Phonon-induced quadrupolar ordering of the magnetic superconductor TmNi 2 B 2 C

We present synchrotron x-ray diffraction studies revealing that the lattice of thulium borocarbide is distorted below ${T}_{Q}\ensuremath{\simeq}13.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ at zero field. ${T}_{Q}$ increases and the amplitude of the displacements is drastically enhanced by a factor of 10 at 60 kOe when a magnetic field is applied along [100]. The distortion occurs at the same wave vector as the antiferromagnetic ordering induced by the $a$-axis field. A model is presented that accounts for the properties of the quadrupolar phase and explains the peculiar behavior of the antiferromagnetic ordering previously observed in this compound.