Switchable Anomalous Valley Hall Effect in Bilayer Mg(FeN)2

Achieving the controllable anomalous valley Hall effect (AVHE) is crucial for valleytronics but remains challenging for bilayer altermagnetic systems. Here, bilayer Mg(FeN)2 is proposed as a stacking-dependent platform for a switchable AVHE. The AA stacking of bilayer Mg(FeN)2 exhibits altermagnetism due to the broken TP(t) symmetry, while the AB stacking is a conventional antiferromagnet protected by TP(t) symmetry. Interestingly, interlayer sliding between AA-1 and AA-2 configurations reverses the out-of-plane ferroelectric polarization and consequently switches the layer-dependent valley polarization. Reversing the magnetic configuration changes the spin occupation of valleys, leading to an opposite Hall voltage signal. Thus, a valleytronic device is constructed for the nonvolatile control of the AVHE. For AB-0 configuration, an external electric field can break layer equivalence and induce layer-dependent valley polarization. Switching the electric field direction or magnetic configuration enables the polarity reversal of the Hall response. This work provides a feasible route for electrically and magnetically controllable AVHE in altermagnets.