Threefold Symmetric Magnetic Two-Ion Coupling in hcp Rare-Earth Metals
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The heavy rare earths crystallize in the hcp structure. Most of the magnetic 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 propagating 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 phenomenon has now also been observed in Ho. Additionally, mean-field calculations 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.
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