Sequence of multipolar transitions: A scenario for URu2Si2

dand f -shells support a large number of local degrees of freedom: dipoles, quadrupoles, octupoles, hexadecapoles, etc. Usually, the ordering of any multipole component leaves the system sufficiently symmetrical to allow a second symmetry breaking transition. To classify the possibilities, one has to construct the symmetry group of the first ordered phase, and then re-classify the order parameters in the new symmetry. While this is straightforward for dipole or quadrupole order, it is less familiar for octupole order. We give a group theoretical analysis, and some illustrative mean field calculations, for the case when a second ordering transition follows Txyz octupolar ordering in a tetragonal system. If quadrupoles appear in the second phase transition, they must be accompanied by a time-reversal-odd multipole as an induced order parameter. For Oxy, Oxz, or Oyz quadrupoles, this would be one of the components of J, which should be easy either to check or to rule out. However, a pre-existing octupolar symmetry can also be broken by a transition to a new octupole–hexadecapole order, or by a combination of O 2 quadrupole and triakontadipole order. We use our results to discuss a scenario for URu2Si2. According to recent NQR results, the onset of hidden order at T0 = 17K is followed by quadrupolar ordering at T ∗ ≈ 13.5K. We extend our symmetry analysis to a sequence of two continuous hidden order transitions, assuming that octupolar ordering happens first.