Large Anomalous Hall Effect in Topologically Trivial Double-$Q$ Magnets

TL;DR

This paper reveals a large anomalous Hall effect in topologically trivial double-$Q$ magnets, driven by orbital hybridization and Berry curvature, challenging the usual association with topological spin textures.

Contribution

It demonstrates a novel mechanism for large Hall responses in trivial double-$Q$ spin textures via orbital hybridization, expanding potential spintronic applications.

Findings

Double-$Q$ magnets show a giant anomalous Hall effect despite topological triviality.

Orbital hybridization enhances Berry curvature, leading to increased Hall response.

The mechanism explains experimental observations in GdRu$_2$Si$_2$ and GdRu$_2$Ge$_2$.

Abstract

Multi-$Q$ magnets consist of superposed spin density waves with distinct magnetic modulation vectors, enabling a wide range of magnetic orders depending on their combination. Among them, topologically nontrivial spin textures, such as a magnetic skyrmion, has been extensively studied owing to the emergence of topological Hall effects induced by real-space scalar spin chirality. Contrary to this expectation, we theoretically investigate another route to enhancing the Hall response under a topologically \textit{trivial} double-$Q$ spin textures. Despite the cancellation of the scalar spin chirality, the double-$Q$ magnetism exhibits a pronounced Hall response with a nonmonotonic dependence on the uniform magnetization, which is in stark contrast to a ferromagnetic state and a single-$Q$ spiral state. Analyzing the multi-orbital Kondo lattice model, we show that orbital hybridization induced by the double-$Q$ superstructure enhances the Berry curvature in $\mathbf{k}$-space, leading to a large anomalous Hall effect. This mechanism accounts for the observed giant anomalous Hall effect in GdRu$_2$Si$_2$ and GdRu$_2$Ge$_2$, thereby highlighting topologically trivial double-$Q$ spin textures as promising spintronic materials.