Altermagnetism and magnetic groups with pseudoscalar electron spin

Understand

We revise existing group-theoretical approaches for a treatment of nonrelativistic collinear magnetic systems with perfect translation invariance.

• We show that full symmetry groups of these systems, which contain elements with independent rotations in the spin and configuration spaces (spin groups), can be replaced by magnetic groups consisting of elements with rotations acting only on position vectors.
• This reduction follows from modified transformation properties of electron spin, which in the considered systems becomes effectively a pseudoscalar quantity remaining unchanged upon spatial operations but changing its sign due to an operation of antisymmetry.
• We introduce a unitary representation of the relevant magnetic point groups and use it for a classification of collinear magnets from the viewpoint of antiferromagnetism-induced spin splitting of electron bands near the center of Brillouin zone.