Threefold Symmetric Magnetic Two-Ion Coupling in hcp Rare-Earth Metals

Abstract

The heavy rare earths crystallize in the hcp structure. Most of the mag- netic couplings between two ions in these metals are independent of the two different orientations of the hexagonal layers. However, trigonal anisotropy terms may occur, reflecting that the c-axis is only a threefold axis. In the presence of a trigonal coupling the symmetry is reduced, and the double-zone representation in the c-direction ceases to be valid. The strong interaction between the transverse optical phonons and the acoustic spin waves prop- agating in the c-direction of Tb detected more than twenty years ago, was the first example of a trigonal coupling found in these systems. A few years ago a careful neutron-diffraction study of the c-axis modulated magnetic structures in Er showed the presence of higher harmonics at positions along the c-axis translated by odd multiple of 2π/c. This indicates distortions of the structures due to trigonal couplings, and the same characteristic phe- nomenon has now also been observed in Ho. Additionally, mean-field calcu- lations show that a trigonal coupling in Ho is required, in order to explain the increase in the commensurable effects observed for the 8 and 10 layered periodic structures, when a field is applied along the c-axis.