Development of ab initio methods for topological Hall effects in magnets with multiple-Q orderings

In magnetic systems characterized by multiple-Q spin orderings, fascinating transport phenomena such as the topological Hall effect emerge, showcasing the intricate interplay of magnetic textures and electronic properties. This talk introduces a new first-principles method to accurately and efficiently calculate the topological Hall effect, specifically in materials that host skyrmion lattice. While calculating the electronic structure of skyrmion materials has been a formidable challenge due to the extensive size of their superlattice configurations, our computational scheme successfully circumvents these limitations, enabling precise calculations that demonstrate excellent agreement with experimental measurements of the topological Hall effect in Gd₂PdSi₃[1].

This talk will also introduce a systematic approach for predicting the magnetic structures of materials exhibiting multiple-Q states, employing the framework of cluster multipole theory[2,3]. By applying this method to CoTa₃S₆, and in combination with density functional theory (DFT) calculation, we determine that the ground state configuration corresponds to a triple-Q all-in all-out state [4]. Based on a symmetry analysis using spin crystallography group, we reveal that this triple-Q state can induce the topological Hall effect even in the absence of spin-orbit coupling [5]. Furthermore, through the derivation of a low-energy effective spin model from first principles[6], we show that biquadratic spin interactions predominantly stabilize the triple-Q state and spin-orbit coupling plays just a minor role[7].