Extrinsic anomalous Hall effect in altermagnets

We find the extrinsic anomalous Hall conductivity (AHC) to be comparable to the intrinsic one in roughly the half of the altermagnetic spin Laue groups in the limit of large exchange splitting.

In materials with the non-zero Dzyaloshinskii–Moriya type interaction linear in spin-orbit coupling, the extrinsic contribution is essential even in the clean limit, and is largely irrelevant otherwise.The extrinsic AHC arises from the intra-band disorder scattering and is prominent in the two-band limit resulting from the large exchange splitting.  The extrinsic Hall conductivity is finite even for the infinitesimal disorder concentration as long the thermodynamic limit applies.  This non-analiticity is linked to the non-analytic dependence of the intrinsic AHC on spin-orbit coupling. Both originates from the lifting of the spin degeneracy along the nodal lines that is specific to altermagnets by a weak SOC.