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.