Key to applications of the newly discovered class of altermagnets is control of the magnetic Néelvector, which indicates which way magnetic moments point. One means of achieving this is through coupling to either a spin-orbit coupling induced ferromagnetic moment (FM)  or the anomalous Hall effect (AHE) moment, motivating the need to understand both these phenomena.

Since both FM and AHE share the same underlying symmetry and are induced by spin-orbit coupling, they are expected to be similar in magnitude. However, numerical electronic structure calculations (or density functional theory (DFT) calculations) reveal that this is not generally the case, in some altermagnets they are similar in magnitude, but in others they are vastly different.

Here, this difference is explained through a three-step process. In the first step the DFT results were reproduced with minimal models developed to describe a wide range of altermagnets. In the second step a symmetry, quasisymmetry, that explains the origin of this difference was identified within the minimal models.

Finally, it was shown that quasisymmetry also applies to the full DFT calculations, highlighting that this provides a general explanation for the varied relationship of these technologically important properties of altermagnets.