Origin of the tiny antiferro-magnetic moment in URu 2Si 2

Abstract

Possible orders in URu 2Si 2 are investigated using a two-channel degenerate Anderson model. The ground state of uranium ions is the non-Kramers quadrupolar doublet Γ 5 with (5f) 2, and its relevalent excited state is the Kramers dipolar doublet Γ 7 with (5f) 1. These states mix with each other via conduction electrons. At low temperatures, the system forms renormalized bands with both quadrupole and dipole degrees of freedom due to the quadrupolar Kondo effect which slightly mixes quadrupolar Γ 5, a primary state of uranium ions, with dipolar Γ 7. At a certain low temperature, conduction electrons in the renormalized bands undergo quadrupolar ordering with a large quadrupolar moment. At a further lower temperature, octupolar ordering occurs, accompanied by a tiny dipolar moment which is attributed to the property of the renormalized bands with primarily the Γ 5-character slightly mixed with the Γ 7-character. These phenomena are well described by the 1/ N-expansion method with pseudo-fermions for the non-Kramers doublet Γ 5 and slave bosons for the Kramers doublet Γ 7.