The anomalous Hall effect is an ubiquitous phenomenon in magnetic materials but it vanishes in time reversal systems. Nevertheless, Sodemann and Fu [1] suggested that a second order response in the electric field is allowed in time reversal invariant materials without inversion symmetry, as a consequence of the shift in the Fermi distribution function when the electrons go out of equilibrium. This nonlinear Hall effect is driven by the curvature dipole (BCD), which motivated several experiments [2,3] and encouraged the exploration of numerous platforms to enhance the resulting Hall current. In this context, topological materials such as Weyl semimetals (WSM) are excellent candidates to exhibit large values of nonlinear Hall effect due to monopoles of Berry curvature. In addition, the Fermi arcs that connect Weyl nodes of opposite chirality have a known impact on the anomalous Hall effect, but an extended analysis of the surface states is still missed at the level of the nonlinear Hall effect, especially in the regime when there is an important tilting of the Weyl cones. In this work [4], we reveal the contribution of the surface states to the BCD in WSM. Starting from a two-band model [5,6] and applying a slab construction method [7], we deduce that the topological nature of the surface states does not play a crucial role on the BCD. Besides, the transition between type I and type II WSM uncovers a strong impact of the Fermi pockets' projections because of a higher number of states at the surface rather than at the bulk. In contrast, after comparing to the bulk instance we notice that track states' projections does not show a profound effect on the BCD. We extend our study to the realistic case of WTe2 thin film using a Wannier-projected tight-binding representation, confirming that there is a notorious thickness dependence on the BCD subjected to the slab under consideration. 
**References** [1] I.Sodemann and L.Fu. Physical Review Letters 115, 216806 (2015).
[2] K.Kang, T.Li, E.Sohn. Nature Materials 18, p. 324-328 (2019).
[3] Q.Ma, S.Xu, H.Shen. Nature 565, p. 337-342 (2019).
[4] D.García Ovalle, A.Pezo and A.Manchon. Arxiv 2206.08681 (2022).
[5] T. Mc Cormick, I.Kimchi and N.Trivedi. Physical Review B 95, 075133 (2017).
[6] C.Zeng, S.Nandy and S.Tewari. Physical Review B 103, 245119 (2021).
[7] G. Manchon, S. Ghosh, C. Barreteau. Physical Review B 101, 174423 (2020). 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/0a0dc515fce3930dfe69d7c2a4dbb6be.png)

Influence of the surface states on the nonlinear Hall effect in Weyl semimetals

The transport of magnons in materials with topological non-trivial ground state has been investigated in various platforms (ferro- and antiferromagnets) and is characterized by anomalous mechanisms such as the thermal Hall effect and the magnon Nernst effect. Usually, these investigations are done in the framework of the Linear Spin Wave Theory and the interactions between magnons are ignored. In fact, due to the bosonic nature of magnons, such interactions can have a dramatic impact on the magnon lifetime [Chernyshev, AL et al., Phys. Rev. Lett. 117, 187203 (2016)] and band structure [Mook et al., Phys. Rev. X 11, 021061 (2021)], as recently demonstrated. In other words, these interactions are ubiquitous and can cause the alteration of the energy bands and the transport properties of the system, including damping and topological phase transitions [Y.S. Lu et al., Phys. Rev. Lett. 127, 217202 (2021)]. In this work, we investigate the influence of magnon-magnon interactions on the anomalous transport of magnons in a topologically non-trivial honeycomb antiferromagnet. Focusing on the magnon spin Nernst effect, we uncover the impact of these interactions on the magnon lifetime, band structure and anomalous transport upon increasing the temperature. 
**References** Chernyshev, AL et al., Phys. Rev. Lett. 117, 187203 (2016)
Mook et al., Phys. Rev. X 11, 021061 (2021)
Y.S. Lu et al., Phys. Rev. Lett. 127, 217202 (2021) 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d04a855b18739e0e3b395c840aa74da4.png)

Impact of Interactions on Topological Magnonic Transport

Two-dimensional magnets based on van der Waals materials are currently fostering great expectations for the advancement of spin-orbitronics, which aims to exploit the spin-orbit coupling in non-centrosymmetric magnetic heterostructures to enable current-driven magnetic torques and stabilize homochiral magnetic textures. Van der Waals magnets are particularly appealing for this purpose as their properties can be tuned by surface engineering at the atomic level. In this talk, I will present our investigation of the spin-orbitronics properties of selected highly promising van der Waals candidates, both in pristine and Janus configurations, from first principles and effective tight-binding models. I will first discuss the spin-orbit torque that emerges from inversion symmetry breaking in magnetic transition metal dichalcogenide monolayers [1] and demonstrate that sizable torques can be obtained, whose magnitude is controlled by the electric dipole due to the chalcogen elements. Most importantly, I will show the existence of a unique spin-orbit torque component that allows for field-free current-driven switching, of highest interest for applications. Then, I will discuss the nature of Dzyaloshinskii-Moriya interaction in these systems, and how they can stabilize magnetic skyrmions, but also magnetic bimerons depending on the magnetic anisotropy properties [2]. Finally, I will discuss the spin-orbitronics properties of Fe3Ge2Te2 and show that in spite of its high symmetry, its inherent mirror symmetry breaking enables the onset of an in-plane Dzyaloshinskii-Moriya interaction that can stabilize planar chiral textures [3].

[1] Smaili et al., arXiv:2007.07579
[2] Laref et al., arXiv:2011.07813 
[3] Laref et al., Physical Review B 102, 060402(R) (2020)


Theory of spin-orbit torque and Dzyaloshinskii-Moriya interaction in van der Walls magnets

COC: Topological Insulators, Dirac Materials, 2D and Layered van der Waals Materials II

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Influence of the surface states on the nonlinear Hall effect in Weyl semimetals

Impact of Interactions on Topological Magnonic Transport

Theory of spin-orbit torque and Dzyaloshinskii-Moriya interaction in van der Walls magnets

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