Isoelectronic perturbations to f-d-electron hybridization and the enhancement of hidden order in URu2Si2

Electrical resistivity measurements were performed on single crystals of URu_2–xOs_xSi₂ up to x = 0.28 under hydrostatic pressure up to P = 2 GPa. As the Os concentration, x, is increased, 1) the lattice expands, creating an effective negative chemical pressure P_ch(x); 2) the hidden-order (HO) phase is enhanced and the system is driven toward a large-moment antiferromagnetic (LMAFM) phase; and 3) less external pressure P_c is required to induce the HO→LMAFM phase transition. We compare the behavior of the T(x, P) phase boundary reported here for the URu_2-xOs_xSi₂ system with previous reports of enhanced HO in URu₂Si₂ upon tuning with P or similarly in URu_2–xFe_xSi₂ upon tuning with positive P_ch(x). It is noteworthy that pressure, Fe substitution, and Os substitution are the only known perturbations that enhance the HO phase and induce the first-order transition to the LMAFM phase in URu₂Si₂. We present a scenario in which the application of pressure or the isoelectronic substitution of Fe and Os ions for Ru results in an increase in the hybridization of the U-5f-electron and transition metal d-electron states which leads to electronic instability in the paramagnetic phase and the concurrent formation of HO (and LMAFM) in URu₂Si₂. Calculations in the tight-binding approximation are included to determine the strength of hybridization between the U-5f-electron states and the d-electron states of Ru and its isoelectronic Fe and Os substituents in URu₂Si₂.

The heavy-fermion superconducting compound URu2Si2 is known for its second-order phase transition into the so-called “hidden-order” (HO) phase at a transition temperature T0 ≈17.5 K. Extensive investigation of the phase space in proximity to the HO phase transition has provided a detailed picture of the electronic and magnetic structure of this unique phase (1–42). However, more than three decades after the initial characterization of URu2Si2 (1–3), the order parameter for the HO phase is still unidentified.Most perturbations to the URu2Si2 compound have the effect of suppressing HO. The application of an external magnetic field (H) suppresses the HO phase (41, 43) and many of the chemical substitutions (x) at the U, Ru, or Si sites that have been explored significantly reduce T0, even at modest levels of substituent concentration (44–52). At present, only three perturbations are known to consistently enhance the HO phase in URu2Si2: 1) external pressure P, 2) isoelectronic substitution of Fe ions for Ru, and 3) isoelectronic substitution of Os ions for Ru. Upon applying pressure P, the HO phase in pure URu2Si2 is enhanced (6) and the system is driven toward a large-moment antiferromagnetic (LMAFM) phase (53). The HO→LMAFM phase transition is identified indirectly by a characteristic “kink” at a critical pressure Pc ≈1.5 GPa in the T0 (P) phase boundary (18, 53, 54) and also directly by neutron diffraction experiments, which reveal an increase in the magnetic moment from μ ∼ (0.03±0.02)μB/U in the HO phase to μ ∼ 0.4 μB/U in the LMAFM phase (13, 55, 56).Recent reports indicate that the isoelectronic substitution of Fe ions for Ru in URu2Si2 replicates the T0(P) behavior in URu2Si2 (57–59). An increase in x in URu2−xFexSi2 enhances the HO phase and drives the system toward the HO→LMAFM phase transition at a critical Fe concentration xc ≈0.15 (58, 60). The decrease in the volume of the unit cell due to substitution of smaller Fe ions for Ru may be interpreted as a chemical pressure, Pch, where the Fe concentration x can be converted to Pch (x) (57, 59). In addition, the induced HO→LMAFM phase transition in URu2−xFexSi2 occurs at combinations of x and P that consistently obey the additive relationship: Pch(x) + Pc ≈1.5 GPa (57, 59). These results have led to the suggestion that Pch is equivalent to P in affecting the HO and LMAFM phases (58, 59).Reports of the isoelectronic substitution of larger Os ions for Ru have shown that an increase in x in URu2−xOsxSi2 1) expands the volume of the unit cell, thus creating an effective negative chemical pressure (Pch ≤0); 2) enhances the HO phase; and 3) drives the system toward a similar HO→LMAFM phase transition at a critical Os concentration of xc ≈0.065 (60–62). These results are contrary to the expectation that a negative Pch would lead to a suppression of HO and complicate the view of chemical pressure as a mechanism affecting the evolution of phases in URu2Si2.In this paper, we report on the behavior of the T(x, P) boundary for the URu2−xOsxSi2 system based on ρ(T) measurements of single crystals of URu2−xOsxSi2 as a function of Os concentration x and applied pressure P. The T(x, P) phase boundary observed here for the URu2−xOsxSi2 system (57–59) is compared to that of the URu2−xFexSi2 system and also with the behavior of T(P) in pure URu2Si2. As an explanation for the enhancement of HO toward the HO→LMAFM phase transition, we suggest a scenario in which each of the perturbations of Os substitution, Fe substitution, and pressure P favors delocalization of the 5f electrons and increases the hybridization of the uranium 5f-electron and transition metal (Fe, Ru, Os) d-electron states. To avoid an ad hoc explanation of the effect of increasing the Os concentration x in URu2−xOsxSi2, compared to the effects of pressure P and Fe substitution, we explain how pressure P, Fe substitution, and Os substitution are three perturbative routes to enhancement of the U-5f- and d-electron hybridization. The importance of the 5f- and d-electron hybridization to the emergence of HO/LMAFM is presented in the context of the Fermi surface (FS) instability that leads to a reconstruction and partial gapping of the FS during the transition from the paramagnetic (PM) phase to the HO and LMAFM phases (2, 6, 20, 22, 24–26, 37, 38, 63).In an effort to further understand the effect of isoelectronic substitution on the 5f- and d-electron hybridization, calculations in the tight-binding approximation were made for compounds from the series UM2Si2 (M = Fe, Ru, and Os). The calculations indicate that the degree of hybridization is largely dependent on the magnitude of the difference between the binding energy of the localized U-5f electrons and that of the transition metal d electrons.     

From hidden order to antiferromagnetism: Electronic structure changes in Fe-doped URu2Si2

In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic and still unsolved example is the transition of the heavy fermion compound URu2Si2 (URS) into the so-called hidden-order (HO) phase when the temperature drops below T0=17.5 K. Here, we show that the interaction between the heavy fermion and the conduction band states near the Fermi level has a key role in the emergence of the HO phase. Using angle-resolved photoemission spectroscopy, we find that while the Fermi surfaces of the HO and of a neighboring antiferromagnetic (AFM) phase of well-defined order parameter have the same topography, they differ in the size of some, but not all, of their electron pockets. Such a nonrigid change of the electronic structure indicates that a change in the interaction strength between states near the Fermi level is a crucial ingredient for the HO to AFM phase transition.

The transition of URu2Si2 from a high-temperature paramagnetic (PM) phase to the hidden-order (HO) phase below T0 is accompanied by anomalies in specific heat (1–3), electrical resistivity (1, 3), thermal expansion (4), and magnetic susceptibility (2, 3) that are all typical of magnetic ordering. However, the small associated antiferromagnetic (AFM) moment (5) is insufficient to explain the large entropy loss and was shown to be of extrinsic origin (6). Inelastic neutron scattering (INS) experiments revealed gapped magnetic excitations below T0 at commensurate and incommensurate wave vectors (7–9), while an instability and partial gapping of the Fermi surface was observed by angle-resolved photoemission spectroscopy (ARPES) (10–16) and scanning tunneling microscopy/spectroscopy (17, 18). More recently, high-resolution, low-temperature ARPES experiments imaged the Fermi surface reconstruction across the HO transition, unveiling the nesting vectors between Fermi sheets associated with the gapped magnetic excitations seen in INS experiments (14, 19) and quantitatively explaining, from the changes in Fermi surface size and quasiparticle mass, the large entropy loss in the HO phase (19). Nonetheless, the nature of the HO parameter is still hotly debated (20–23).The HO phase is furthermore unstable above a temperature-dependent critical pressure of about 0.7 GPa at T=0, at which it undergoes a first-order transition into a large moment AFM phase where the value of the magnetic moment per U atom exhibits a sharp increase, by a factor of 10 to 50 (6, 24–30). When the system crosses the HO → AFM phase boundary, the characteristic magnetic excitations of the HO phase are either suppressed or modified (8, 31), while resistivity and specific heat measurements suggest that the partial gapping of the Fermi surface is enhanced (24, 27).As the AFM phase has a well-defined order parameter, studying the evolution of the electronic structure across the HO/AFM transition would help develop an understanding of the HO state. So far, the experimental determination of the Fermi surface by Shubnikov de Haas (SdH) oscillations only showed minor changes across the HO → AFM phase boundary (32). Here, we take advantage of the HO/AFM transition induced by chemical pressure in URu2Si2, through the partial substitution of Ru with Fe (33–37), to directly probe its electronic structure in the AFM phase using ARPES. As we shall see, our results reveal that changes in the Ru 4d–U 5f hybridization across the HO/AFM phase boundary seem essential for a better understanding of the HO state.