  Novel electronic states resulting from entangled spin and orbital degrees of
freedom are hallmarks of strongly correlated f-electron systems. A spectacular
example is the so-called 'hidden-order' phase transition in the heavy-electron
metal URu2Si2, which is characterized by the huge amount of entropy lost at
T_{HO}=17.5K. However, no evidence of magnetic/structural phase transition has
been found below T_{HO} so far. The origin of the hidden-order phase transition
has been a long-standing mystery in condensed matter physics. Here, based on a
first-principles theoretical approach, we examine the complete set of multipole
correlations allowed in this material. The results uncover that the
hidden-order parameter is a rank-5 multipole (dotriacontapole) order with
'nematic' E^- symmetry, which exhibits staggered pseudospin moments along the
[110] direction. This naturally provides comprehensive explanations of all key
features in the hidden-order phase including anisotropic magnetic excitations,
nearly degenerate antiferromagnetic-ordered state, and spontaneous
rotational-symmetry breaking.
