arXiv2026
As an emerging magnetic phase, altermagnets (AMs) with collinear compensated magnetism in real space and alternating spin splitting in the band structure have attracted widespread attention. Here, based on first-principles calculations, we demonstrate that the layer stacking imposes symmetry constraints on the spin and valley degrees of freedom (DOFs) in an AM bilayer composed of two tetragonal altermagnetic monolayers, thereby enabling the tuning of these DOFs through interlayer sliding as well as by an external electric field. Using several representative AM bilayers, we reveal that the [C2||P] and [C2||Mz] symmetries intrinsically enforce spin degeneracy, while the coupling between spin and layer DOFs establishes a general framework for achieving electric field control of spin states. Appropriate interlayer sliding breaks the [C2||Md] symmetry of AM bilayers, thereby giving rise to a spontaneous valley splitting and driving a transition to a fully compensated ferrimagnetic state. Furthermore, owing to the tunable valley splitting induced by interlayer sliding, enhanced tunneling magnetoresistance (TMR) can be realized by AM bilayers. This work highlights the intrinsic correlation among spin, valley, and layer DOFs, offering symmetry-based design principles for layer-based spintronic and valleytronic devices.