Lattice Modulations Induced by Magnetoelastic Effect in Crystals Containing Rare Earth Elements

Lattice modulations associated with magnetic order in Tm and Er were investigated by means of X-ray diffraction. Satellite peaks at wave vectors (0 0 2 q 0 ) and (0 0 4 q 0 ) were observed in Tm where q 0 is the fundamental wave number specifying the modulations of the magnetic moment along the hexagonal c -axis. The modulation amplitude, the atomic displacement along the c -axis, was estimated to be of the order of 10 -3 Å. No peak was detected at q 0 . Peaks for 2 q 0 and 4 q 0 were observed also in Er. The amplitude of the 2 q 0 modulations decreased with decreasing temperature below 30 K. A model based on the magnetoelastic interactions was constructed to calculate these amplitudes of lattice modulations. It involves the elastic, exchange and crystal field energies. The latter two magnetic energies were assumed to vary with the interatomic distance. This model, combined with the temperature variations of the magnetic moment, was found to reproduce the temperature dependence of the lattice modulations in Tm and Er. X-ray diffraction measurements were also made for UPdIn and NdCo 2 Si 2 . The magnetoelastic effects in these materials appear to be much weaker than those in Tm and Er.