The nature of order in low-temperature phases of some materials is not directly observable in experiments. These so-called “hidden orders” (HOs) have inspired decades of research aimed at identifying the mechanisms underlying these exotic states of matter. In insulators, HO phases originate from degenerate many-electron states on localized f-shells, which may harbor high-rank multipole moments. We demonstrate that the ground-state order and magnetic excitations of the prototypical HO system NpO₂ can be fully described by a low-energy Hamiltonian derived using a many-body ab initio force-theorem method. A primary non-collinear order of time-odd rank-5 (triakontadipolar) moments has been predicted [1]. We also show that the exotic, non-chiral magnetic order in PrO₂ results from strong high-rank multipolar interactions within the full ⟨JM*⟩ ground-state multiplet. The unusual magnetization process in PrO₂ is shown to arise from dominant multipolar superexchange interactions [2].

 

As shown by Kotliar and Haule in 2007, the canonical and perhaps most extensively studied metallic hidden-order material, URu₂Si₂, can develop a hidden multipolar order (hexadecapolar) due to a localized 5f² configuration at low temperatures. At higher temperatures, hybridization of the localized 5f levels leads to Kondo behavior—a phenomenon described by the "Kondo arrest" scenario. At very low temperatures, the hidden-order phase coexists with superconductivity. Based on correlated ab initio calculations, we reveal a close analogy between the normal-state behavior of URu₂Si₂ and that of the newly discovered heavy-fermion superconductor UTe₂.

 

The UTe₂ compound is regarded as a heavy-fermion, mixed-valence system with highly unusual properties in both its normal and superconducting states. It exhibits no signs of magnetic order but shows strong magnetic susceptibility anisotropy and a highly anisotropic superconducting critical field. In addition to heavy-fermion-like behavior in the normal state, UTe₂ displays a distinctive Schottky-type anomaly around 12 K and a characteristic excitation gap near 35–40 K. Using dynamical mean-field theory (DMFT) with a quasi-atomic treatment of electron correlations, we show that the ab initio-derived crystal-field splitting of the 5f² ionic configuration is consistent with these experimental observations. We further analyze the symmetry of magnetic and multipolar moment fluctuations that may drive the superconducting pairing at low temperatures [3]. We speculate that the critical fluctuations mediating superconductivity in both UTe₂ and URu₂Si₂ could share a common origin..

 

 

[1] L. V. Pourovskii and S. Khmelevskyi, Proc Natl Acad Sci USA (PNAS), 118 e2025317118 (2021)

[2] S. Khmelevskyi, and L. V. Pourovskii, Commun. Phys. 7, 12 (2024).

[3] S. Khmelevskyi, L. V. Pourovskii, E.A. Tereshina-Chitrova, Phys. Rev. B 107, 214501 (2023).