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Register a new userInterplay of magnetism, Fermi surface reconstructions, and hidden-order in the heavy-fermion material URu$_2$Si$_2$
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URu$_2$Si$_2$ is surely one of the most mysterious of the heavy-fermion compounds. Despite more than twenty years of experimental and theoretical works, the order parameter of the transition at $T_0 = 17.5$ K is still unknown. The state below $T_0$ remains called hidden-order phase and the stakes are still to identify the energy scales driving the system to this phase. We present new magnetoresistivity and magnetization measurements performed on very-high-quality single crystals in pulsed magnetic fields up to 60 T. We show that the transition to the hidden-order state in URu$_2$Si$_2$ is initially driven by a high-temperature crossover at around 40-50 K, which is a fingerprint of inter-site electronic correlations. In a magnetic field $mathbf{H}$ applied along the easy-axis $bf{c}$, the vanishing of this high-temperature scale precedes the polarization of the magnetic moments, as well as it drives the destabilization of the hidden-order phase. Strongly impurity-dependent magnetoresistivity confirms that the Fermi surface is reconstructed below $T_0$ and is strongly modified in a high magnetic field applied along $mathbf{c}$, i.e. at a sufficiently-high magnetic polarization. The possibility of a sharp crossover in the hidden-order state controlled by a field-induced change of the Fermi surface is pointed out.
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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$_2$.
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.
A second-order phase transition is associated with emergence of an order parameter and a spontaneous symmetry breaking. For the heavy fermion superconductor URu$_2$Si$_2$, the symmetry of the order parameter associated with its ordered phase below 17.5 K has remained ambiguous despite 30 years of research, and hence is called hidden order (HO). Here we use polarization resolved Raman spectroscopy to specify the symmetry of the low energy excitations above and below the HO transition. These excitations involve transitions between interacting heavy uranium 5f orbitals, responsible for the broken symmetry in the HO phase. From the symmetry analysis of the collective mode, we determine that the HO parameter breaks local vertical and diagonal reflection symmetries at the uranium sites, resulting in crystal field states with distinct chiral properties, which order to a commensurate chirality density wave ground state.
We present measurements of the resistivity $rho_{x,x}$ of URu2Si2 high-quality single crystals in pulsed high magnetic fields up to 81~T at a temperature of 1.4~K and up to 60~T at temperatures down to 100~mK. For a field textbf{H} applied along the magnetic easy-axis textbf{c}, a strong sample-dependence of the low-temperature resistivity in the hidden-order phase is attributed to a high carrier mobility. The interplay between the magnetic and orbital properties is emphasized by the angle-dependence of the phase diagram, where magnetic transition fields and crossover fields related to the Fermi surface properties follow a 1/$costheta$-law, $theta$ being the angle between textbf{H} and textbf{c}. For $mathbf{H}parallelmathbf{c}$, a crossover defined at a kink of $rho_{x,x}$, as initially reported in [Shishido et al., Phys. Rev. Lett. textbf{102}, 156403 (2009)], is found to be strongly sample-dependent: its characteristic field $mu_0H^*$ varies from $simeq20$~T in our best sample with a residual resistivity ratio RRR of $225$ to $simeq25$~T in a sample with a RRR of $90$. A second crossover is defined at the maximum of $rho_{x,x}$ at the sample-independent characteristic field $mu_0H_{rho,max}^{LT}simeq30$~T. Fourier analyzes of SdH oscillations show that $H_{rho,max}^{LT}$ coincides with a sudden modification of the Fermi surface, while $H^*$ lies in a regime where the Fermi surface is smoothly modified. For $mathbf{H}parallelmathbf{a}$, i) no phase transition is observed at low temperature and the system remains in the hidden-order phase up to 81~T, ii) quantum oscillations surviving up to 7~K are related to a new and almost-spherical orbit - for the first time observed here - at the frequency $F_lambdasimeq1400$~T and associated with a low effective mass $m^*_lambda=(1pm0.5)cdot m_0$, and iii) no Fermi surface modification occurs up to 81~T.
At T$_0$ = 17.5 K an exotic phase emerges from a heavy fermion state in {ur}. The nature of this hidden order (HO) phase has so far evaded explanation. Formation of an unknown quasiparticle (QP) structure is believed to be responsible for the massive removal of entropy at HO transition, however, experiments and ab-initio calculations have been unable to reveal the essential character of the QP. Here we use femtosecond pump-probe time- and angle-resolved photoemission spectroscopy (tr-ARPES) to elucidate the ultrafast dynamics of the QP. We show how the Fermi surface is renormalized by shifting states away from the Fermi level at specific locations, characterized by vector $q_{<110>} = 0.56 pm 0.08$ {an}. Measurements of the temperature-time response reveal that upon entering the HO the QP lifetime in those locations increases from 42 fs to few hundred fs. The formation of the long-lived QPs is identified here as a principal actor of the HO.
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