Magnons with nontrivial Berry curvatures have emerged as a new research area in magnetism and spintronics due to their fundamental interest as well as practical utilities such as back-scattering-free spin-transport channels of topological magnons. In this talk, we will discuss recent developments in the Berry-curvature physics of magnons and their related cousins in two-dimensional (2D) magnets. We will begin by discussing one of the first magnonic topological insulators realized in a honeycomb 2D ferromagnet such as CrI3, which is shown to give rise to the thermal Hall effect via the finite Berry curvature of magnons [1]. Recently, the field of topological magnons has been expanded into the field of topological bosons beyond simple magnons. As one concrete example, we will introduce a new concept of topologically non-trivial magnon-phonon hybridized mode called a topological magnon-polaron, which can be realized in a 2D ferromagnet [2] and antiferromagnet [3] such as MnPS3 via generic magnetoelastic coupling. In the last part of the talk, we will discuss the recently-discovered relation between the Berry curvature of magnons and the scalar spin chirality in 2D magnets, which gives rise to the intrinsic Hall effect of the scalar spin chirality without any spin-orbit coupling [4, 5]. The talk will be concluded with a future outlook on the research of topological magnons and beyond.

[1] S. K. Kim, H. Ochoa, R. Zarzuela, and Y. Tserkovnyak, “Realization of the Haldane-Kane-Mele Model in a System of Localized Spins,” Phys. Rev. Lett. 117, 227201 (2016)

[2] G. Go, S. K. Kim, and K.-J. Lee, "Topological Magnon-Phonon Hybrid Excitations in Two-Dimensional Ferromagnets with Tunable Chern Numbers," Phys. Rev. Lett. 123, 237207 (2019)

[3] S. Zhang, G. Go, K.-J. Lee, S. K. Kim, "SU(3) Topology of Magnon-Phonon Hybridization in 2D Antiferromagnets," Phys. Rev. Lett. 124, 147204 (2020)

[4] G. Go, D. An, H.-W. Lee, and S. K. Kim, "Magnon Orbital Nernst Effect in Honeycomb Antiferromagnets without Spin–Orbit Coupling," Nano Lett. 24, 5968 (2024)

[5] G. Go, D. P. Goli, N. Esaki, Y. Tserkovnyak, S. K. Kim, "Scalar Spin Chirality Hall Effect," arXiv:2411.03679

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