Itinerant multipolar order in URu2Si2 and its signature in magnetic and lattice properties

The high degeneracy of partly filled f shells leads to exotic type of multipolar hidden order (HO). In URu [GRAPHICS] Si [GRAPHICS] , it has been particularly difficult to establish its symmetry due to dominating itinerant character of 5f electrons. There are now, however, magnetic torque measurements, cyclotron resonance experiments and high precision x-ray investigations that advocate a breaking of the fourfold rotational symmetry in the HO phase. We show that these observations, especially the magnetic torque oscillations, are only compatible with a doubly degenerate E-type symmetry of the HO and in particular exclude the hexadecapole HO. These experiments, however, cannot determine the even or odd character of HO under time reversal. We argue that within the context of an itinerant 5f model, the HO is due to a commensurate nesting with Q = (0,0,1) of electron-hole pockets with predominantly [GRAPHICS] character. This leads to an instability of the multipolar susceptibility corresponding to the odd rank-5 dotriakontapole E [GRAPHICS] HO. We also discuss the consequences of prominent HO candidates on elastic constant anomalies.