Anomalous-Hall Neel textures in altermagnetic materials

Recently, the altermagnets, a new kind of colinear antiferromagnet with zero net magnetization and momentum-dependent spin-splitting of bands, have sparked great interest. Despite simple magnetic structures, these altermagnets exhibit intriguing and intricate dependence of AHE on the N\'eel vector, in contrast to the conventional perpendicular configuration of Hall current with magnetization in ferromagnets. In spite of being a crucial aspect in AHE research, the relationship between the AHE and the N\'eel vector remains largely elusive. Here, we propose a powerful "extrinsic parameter" method and further reveal diverse unconventional anomalous Hall textures in the N\'eel vector space, dubbed anomalous-Hall N\'eel textures (AHNTs) for altermagnets. Notably, we find that AHNTs resemble the spin textures in momentum space, and further reveal their symmetry origin. We identify 10 types across four categories of AHNTs in altermagnets. Meanwhile, we examine our key discoveries in prototypical altermagnets. Our work offers a complete classification of AHNTs and a thorough understanding of AHE in altermagnets.