Microscopic Theory of Γ₃ Quadrupole Ordering in Pr Compounds on the Basis of a j-j Coupling Scheme

In recent decades, multipole ordering in f²-electron systems such as Pr and U compounds have attracted continuous attention in the research field of condensed matter physics. In fact, peculiar modulated antiferro non-Kramers Γ₃ quadrupole ordering in PrPb₃ has been reported in 2005 [1], but the mechanism has been still under debate.
To understand such incommensurate Γ₃ quadrupole ordering in PrPb₃, we develop a microscopic theory of multipole ordering in f²-electron systems from an itinerant picture on the basis of a j-j coupling scheme [2]. For the purpose, we introduce the Γ₇-Γ₈ Hubbard model on a simple cubic lattice with the effective interactions which induce local Γ₃ states. By evaluating multipole susceptibility in a random phase approximation, we find that the hybridization between Γ₇ and Γ₈ orbitals plays a key role for the emergence of Γ₃ quadrupole ordering. We propose that Γ₃ quadrupole ordering can be explained from a combined concept of “multipole nesting”, which contains a couple of pieces of information about nesting properties and multipole density distribution on the Fermi surfaces.
[1] T. Onimaru, T. Sakakibara, N. Aso, H. Yoshizawa, H. S. Suzuki, and T. Takeuchi: Phys. Rev. Lett. 94 (2005) 197201.
[2] T. Hotta and K. Ueda: Phys. Rev. B 67 (2003) 104518.