Spin-layer coupling in two-dimensional altermagnetic bilayers with tunable spin and valley splitting properties

Recently, the discovery of collinear symmetric-compensated antiferromagnets (AFMs) with intrinsic spin splitting has attracted enormous interest of many researchers. In this paper, we predict the spin-layer coupling in altermagnetic bilayers with tunable spin and valley splitting properties via first-principles calculations. Based on the analysis of magnetic symmetry, we find manipulating magnetic order and stacking configuration as a strategy. Compared with conventional AFM bilayers, the joint symmetry in altermagnetic bilayer can be significantly modulated by different magnetic orders and stackings of the two sublayers. Furthermore, we demonstrate that the layer-dependent spin degeneracy/splitting widely exists in altermagnets with different crystal structures. The spin splitting in an altermagnetic bilayer with various interlayer couplings is highly tunable by external electric field. In contrast with spin splitting introduced by conventional spin-orbit coupling, the concepts of emerging layertronics and altermagnets are combined to manipulate spin properties by spin-layer coupling, ensuring both long spin relaxation time and complete spin splitting for practical applications of spintronic devices.