, we show that the topological Hall effect is expected to exist in ferrimagnets with skyrmion crystal, by extending the magnetic texture-induced thermal Hall effects of magnons in skyrmion crystal phases of FMs proposed by Hoogdalem et al. [Phys. Rev. B 87, 024402 (2013)] into ferrimagnets. One particular feature of the topological Hall effect of ferrimagnets is that it is thermally tunable in that the direction of heat flux changes across the angular momentum compensation point at which the angular momentum changes its sign with respect to the magnetization direction. Last, by enumerating the recent development of experimental techniques, we give our perspective and provide a platform to discuss a direction for further development of topological magnonics.

中文翻译：

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Ferrimagnets中的磁振子的拓扑霍尔效应

本文回顾了过去有关绝缘磁体中的磁振子的霍尔效应的霍尔效应的工作，其中特别着重于铁氧体。首先，我们讨论由阿哈罗诺夫-卡希尔效应引起的铁磁体中的强子量子霍尔效应。具体而言，从Meier和Loss提出的经典的磁振子霍尔效应开始。莱特牧师 90，167204（2003）]，我们通过铁磁体中的Aharonov–Casher效应建立了具有适当电场配置的磁振子的Landau量化。示出了马可农形成兰道能级，从而产生手性边缘马可农状态。第二，通过利用绝缘反铁磁体的Néel磁阶，我们证明可以通过Aharonov-Casher效应通过电场梯度建立电子拓扑绝缘体的玻色对应物，从而将对称受保护拓扑相的概念扩展到反铁磁绝缘体。使用具有与Néel阶相关的相反磁偶极矩的磁振子，我们建立了以螺旋边缘磁振子状态为特征的量子自旋霍尔效应的磁悬浮模拟物。我们将反铁磁体的这个已知结果推广到铁锰矿，导致对大部分铁蛋白中的马农的拓扑霍尔效应的讨论。第三，我们证明了通过扩展Hoogdalem等人提出的FM的Skyrmion晶体相中的磁振子的磁织构感生的热Hall效应，有望在具有Skyrmion晶体的铁酸盐中存在拓扑霍尔效应。[物理 版本B87，024402（2013）]为亚铁磁体。铁酸盐的拓扑霍尔效应的一个特殊特征是它是可热调谐的，因为热通量的方向在角动量补偿点上变化，在该角动量补偿点处，角动量相对于磁化方向改变其符号。最后，通过列举实验技术的最新发展，我们给出了自己的观点并提供了一个平台，以讨论进一步发展拓扑磁电机的方向。