Layer Hall and layer spin Hall effects in two-dimensional altermagnets induced by spin-layer coupling

Altermagnets represent a novel class of collinear magnets characterized by alternating spin-split bands and zero net magnetization, allowing for anomalous transport phenomena without stray fields and enabling ultrafast spin dynamics. Here, through group theory analysis and first-principles calculations, we explore the layer Hall and layer spin Hall effects in two-dimensional (2D) monolayer altermagnets. Using Ca(CoN)₂ as a representative example, we identify symmetry-enforced spin–layer coupling configurations that lead to a vanishing anomalous Hall conductivity due to the cancellation of oppositely signed layer-resolved contributions. In contrast, the spin Hall conductivity remains symmetry-permitted and exhibits distinct layer-dependent behavior. These effects stem from layer-locked ordinary and spin Berry curvatures, governed by the underlying spin–layer coupling. Our results provide new insights into the charge and spin transport properties of 2D layered altermagnets and pave the way for advances in altermagnetic spintronics and layertronics.