Structural phase transition and anti-quadrupolar ordering in PrFe4P12 and PrRu4P12

We show that the structural phase transition which occurs in PrFe4P12 and PrRu4P12 coincides with anti-quadrupolar ordering of the Pr 4f(2) electrons. Coupling between phonon modes of the displacements of the Fe/Ru ions and the Pr 4f2 ground state doublet leads to a symmetry lowering (1, 1, -2) type distortion of the Fe/Ru positions and a simultaneous splitting of the 42 doublet into eigenstates with quadrupole moments +/-8. The sign of both the distortion and the quadrupole moment alternate from site to site, resulting in anti-quadrupolar ordering. (C) 2002 Elsevier Science B.V. All rights reserved.