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 the Brillouin zone. We prove that the recently revealed different altermagnetic classes correspond in a unique way to all nontrivial magnetic Laue classes, i.e., to the Laue groups containing the operation of antisymmetry only in combination with a spatial rotation. Four of these Laue classes are found to be compatible with a nonzero spin conductivity. Subsequent inspection of a simple model allows us to briefly address the physical mechanisms responsible for the spin splitting in real systems.

中文翻译：

---

具有赝标量电子自旋的交替磁性和磁性群

我们修改了现有的群论方法来处理具有完美平移不变性的非相对论共线磁系统。我们展示了这些系统的完全对称群，其中包含在自旋和配置空间中具有独立旋转的元素（自旋群），可以被由仅作用于位置矢量的旋转的元素组成的磁群所取代。这种减少源于电子自旋的修改变换特性，在所考虑的系统中，它实际上变成了一个伪标量，在空间操作时保持不变，但由于反对称操作而改变其符号。我们引入了相关磁点群的统一表示，并将其用于从反铁磁性引起的布里渊区中心附近的电子带自旋分裂的角度对共线磁体进行分类。我们证明了最近揭示的不同的交替磁类以独特的方式对应于所有非平凡的磁劳厄类，即仅与空间旋转相结合的包含反对称操作的劳厄群。发现这些劳厄类别中有四个与非零自旋电导率兼容。随后对一个简单模型的检查使我们能够简要地解决实际系统中导致自旋分裂的物理机制。我们证明了最近揭示的不同的交替磁类以独特的方式对应于所有非平凡的磁劳厄类，即仅与空间旋转相结合的包含反对称操作的劳厄群。发现这些劳厄类别中有四个与非零自旋电导率兼容。随后对一个简单模型的检查使我们能够简要地解决实际系统中导致自旋分裂的物理机制。我们证明了最近揭示的不同的交替磁类以独特的方式对应于所有非平凡的磁劳厄类，即仅与空间旋转相结合的包含反对称操作的劳厄群。发现这些劳厄类别中有四个与非零自旋电导率兼容。随后对一个简单模型的检查使我们能够简要地解决实际系统中导致自旋分裂的物理机制。