Activation of anomalous Hall effect and orbital magnetization by domain walls in altermagnets

Altermagnets are an emerging class of unconventional antiferromagnets, characterized by a Néel ordering that does not break the translational symmetry of the underlying lattice. Depending on the orientation of the Néel vector, the anomalous Hall effect (AHE) may or may not exist. In the so-called pure altermagnets, the AHE is forbidden by magnetic symmetry. Here, we demonstrate that in pure altermagnets, domain walls can lift the symmetry constraints, thereby activating the AHE and orbital magnetization. Taking a representative example of a rutile-lattice tight-binding minimal model in slab geometry, we use linear response theory to demonstrate the emergence of the domain-wall AHE, finding that it is closely related to the orbital magnetization, while the spin magnetization does not play a significant role. Using Landau theory, we argue that, while for a random arrangement of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>π</a:mi> </a:math> domain walls, the contributions from the individual domain walls will cancel one another, an external magnetic field will favor domain-wall arrangements with specific chirality giving rise to a net AHE signal. Using group theory, we discuss how these findings can be straightforwardly generalized to certain other classes of altermagnets. Our work reveals a crucial role for domain walls in understanding Hall transport and orbital magnetism of altermagnets. Our work generally calls for a rigorous analysis of Hall-transport data for an altermagnet, ideally in conjunction with imaging data, in order to unambiguously assign an observed Hall effect to magnetic domains or to domain walls.