On the origin of multiple ordered phases in PrFe₄P₁₂

The nature of multiple electronic orders in skutterudite PrFe ₄P₁₂ is discussed on the basis of a model with antiferro-quadrupole (AFQ) interaction of Γ₃ symmetry. The high-field phase can be reproduced qualitatively provided (i) ferro-type interactions are introduced between the dipoles as well as between the octupoles of localized f -electrons, and (ii) separation is vanishingly small between the Γ₁-Γ₄⁽¹⁾ crystalline electric field (CEF) levels. The high-field phase can have either the same ordering vector q = (1, 0, 0) as in the low-field phase, or a different one q = 0 depending on the parameters. In the latter case, distortion of the crystal perpendicular to the (111) axis is predicted. The corresponding anomaly in elastic constants should also appear. The electrical resistivity is calculated with account of scattering within the CEF quasi-quartet. It is found that the resistivity as a function of the direction of magnetic field shows a sharp maximum around the (111) axis at low temperatures because of the level crossing.