Magnon nonlinear Hall effect in two-dimensional antiferromagnetic insulators

The efficient detection of the magnetism in 2D antiferromagnetic (AFM) insulators is crucial for the advancement of 2D AFM spintronics and remains a challenging problem. In this paper, we introduce the magnon nonlinear Hall current, a second-order Hall response of collective spin excitations in ordered magnets, as a probe for 2D layered AFM insulators. We theoretically demonstrate that such the nonlinear Hall response is intrinsically coupled to the underlying spin configuration. In particular, it exhibits a pronounced layer dependence in layered antiferromagnets, enabling direct characterization of the nature and strength of interlayer magnetic coupling in multilayer AFM insulators. Furthermore, in contrast to the weak linear Hall response, even a slight external field can significantly enhance the second-order Hall response of magnons. This field-induced giant nonlinear Hall response, along with its reversible nature, effectively addresses the inherent limitations of 2D AFM insulators with zero magnetization and weak field sensitivity, broadening their application potential.