Anomalous Hall effect in two-dimensional vanadium tetrahalogen with altermagnetic phase

Recently, a novel collinear antiferromagnetic (AFM) phase termed altermagnet has been identified. It displays combined crystal and spin rotation symmetry, inducing significant spin splitting without spin-orbit coupling (SOC). This mechanism shifts the paradigm in spintronics, enabling AFMs to contribute to novel spintronic devices. However, previous work has mainly concentrated on bulk systems, with less attention given to two-dimensional (2D) materials due to their reduced dimensionality. To address this challenge and shed light on 2D materials, we have proposed a series of 2D altermagnets, namely, $\mathrm{V}{X}_{4}$ $(X=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I})$, which feature an altermagnetic phase and substantial nonrelativistic spin splitting. Furthermore, we have explored their potential applications in the anomalous Hall effect (AHE). Our findings reveal that compared to other bulk materials, the anomalous Hall conductivities (AHC) of these 2D altermagnets are competitive. Moreover, the predicted AHE in these altermagnetic monolayers displays pronounced anisotropy, which allows for precise manipulation of electron spins via external fields. Our work provides insight into the potential of 2D materials in the exploration of altermagnets, paving an alternative way toward low-dimensional spintronic devices.