Spontaneous Anomalous Hall Effect in Two-Dimensional Altermagnets

TL;DR

This paper develops symmetry-based principles for realizing the anomalous Hall effect in two-dimensional altermagnets, demonstrating through first-principles calculations that specific bilayer structures exhibit measurable AHE linked to their magnetic order.

Contribution

It introduces a symmetry analysis framework for 2D altermagnets to predict AHE, validated by first-principles simulations on bilayer MnPSe3 and MnSe.

Findings

Only two of seven spin layer groups show in-plane AHE.

AHE depends linearly and cubically on the Ne9el vector.

AHE can detect magnetic order and Ne9el vector reversal.

Abstract

The anomalous Hall effect (AHE) is an efficient tool for detecting the N\'eel vector in collinear compensated magnets with spin-split bands, known as altermagnets (AMs). Here, we establish design principles for obtaining non-zero anomalous Hall conductivity in the recently proposed two-dimensional (2D) AMs using spin and magnetic group symmetry analysis. We show that only two of the seven nontrivial spin layer groups exhibit an unconventional in-plane AHE in which the N\'eel vector lies within the plane of the Hall current. Through first-principles simulations on bilayers of MnPSe$_3$ and MnSe, we demonstrate the validity of our group theoretic framework for obtaining AHE with $d$ and $i$-wave altermagnetic orders, depending on the stacking of the bilayers. We find that the spin group symmetry is successful in determining the linear and cubic dependence of anomalous Hall conductivity in N\'eel vector space, although AHE is a relativistic effect. This work shows that the AHE in 2D AMs can probe the altermagnetic order and N\'eel vector reversal, thereby facilitating the miniaturization of altermagnetic spintronics.