Fig. 1: Order parameters and possible structural and magnetic phases.
From: Structure, control, and dynamics of altermagnetic textures
All the ferromagnetic (a–c), structural (d, f), and staggered magnetic (g–i) phases can be obtained from the hypothetical high symmetry phase (e) with no magnetic order and isotropic local environment of magnetic atoms (shown with circles). d, f Deformation of the local environment (ellipses) leads to two different structural phases with equal (\({\hat{U}}^{(1)}={\hat{U}}^{(2)}\)) or staggered (\({\hat{U}}^{(1)}=-{\hat{U}}^{(2)}\)) local environment. Magnetic ordering leads to either ferromagnetic (M1 = M2, (a–c)) or staggered (M1 = − M2 (g–i)) magnetic structures, depending on the sign of the exchange coupling between atoms 1 and 2. The combination of the staggered environment and the staggered magnetic order parameters leads to an altermangetic phase (i). The positions of the atoms are schematic, in real structures atoms 1 and 2 can be shifted in the vertical direction, e.g., in RuO2.
