First-Principles Study of the Topological Hall Effect Induced by Spin Textures*

Topological spin textures, such as skyrmions, are stable magnetic structures protected by the topology of spin orientation. Their noncoplanar spin alignment grants them the intriguing "real-space Berry phase," simulating an effective magnetic field and thereby giving rise to the so-called topological Hall effect. This particular Hall effect stands as a unique and discernible quantity, observable exclusively in non-trivial topological spin textures, thus paving the way for detecting and understanding skyrmions.

In this study, we introduce a first-principle methodology rooted in density functional theory for the computation of topological Hall conductance. Our method models the exchange-correlation potential generated by the skyrmion, which allows us to quantify the interaction between transport electrons and these topological spin textures. Subsequently, we employ the results to investigate the topological Hall effect using the Boltzmann transport equation and Kubo formalism.

As a practical application, we apply our methodology to the skyrmion lattice phase of the centrosymmetric magnet GdRu2Si2 and identify a substantial Hall conductance originating solely from the non-trivial topological spin textures, as revealed by experiments [1]. Overall, our work establishes a novel numerical technique in the field of spin-magnet systems and advances the understanding of the topological Hall effect induced by topological spin textures.

[1] N. Khanh, et. al. Nat. Nanotech. 15. 444-449 (2020)