As a unique electromagnetic phenomenon of magnetic materials, the anomalous Hall effect generates a voltage perpendicular to the directions of the current flow and the external magnetic field when an electric current passes through magnetic materials. During the anomalous Hall transport, the current carriers undergo a transverse deflection. The key parameter of anomalous Hall effect, anomalous Hall angle, represents the ability of a longitudinal current density to drive a transverse anomalous Hall current density. A large anomalous Hall angle plays a critical role in applications such as anomalous Hall magnetic sensing and spintronic magnetic-domain switching. Over the past 70 years, the anomalous Hall angle has remained at a relatively low level of 0.1–3° (0.2%–5%), and the lack of modulation model and experimental scheme has prevented this important physical effect from being effectively utilized.

In recent years, the discovery of magnetic topological materials has provided a material platform for studying spin-related topological states and physical properties, while their topology-enhanced electronic transport properties have also opened opportunities for modulating the anomalous Hall angle. The magnetic Weyl semimetal Co₃Sn₂S₂ exhibits a large intrinsic anomalous Hall effect, making it an ideal candidate for realizing the modulation of anomalous Hall angle.

Recently, the research team led by Enke Liu in Institute of Physics, Chinese Academy of Sciences, made new progress in the study of magnetic topological materials and physics. They proposed a dual-variable mathematical model for the anomalous Hall angle, expressing the anomalous Hall angle as a function of the product of longitudinal resistivity and anomalous Hall conductivity for the first time. In the metallic region, the anomalous Hall angle increases with the product of these two parameters. For systems with a determined intrinsic anomalous Hall conductivity, the anomalous Hall angle exhibits a maximum value as the longitudinal resistivity increases. Considering the characteristics of intrinsic and extrinsic mechanisms of anomalous Hall conductivity, they proposed experimental schemes for modulating the anomalous Hall angle based on magnetic topological materials.

By leveraging intrinsic and extrinsic degrees of freedom such as topological states, slight doping, temperature, and dimensionality, they designed and validated experiments in the Co₃Sn₂S₂ system, achieving simultaneous significant enhancements in longitudinal resistivity and anomalous Hall conductivity. This resulted in a zero-field giant anomalous Hall angle of 25° (46%), which is an order of magnitude higher than those of conventional magnetic materials. Additionally, they developed a novel anomalous Hall sensor, achieving a low-frequency magnetic field detectability of 23 nT/Hz^0.5@1Hz and a Hall sensitivity of 7028 μΩ cm/T, which are 3 times and 10 times higher, respectively, than those of currently known anomalous Hall sensors.

This study provides a feasible scheme for modulating the anomalous Hall angle, opening a new era of giant anomalous Hall angles of magnetic materials and demonstrating the topology-principle of high-performance magnetic sensing.

The related findings were published in Nature Electronics on April 2, 2025, under the title "Modulation of the anomalous Hall angle in a magnetic topological semimetal."

The first author of the paper is Ph.D. student Jinying Yang, and the corresponding author is Professor Enke Liu. The NV center magnetic measurements for micro-nano devices were supported by Gangqin Liu's team at the Institute of Physics. The research also received support and guidance from Academician Baogen Shen of the Institute of Physics, Professor Yizheng Wu of Fudan University, Professor Stuart Parkin of the Max Planck Institute for Microstructure Physics, and Professor Claudia Felser of the Max Planck Institute for Chemical Physics of Solids. The work was supported by projects including the NSFC General Program, the Ministry of Science and Technology's Key R&D Program, the CAS Stable Support for Youth Teams, the CAS Major Research Instrument Development Program, and the CAS-Max Planck Joint Research Unit.