Modulation of anomalous Hall angle in a magnetic topological semimetal

Technical Summary: Modulation of Anomalous Hall Angle in a Magnetic Topological Semimetal

Problem Statement
The anomalous Hall angle ($\theta_A$), defined as the angle between the total current density and the driving current density, is a critical metric for the efficiency of converting longitudinal electric current into transverse spin-polarized Hall current. A large $\theta_A$ is essential for enhancing the sensitivity of anomalous Hall (AHE) sensors and for generating efficient spin currents for spin-transfer torque applications. However, in most conventional magnetic materials, $\theta_A$ is typically small (0.1° to 3°, corresponding to $\tan\theta_A$ of 0.1 to 0.05), limiting the technological application of AHE. While topological magnets with Weyl fermions exhibit large intrinsic anomalous Hall conductivity ($\sigma^A_H$), systematic modulation schemes to maximize $\theta_A$ and the underlying physical rules governing this parameter have not been fully investigated.

Methodology and Physical Scheme
The authors propose a theoretical framework to modulate $\theta_A$ by establishing a relationship between the anomalous Hall angle and two experimentally accessible parameters: longitudinal resistivity ($\rho_{xx}$) and anomalous Hall conductivity ($\sigma^A_H$).

• Theoretical Formulation: Based on the Drude model and tensor conversion, the authors derive that $\tan\theta_A$ is a function of the product $\rho_{xx}\sigma^A_H$. They identify two mathematical solutions for this relationship, focusing on the metallic region solution ($\tan\theta_{A1}$) which dominates electronic transport.
• Modulation Strategy: The study identifies that to achieve a large $\tan\theta_A$, one must simultaneously increase both $\rho_{xx}$ and $\sigma^A_H$. The authors propose a "chimney-like" distribution where low values of either parameter result in low $\tan\theta_A$. The most efficient path involves operating in a "transition region" where the intrinsic $\sigma^A_H$ remains high while $\rho_{xx}$ is increased (e.g., via scattering mechanisms) without significantly degrading the band structure.
• Experimental Approach: The magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$ was selected as the testbed due to its giant intrinsic $\sigma^A_H$. The researchers employed three primary degrees of freedom to modulate the parameters:
  1. Temperature: Utilizing electron-magnon scattering to increase $\rho_{xx}$ while maintaining intrinsic $\sigma^A_H$ at low temperatures.
  2. Thickness: Reducing the thickness of single-crystalline nanoflakes to increase $\rho_{xx}$ via surface scattering.
  3. Chemical Doping: Introducing Fe doping to simultaneously enhance $\rho_{xx}$ (via impurity scattering) and $\sigma^A_H$ (via extrinsic contributions and potential band structure modifications).

Key Results

• Modulation of $\tan\theta_A$: By combining Fe doping with thickness reduction in Co$_3$Sn$_2$S$_2$ nanoflakes, the authors successfully modulated $\tan\theta_A$ to a magnitude of 0.46, corresponding to an angle of approximately 25°. This represents an order-of-magnitude improvement over many conventional magnetic materials.
• Mechanism Verification:
  • Temperature-dependent measurements on bulk and nanoflake samples confirmed that $\sigma^A_H$ remains intrinsic and stable below 90 K, while $\rho_{xx}$ increases significantly, driving $\tan\theta_A$ up.
  • Thickness reduction further increased $\rho_{xx}$, pushing the system into the transition region where $\tan\theta_A$ peaks.
  • Fe doping introduced extrinsic scattering that increased $\rho_{xx}$ to 200–300 $\mu\Omega\cdot$cm while maintaining a high $\sigma^A_H$ (~1300–1600 $\Omega^{-1}\cdot$cm$^{-1}$), resulting in the record-high $\tan\theta_A$.
• Device Performance: Microfabricated anomalous Hall devices using Fe-doped Co$_3$Sn$_2$S$_2$ nanoflakes demonstrated:
  • A Hall sensitivity of 7028 ± 341 $\mu\Omega\cdot$cm/T.
  • A magnetic field detectability of 23.5 ± 1.7 nT/$\sqrt{\text{Hz}}$ at 1 Hz.
  • These metrics show a competitive advantage over existing AHE sensor materials.

Significance and Claims
The paper claims to provide a general physical scheme for tuning the anomalous Hall angle, moving beyond the traditional focus solely on maximizing anomalous Hall conductivity. By demonstrating that $\tan\theta_A$ can be optimized by balancing resistivity and conductivity, the authors enable a "giant jump" in the performance of magnetic metals, elevating $\theta_A$ to a new level previously unattainable in metallic systems.

The authors assert that this scheme has significant potential for advancing applications in magneto-electronics and spintronics, specifically citing:

• High-sensitivity magnetic field detection: The demonstrated low noise and high sensitivity make these materials suitable for next-generation sensors.
• Spintronic devices: The large anomalous Hall angle serves as an efficient source of spin currents for spin-transfer torque applications.
• Specific Applications: The work suggests potential utility in automatic intelligent vehicles and hard disk readers.

The study concludes that this modulation strategy could be extended to other topological magnets to generate giant anomalous Hall currents and potentially giant spin Hall currents, thereby promoting the integration of topological materials into practical electronic devices.