Direct bulk-sensitive probe of 5 f symmetry in URu ₂ Si ₂

Abstract

The second-order phase transition into a hidden order phase in URu 2 Si 2 goes along with an order parameter that is still a mystery, despite 30 years of research. However, it is understood that the symmetry of the order parameter must be related to the symmetry of the low-lying local electronic f-states. Here, we present results of a spectroscopic technique, namely core-level nonresonant inelastic X-ray scattering (NIXS). This method allows for the measurement of local high-multipole excitations and is bulk-sensitive. The observed anisotropy of the scattering function unambiguously shows that the 5f ground-state wave function is composed mainly of the Γ 1 with majority Jz = |4 + |−4 and/or Γ 2 singlet states. The incomplete dichroism indicates the possibility that quantum states of other irreducible representation are mixed into the ground state. strongly correlated electron systems | X-ray spectroscopy | crystal-electric field | heavy fermions | hidden order I n heavy fermion rare earth or actinide compounds, the f electrons are well localized at high temperatures, but as temperature is lowered, hybridization with conduction electrons becomes increasingly effective, resulting in a more itinerant f -electron character at low temperatures. These hybridized f electrons form narrow bands and have large effective masses. Quasiparticle interaction effects in these narrow bands are responsible for the many exciting phenomena present in heavy fermion compounds: multipolar order (1), unconventional superconductivity (2), or quantum criticality (3). The hidden order phase in URu2Si2 is one example of the exotic low-temperature phases found in this material class. URu2Si2 is a tetragonal heavy fermion compound that undergoes two phase transitions, the nonmagnetic hidden order (HO) transition at THO = 17.5 K, which involves an appreciable loss of entropy, and a superconducting transition at about 1.5 K (4-7). Below the HO transition, small-ordered magnetic moments were observed in the earlier studies but were determined later to belong to a parasitic minority phase. With applied pressure (p ≥ 0.7 GPa), the HO order is replaced by an antiferromagnetic phase with large-ordered moments (so-called LMAF -phase) (8). The order parameter of the HO phase has been the subject of intense investigations for more than 30 years but, so far, has remained hidden, which has been the inspiration for its name. This second-order transition into an electronically ordered state involves a reconstruction of the Fermi surface (9, 10) and a change of quasiparticle scattering rate (11). The Fermi surfaces of the HO and high-pressure LMAF phase are very similar (12).In URu2Si2 three-energy scales have been identified: a hybridization gap of ∆ hyb ≈ 13 meV [150 K] (13) that opens below 27 K, another gap that opens in the HO phase with ∆HO ≈ 4.1 meV [50 K] in the charge (9, 10, 14, 15) as well as spin channel (16,17), and a resonance mode that appears in the HO gap at ∼ =1.6 meV [18 K], also in both channels (18)(19)(20). Furthermore, with entering ...

Fermi-surface selective determination of the g -factor anisotropy in URu2Si2

“…However, recent nonresonant inelastic X-ray scattering experiments show that the ground state consists mainly of singlet states in the U 4+ 5f 2 configuration. 25 The g tensor has never been determined for any heavy fermion system from electronic band-structure calculations. A main difficulty is to know the real crystalline electric ground state of the magnetic ions.…”

“…23,24 In the localized picture the Ising character of the localized f states of the uranium ions is transferred by hybridization to the heavy quasiparticles forming a Fermi surface. However, the magnetic and crystal electric field ground-state wave function in URu 2 Si 2 is still under discussion 25 and even the localized or itinerant character of the 5f electrons.…”

High temperature singlet-based magnetism from Hund’s rule correlations

“…Density functional theory suggests that the charge and spin density on uranium are significantly modified by itinerancy effects [14,15] (see also Supplementary Note 1), as we will discuss in the analysis below, making it difficult to address this question from secondary characteristics such as the local or ordered moment. However, analyses in 2014-2016 have shown that resonant fine structure at the O-edge (5dà5f transition) provides a distinctive fingerprint for identifying the nominal valence state and electronic multiplet symmetry on uranium [16][17][18][19]. X-ray absorption spectra (XAS) of UBi 2 and USb 2 were measured by the total electron yield (TEY) method, revealing curves that are superficially similar but quantitatively quite different ( Fig.…”

Large positive correlation between the effective electron mass and the multipolar fluctuation in the heavy-fermion metal Ce1 − x La x B6

“…This sudden increase of γ 0 can be triggered if itinerant electrons which might have been segregated to form the high-entropy region are participating in the correlation phenomenon relevant to m * in phase IV. In the near future, we hope experimental techniques such as scanning tunneling spectroscopy, 46 nonresonant inelastic X-ray scattering 4 and inelastic NS 47 are accessible for the further characterization of both the heavy itinerant electronic state and the multipolar state in Ce 1−x La x B 6 . Also, high-quality single crystals with 0.75 < x < 1 will allow us to scrutinize the existence of a putative QCP and its possible conjunction with the SC which emerges as x approaches to unity.…”