Topological Hall Effect Driven By Spin Chirality

Topological excitations of quantum matter are the subject of extensive interest in condensed matter physics.They have been theoretically predicted and experimentally observed in electron systems.Topological band structure of electrons can be probed by the Hall effect,linked to the Berry curvature throughout the Brillouin zone.In principle,the concept of topological band theory is independent of the statistical nature of?quasi-?particles.Therefore,the concepts of topological excitations can be extended to neutral bosonic systems such as magnons.In this thesis,we first review the research of topological magnons in ordered mag-netic insulators and confirm them as the analogue of Chern insulators requires inherently to break time-reversal symmetry.For ferromagnets,the scalar spin chirality can emerge in the form of ring exchange and provides a fictitious magnetic field for the magnons.Based on the linear response theory,the Hall conductivity has proven to be closely con-nected to the Berry curvature.On the other hand,for antiferromagnets such as frustrated Kagome magnets,a noncoplanar spin configuration with finite averaged scalar spin chi-rality breaks time-reversal symmetry macroscopically and is believed to respond to the nontrivial topology and the corresponding magnon Hall effect.The detailed analysis suggests that,unlike the cases of ferromagnets,the role of the spin chirality on magnon Hall effects in antiferromagnets still remains puzzling in many aspects.In next chapter,the Hall-like transport has been proved to be a chirality-driven effect in purely spin systems.We have developed the theory of magnon thermal Hall effects in antiferromagnetic systems by revealing an underlying relation between the Dzyaloshinskii-Moriya interaction?DMI?and the scalar spin chirality.The dynamic fluctuation of the spin chirality is shown to directly respond to the nontrivial topology of magnon bands.In materials such as the jarosites compounds KFe₃?OH?₆?SO₄?₂and veseignite BaCu₃V₂O₈?OH?₂in the presence of in-plane DMI,the time-reversal sym-metry can be broken by the fluctuations of spin chirality even in the case of coplanar q=0 magnetic configuration.The spin-wave Hamiltonian is influenced by a ficti-tious magnetic flux determined by the in-plane DMI.Topological magnon bands and corresponding nonzero Chern numbers are presented without the need of a canted non-coplanar magnetic ordering.The canting angle dependence of thermal Hall conductivity is discussed in detail as well.These results provide a clear principle of chirality-driven topological Hall effects in magnetic systems.