Theory of metal–insulator transition in PrFe4P12 and PrRu4P12 Original Research Article

We derive all symmetry allowed couplings between Fe/Ru or P ion displacements and the Pr ion 4f2 ground state doublet in PrFe4P12 and PrRu4P12. A (1,1,−2)-type distortion of the Fe/Ru positions splits the 4f2 doublet into non-magnetic eigenstates with opposite quadrupole moments. The sign of both the distortion and the quadrupole moment alternate from site to site, resulting in anti-quadrupolar ordering. A (1,1,1)-type distortion does not lift the degeneracy of the 4f2 doublet. Either distortion may also open a gap at the Fermi surface, causing a metal–insulator transition in PrRu4P12 and a partial metal–insulator transition in PrFe4P12.