Crystalline Electric Field Effects and Hidden Order in URu2Si2

We show that an antiferro-octupole order of E-u(x(y(2) - z(2)), y(z(2) - x(2))) symmetry accounts for the rotational symmetry (RS) reduction of the basal plane magnetic susceptibility in the hidden order (HO) phase of URu2Si2. We determine the crystalline electric field level scheme with lower singlet-doublet levels, which can stabilize the Eu octupole order, as well as the quadrupole order of Eg(y(z), z(x)) symmetry. Both orders can explain the RS reduction, but the octupole order breaks the time reversal symmetry, in agreement with the ligand NMR measurements, while the quadrupole order does not. Consequently, the E-u octupole order is favorable for the HO of URu2Si2.