We propose a scenario to explain the anomalous pressure dependence of the a
ntiferro-magnetic moment observed in URu2Si2, the steep change from tiny to
large moments at lower pressures (P < P-c = 15 GPa) and the gradual change
of large moment at higher pressures (P > P-c). We speculate that at ambien
t pressure the ionic ground state of U is non-magnetic quadrupolar doubler
Gamma (5) with (5f)(2), which is hybridized with the excited state of magne
tic dipolar doubler Gamma (7) with (5f)(1) via conduction electrons due to
the Kondo effect with respect to quadrupolar degrees of freedom. By decreas
ing temperature T, quadrupolar order sets in at a certain temperature T, an
d then octupolar order sets in additionally at a certain lower temperature
T-1 < T-o leading to a tiny magnetic moment induced through the weak hybrid
ization of the magnetic excited state to the nonmagnetic ground state. By i
ncreasing P, the hybridization energy increases steeply and so does the ind
uced magnetic moment at P < P-c. On the other hand, at P > P-c, the charact
er of the ground state of uranium ions changes to be magnetic somehow. Then
the magnetic order with large magnetic moment manifests itself at T < T-o.
This scenario is confirmed by using a two-channel Anderson lattice model.
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