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Register a new userImpact of Fe substitution on the electronic structure of URu$_2$Si$_2$
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The application of pressure as well as the successive substitution of Ru with Fe in the hidden order (HO) compound URu$_2$Si$_2$ leads to the formation of the large moment antiferromagnetic phase (LMAFM). Here we have investigated the substitution series URu$_{2-x}$Fe$_x$Si$_2$ with $x$ = 0.2 and 0.3 with non-resonant inelastic x-ray scattering (NIXS) and 4$f$ core-level photoelectron spectroscopy with hard x-rays (HAXPES). NIXS shows that the substitution of Fe has no impact on the symmetry of the ground-state wave function. In HAXPES we find no shift of spectral weight that would be indicative for a change of the 5$f$-electron count. Consequently, changes in the exchange interaction $cal{J}$ due to substitution must be minor so that the conjecture of chemical pressure seems unlikely. An alternative scenario is discussed, namely the formation of long range magnetic order due the substitution induced local enhancement of the magnetization in the vicinity of the $f$-electron ions while the overall electronic structure remains unchanged.
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We have used specific heat and neutron diffraction measurements on single crystals of URu$_{2-x}$Fe$_x$Si$_2$ for Fe concentrations $x$ $leq$ 0.7 to establish that chemical substitution of Ru with Fe acts as chemical pressure $P_{ch}$ as previously proposed by Kanchanavatee et al. [Phys. Rev. B {bf 84}, 245122 (2011)] based on bulk measurements on polycrystalline samples. Notably, neutron diffraction reveals a sharp increase of the uranium magnetic moment at $x=0.1$, reminiscent of the behavior at the hidden order (HO) to large moment antiferromagnetic (LMAFM) phase transition observed at a pressure $P_xapprox$ 0.5-0.7~GPa in URu$_2$Si$_2$. Using the unit cell volume determined from our measurements and an isothermal compressibility $kappa_{T} = 5.2 times 10^{-3}$ GPa$^{-1}$ for URu$_2$Si$_2$, we determine the chemical pressure $P_{ch}$ in URu$_{2-x}$Fe$_x$Si$_2$ as a function of $x$. The resulting temperature $T$-chemical pressure $P_{ch}$ phase diagram for URu$_{2-x}$Fe$_x$Si$_2$ is in agreement with the established temperature $T$-external pressure $P$ phase diagram of URu$_2$Si$_2$.
The three-dimensional (3D) electronic structure of the hidden order compound URu$_2$Si$_2$ in a paramagnetic phase was revealed using a 3D angle-resolved photoelectron spectroscopy where the electronic structure of the entire Brillouin zone is obtained by scanning both incident photon energy and detection angles of photoelectrons. The quasi-particle bands with enhanced contribution from the $mathrm{U}~5f$ state were observed near $E_mathrm{F}$, formed by the hybridization with the $mathrm{Ru}~4d$ states. The energy dispersion of the quasi-particle band is significantly depend on $k_z$, indicating that they inherently have a 3D nature. The band-structure calculation qualitatively explain the characteristic features of the band structure and Fermi surface although the electron correlation effect strongly renormalizes the quasi-particle bands. The 3D and strongly-correlated nature of the quasi-particle bands in URu$_2$Si$_2$ is an essential ingredient for modeling its hidden-order transition.
We report a comprehensive investigation of the lattice dynamics of URu$_2$Si$_2$ as a function of temperature using Raman scattering, optical conductivity and inelastic neutron scattering measurements as well as theoretical {it ab initio} calculations. The main effects on the optical phonon modes are related to Kondo physics. The B$_{1g}$ ($Gamma_3$ symmetry) phonon mode slightly softens below $sim$100~K, in connection with the previously reported softening of the elastic constant, $C_{11}-C_{12}$, of the same symmetry, both observations suggesting a B$_{1g}$ symmetry-breaking instability in the Kondo regime. Through optical conductivity, we detect clear signatures of strong electron-phonon coupling, with temperature dependent spectral weight and Fano line shape of some phonon modes. Surprisingly, the line shapes of two phonon modes, E$_u$(1) and A$_{2u}$(2), show opposite temperature dependencies. The A$_{2u}$(2) mode loses its Fano shape below 150 K, whereas the E$_u$(1) mode acquires it below 100~K, in the Kondo cross-over regime. This may point out to momentum-dependent Kondo physics. By inelastic neutron scattering measurements, we have drawn the full dispersion of the phonon modes between 300~K and 2~K. No remarkable temperature dependence has been obtained including through the hidden order transition. {it Ab initio} calculations with the spin-orbit coupling are in good agreement with the data except for a few low energy branches with propagation in the (a,b) plane.
Phase transitions and symmetry are intimately linked. Melting of ice, for example, restores translation invariance. The mysterious hidden order (HO) phase of URu$_2$Si$_2$ has, despite relentless research efforts, kept its symmetry breaking element intangible. Here we present a high-resolution x-ray diffraction study of the URu$_2$Si$_2$ crystal structure as a function of hydrostatic pressure. Below a critical pressure threshold $p_capprox3$ kbar, no tetragonal lattice symmetry breaking is observed even below the HO transition $T_{HO}=17.5$ K. For $p>p_c$, however, a pressure-induced rotational symmetry breaking is identified with an onset temperatures $T_{OR}sim 100$ K. The emergence of an orthorhombic phase is found and discussed in terms of an electronic nematic order that appears unrelated to the HO, but with possible relevance for the pressure-induced antiferromagnetic (AF) phase. Existing theories describe the HO and AF phases through an adiabatic continuity of a complex order parameter. Since none of these theories predicts a pressure-induced nematic order, our finding adds an additional symmetry breaking element to this long-standing problem.
The observation of Ising quasiparticles is a signatory feature of the hidden order phase of URu$_2$Si$_2$. In this paper we discuss its nature and the strong constraints it places on current theories of the hidden order. In the hastatic theory such anisotropic quasiparticles are naturally described described by resonant scattering between half-integer spin conduction electrons and integer-spin Ising moments. The hybridization that mixes states of different Kramers parity is spinorial; its role as an symmetry-breaking order parameter is consistent with optical and tunnelling probes that indicate its sudden development at the hidden order transition. We discuss the microscopic origin of hastatic order, identifying it as a fractionalization of three body bound-states into integer spin fermions and half-integer spin bosons. After reviewing key features of hastatic order and their broader implications, we discuss our predictions for experiment and recent measurements. We end with challenges both for hastatic order and more generally for any theory of the hidden order state in URu$_2$Si$_2$.
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