Axial Hall Effect in Altermagnetic Lieb Lattices

We predict a so-called axial Hall effect, a Berry-curvature-driven anomalous Hall response, in Lieb-lattice altermagnets. Using a tight-binding model, we reveal a hidden topological degree of freedom: the axial pseudospin. Breaking the double degeneracy of axial symmetry exposes this pseudospin, generating a substantial Berry curvature and pronounced intrinsic anomalous Hall conductivity. Subsequent first-principles calculations confirm the emergence of this effect in the family of strained ternary transition-metal dichalcogenides. Focusing on Mn₂WS₄, we demonstrate that the axial Hall effect essentially arises from the interplay between Dresselhaus spin-orbit coupling and the piezomagnetic response, resulting in highly localized and enhanced Berry curvature. Remarkably, the magnitude of this effect is significant and remains constant under varying strain, underscoring the topological nature of the axial degree of freedom. Beyond monolayers, this effect manifests as a distinctive thickness-dependent modulation of both anomalous and spin Hall responses in multilayer structures. These findings emphasize the critical role of spin-orbit coupling and noncollinear spin textures in altermagnets, an area that has received limited attention, and open new pathways for exploring and tuning intrinsic Hall phenomena and spintronic applications in topological altermagnets.