Symmetric and antisymmetric anisotropic exchange energies as crucial factors for the magnetic structures in Ho and Er

The exchange energies for different magnetic phases in the heavy rare earths have been studied by means of an anisotropic band model. Calculations on Ho and Er show that the model predicts the correct magnetic ground states. The results show that the anisotropic rather than the isotropic exchange energy is crucial for the stability of competing magnetic structures. Particularly, in Er the strong spin-orbit coupling gives rise to an antisymmetric contribution to the anisotropic exchange energy. This antisymmetric contribution is a prerequisite for the conical configuration that takes place at low temperatures.