Multipole fluctuations of itinerant f electrons and triakontadipole order in URu₂Si₂

Novel electronic states are hallmarks of strongly correlated f-electron systems. The spin-orbital coupled degrees of freedom can lead to an exotic type of multipole hidden order (HO). A well-known HO is observed at the 17.5 K phase transition in URu₂Si₂, which is a long-standing mystery since its discovery in 1985. The dominating itinerant character of the 5f electrons complicates a theoretical description of this phenomenon. Here we review recent progress on a first-principles theoretical approach that allows catching the itinerant feature of f electrons. We show that in the itinerant 5f-electron model of URu₂Si₂, the most divergent multipole susceptibility indicates an instability to a triakontadipole order, with a doubly degenerate E-type symmetry. This itinerant-type multipole order is consistent with key features in the HO state, including the broken fourfold rotational symmetry observed in recent experiments.