Dissipation properties of anomalous Hall effect: intrinsic vs. extrinsic magnetic materials

TL;DR

This study probes the dissipation of anomalous Hall currents injected into a lateral load for three magnetic materials with distinct AHE origins: an intrinsic altermagnet Mn$_{5}$Si$_{3}$, an extrinsic-AHE ferrimagnet Co$_{75}$Gd$_{25}$, and a Planar Hall-effect–dominated Ni$_{80}$Fe$_{20}$. Using a phenomenological edge-screening framework, it derives universal expressions for transverse voltages and load dissipation that depend primarily on the Hall angle $\Theta$ and the load ratio $\alpha=R/R_{\ell}$. Experiments show that the dissipated power scales as $\Theta^2$ and that the normalized power curves for the three materials collapse onto a single profile at leading order, with maximum dissipation occurring at resistance matching ($R=R_{\ell}$). These results imply that macroscopic dissipation in Hall devices is governed by edge charge accumulation rather than the microscopic Berry-curvature mechanism, offering design insights for spin–orbit torque devices and motivating exploration of next-to-leading order effects and altermagnetic materials.

Abstract

A comparative study of anomalous-Hall current injection and anisotropic current injection (through planar Hall effect) are studied in Hall devices contacted to a lateral load circuit. Hall currents are injected into the load circuit from three different kinds of magnetic Hall bars: Mn5Si3 altermagnet, Co75Gd25 ferrimagnet, and Ni80Fe20 ferromagnet. The current, the voltage and the power are measured as a function of the load resistance and the Hall angle. It is observed that the power dissipated for the three kinds of materials fellow the same law as a function of load resistance and Hall angle, at the leading order in the Hall angle. Since the anomalous Hall effect in the altermagnetic Hall-bar is due to the intrinsic topological structure (i.e. due to the presence of a Berry phase in the reciprocal space), these observations suggest that the dissipative properties of anomalous Hall effect are dominated by the injection of electric charges accumulated at the edges (including electric screening), instead of the very mechanism responsible for it.

Figures (4)

• Figure 1: :(a) Diagram of the Hall bar contacted to a load resistance. An electric generator imposes a constant current through the longitudinal bar ($x$ direction). A transverse anomalous-Hall current is generated inside the materials (Mn$_{5}$Si$_{3}$, CoGd, and NiFe), and injected through the lateral electrodes ($y$ direction). Angles $\theta$ and $\varphi$ give the direction for the magnetization $\vec{m}$ (or for the magnetic order parameter for the altermagnet). (b) Optical picture of a Hall cross with the definition of width 2${\ell}$ and length L.
• Figure 2: Left: Planar Hall voltages in Ni$_{80}$Fe$_{20}$ versus in-the plane azimuthal angle $\varphi$ of the applied field $H_a$ at $H_a=1.5$ T. Right Anomalous Hall voltages in GdCo versus out-of-plane radial angle $\theta$ of the applied field $H_a$ at $H_a=1.5$ T. The magnetization of Co$_{75}$Gd$_{25}$ is not fully saturated at $1.2$ T. The model is the result of the calculation of the equilibrium states of the magnetization for each orientation $\theta$ of the applied field (see reference Dan).
• Figure 3: Hall voltages in Mn$_{5}$Si$_{3}$ versus out-of-plane angle $\theta$ for an applied field $H_{a} = 1.2$T (white circles), measured at T=70K. The current is injected along the $[2 \overline 1 \overline 1 0]$ direction Baltz2.
• Figure 4: Normalized dissipated power in the load resistance for the three materials as a function of Normalized Hall angle (left) and Normalized load resistance (right). Continuous black line are deduced from the model discussed in the text. The error bars on the left indicate the uncertainty due to the hysteresis shown in Fig.3.