Multipolar ordering in NpO 2 below 25 K

The phase transition at T 0 = 25 K in NpO 2 and the single-ion nature of the Np 5f electrons is examined in the light of the results of resonant x-ray scattering experiments at the M 4 Np edge. These experiments exclude usual magnetic dipole ordering at T 0 , and provide direct evidence of long-range order of the electric quadrupole moment with Γ 5 symmetry. The phase transition is purely electronic and does not involve either internal or external crystallographic distortions, so the symmetry of the system remains cubic. The primary order parameter (OP) is associated with Γ 4 t magnetic octupoles, ordering in a triple- q longitudinal structure defined by the three wavevectors of the ⟨001⟩ star. Magnetic octupolar order breaks invariance under time reversal and induces the order of electric quadrupoles as the secondary OP. The resulting ground state is a singlet with zero dipole magnetic moment.