Fermi surface nesting in the filled skutterudite compounds

The filled skutterudite with a general formula RT4X12 (R = Rare earth, Th or U; T = Fe, Ru or Os; X = P, As or Sb) crystallizes in a unique BCC structure of a space group Im3 (Th5, No.204). Among these compounds, PrRu4P12 shows a metal-insulator (M-I) transition at TMI = 60 K and PrFe4P12 undergoes a non-magnetic ordering at TA = 6.5 K, resulting in a low carrier system, which exhibits heavy-fermion states in applied magnetic field. The filled skutterudite compound PrT4P12 (T = Fe/Ru) is an uncompensated metal with Pr3+, then it could not be an insulator or a semi-metal within the same primitive unit cell. The study of Fermi surface reveals that the main Fermi surface of LaFe4P12 is a distorted cube and the volume is almost a half of the BCC BZ with a sharp peak in the density of states, indicating that the nesting with q = (1,0,0) is likely in the skutterudite compounds. In fact, structural phase transitions with q (1,0,0) are observed below TMI and TA in PrRu4P12 and PrFe4P12, respectively. These experiments show that the unit cell becomes doubled from BCC to simple lattice, then they could be a semi-metal or an insulator, though the atomic displacements remain undetermined experimentally. We have performed band structure calculations for the doubled unit cell (34 atoms) by using the FLAPW-LDA+U method with many types of lattice distortions. Then we have found solutions for an insulator only in PrRu4P12 with the space group Pm3 (Th1, No.200), in which P atoms are distorted by about 5 % of a lattice constant with G1 mode. The result shows that the distortion coupled with anti-quadrupolar ordering of Pr 4f 2 states, which is discussed with T displacements, is not necessary for the M-I transition of PrRu4P12. The M-I transition is caused by the perfect 3-dimensional nesting of the Fermi surface consisting of the P12 molecular orbital with the symmetry xyz, which is the only one Fermi surface in the mother structure of PrRu4P12