Theory of Metal-Insulator Transition in PrRu4P12 and PrFe4P12

TL;DR

This paper develops a theoretical framework for understanding the metal-insulator transition in PrRu4P12 and PrFe4P12, emphasizing the role of lattice displacements and symmetry changes in electronic structure modifications.

Contribution

It introduces a symmetry-based model linking lattice displacements to electronic transitions, supported by band-structure calculations showing gap opening due to phosphorus ion displacements.

Findings

Displacements can change crystal symmetry and split degeneracies.

Symmetry lowering can induce anti-quadrupolar ordering.

Phosphorus displacements open a gap on the Fermi surface.

Abstract

All symmetry allowed couplings between the 4f^2-electron ground state doublet of trivalent praseodymium in PrRu4P12 and PrFe4P12 and displacements of the phosphorus, iron or ruthenium ions are considered. Two types of displacements can change the crystal lattice from body-centred cubic to simple orthorhombic or to simple cubic. The first type lowers the point group symmetry from tetrahedral to orthorhombic, while the second type leaves it unchanged, with corresponding space group reductions Im3 --> Pmmm and Im3 --> Pm3 respectively. In former case, the lower point-group symmetry splits the degeneracy of the 4f^2 doublet into states with opposite quadrupole moment, which then leads to anti-quadrupolar ordering, as in PrFe4P12. Either kind of displacement may conspire with nesting of the Fermi surface to cause the metal-insulator or partial metal-insulator transition observed in PrFe4P12 and PrRu4P12. We investigate this scenario using band-structure calculations, and it is found that displacements of the phosphorus ions in PrRu4P12 (with space group reduction Im3 --> Pm3) open a gap everywhere on the Fermi surface.