Session P16: Heavy Fermions- Mostly URu2Si2

Fano resonance and hybridization gap in the Kondo lattice URu$_{2}$Si$_{2}^{\ast }$

The nature of the `hidden' order transition in URu$_{2}$Si$_{2}$ remains puzzling despite intensive research over the past two and half decades. A key question under debate is whether a hybridization gap between the renormalized bands can be identified as the long-sought hidden order parameter. We report on the measurement of a hybridization gap in URu$_{2}$Si$_{2}$ employing a spectroscopic technique based on quasiparticle scattering across a ballistic metallic junction [1]. The differential conductance data exhibit an asymmetric double-peak structure, a signature for a Fano resonance in a Kondo lattice [2]. The extracted hybridization gap opens well above the hidden order transition temperature, indicating that it is not the order parameter for the hidden order phase. Our results place constraints on the origin of the hidden order transition in URu$_{2}$Si$_{2}$.\\[4pt] [1] W. K. Park \textit{et al}., arXiv:1110.5541.\\[0pt] [2] M. Maltseva, M. Dzero, P. Coleman, PRL 103, 206402 (2009).   

Tuning soft point-contact spectroscopy of URu$_{2}$Si$_{2}$ from hidden order to antiferromagnetic state through pressure

We have extended the soft point-contact spectroscopy technique under nearly hydrostatic pressure to make charge-spectroscopy measurements of URu$_{2}$Si$_{2}$ in both hidden order (HO) and large-moment antiferromagnetic (LMAF) states. In the HO state at ambient pressure, the spectroscopy shows two asymmetric peaks around the Fermi energy that emerge below the hidden order temperature T$_{HO}\sim $ 17.5 K. In the LMAF state at higher pressures, the spectra are remarkably similar to those in the HO state, indicating a similar Fermi surface gapping in the HO and LMAF states. The energy scale of this gap is, within experimental uncertainty, consistent with that of the incommensurate spin resonance at Q$_{1}$= (1$\pm $0.4, 0, 0), which also is present in both HO and LMAF states. Our results provide a new clue to unraveling the puzzling HO state.   

Temperature-dependent phonon dispersions in URu$_{2}$Si$_{2}$

The acoustic and low-energy optical phonon modes of a single crystal of URu$_{2}$Si$_{2}$ were studied via inelastic neutron scattering. The temperature dependence of the phonon dispersions will be compared with results of prior studies of phonons in this material. Our measurements were also sensitive to the temperature evolution of magnetic excitations in the hidden order phase. We will reflect on implications for the nature of the hidden order parameter.   

Hidden Order Transition in URu$_2$Si$_2$: Evidence for the Emergence of a Coherent Anderson Lattice from Scanning Tunneling Spectroscopy

The heavy-fermion compound URu$_2$Si$_2$ exhibits an onset of Kondo screening around T $\approx$ 55K and undergoes a second order phase transition at T$_0$ = 17.5K into a state with a still unknown hidden order parameter. Recent scanning tunneling spectroscopy experiments have provided insight into the temperature evolution of the electronic structure. Above the hidden order transition, the differential conductance, dI/dV, exhibits a characteristic Fano lineshape. In contrast, below T$_0$, a soft gap opens up in dI/dV and a quasi-particle interference (QPI) analysis reveals a band structure similar to that expected in a screened Kondo lattice. We demonstrate that the experimental dI/dV and QPI results below T$_0$ are consistent with the formation of a coherent Anderson lattice (CAL). In particular, dI/dV exhibits characteristic signatures of the Anderson lattice band structure, such as an asymmetric gap and a peak inside the gap which arises from the van Hove singularity of the heavy f-electron band. We identify several branches of the QPI pattern arising from intra- and interband scattering. Finally, the temperature evolution of dI/dV suggests that the formation of the CAL below the HOT is primarily driven by a strong increase of the lifetime of the heavy quasi-particles.   

Nuclear Magnetic Resonance Study of the Paramagnetic State of URu2Si2

URu2Si2 is a heavy fermion system that has challenged researchers for many years due to its transition into a hidden order (HO) state at 17.5K. We present new nuclear magnetic resonance (NMR) data in the paramagnetic phase near the HO phase transition. An analysis of the spin-lattice relaxation rate indicates a suppression of the spin fluctuations above the HO phase transition extending up to approximately 30 K. We analyze this data in the context of several different models for the spin lattice relaxation.   

Evidence of New Features in the c-axis Optical Conductivity of URu$_2$S$i_2$

The hidden order state of URu$_2$S$i_2$ remains mysterious despite many years of investigation. High quality, low noise optical data on both cleaved and cut-and-polished faces with in-plane c-axis of the tetragonal structure offer new insight into the electronic behavior at the ordering temperature. As the gap opens in the density of states, a new mode appears in the gap region that is visible in the conductivity only when reflectance is measured with light polarized along the crystal c-direction. A marked anisotropy in the gap energy seen in the optical conductivity between a-axis and c-axis provides further insight into the structure and magnitude of the energy gap and the behavior of the electrons near the greatly-reduced Fermi surface.   

Linear and Nonlinear Susceptibility Measurements in URu2Si2 and UPt3

We will discuss both DC and AC susceptibility measurements in single crystals of URu2Si2 and UPt3. In URu2Si2 we detect a ferromagnetic signature separated only by $\sim $ 1 K from the well established antiferromagnetic signature due to the hidden order at 17.5 K. This ferromagnetic signature appears to be well pronounced only in those samples where a strong ferromagnetic anomaly (also observed by others previously) appears at 35 K. This new ferromagnetic signature is further apparent in AC measurements, with its fingerprint appearing in a pronounced manner in first order, third order and fifth order susceptibility measurements. In contrast at the hidden order transition signatures are seen only in the first order and the fifth order susceptibility with no apparent change in the third order susceptibility. In UPt3, the DC third order susceptibility measurements reveal a broad peak at $\sim $10 K which is at half the temperature where a peak in the linear susceptibility is observed. This proportionality appears thus far to be universal across the f-electron based strongly correlated metals .   

Small Angle Neutron Scattering Studies of the Vortex Lattice of UPt$_3$

Although a paradigm for unconventional superconductivity, the true nature of the superconducting order parameter in UPt$_3$ is still an open question. We present results from small angle neutron scattering (SANS) studies on the vortex lattice (VL) of UPt$_3$, for fields both perpendicular and parallel to the crystal \textbf{c}-axis, that have implications for the superconducting order parameter. For perpendicular fields, an unconventional temperature dependence of the VL form factor -- and thus penetration depth -- is seen, with different dependences in the A and B-phases. This bulk measurement of the penetration depth indicates the presence of nodes in the superconducting gap. For parallel fields, we report the first measurement of a rocking curve from the VL. This is an encouraging result for the viability of using SANS to detect signatures of time reversal symmetry breaking, as the \textbf{c}-axis is taken as the chiral axis in these order parameter theories.   

Hidden order and unconventional superconductivity in URu$_2$Si$_2$

The nature of the so-called hidden order in URu$_2$Si$_2$ and the subsequent superconducting phase have remained a puzzle for over two decades. Motivated by evidence for rotational symmetry breaking seen in recent magnetic torque measurements [Okazaki et al. Science {\bf 331}, 439 (2011)], we derive a simple tight-binding model consistent with experimental Fermi surface probes and ab-initio calculations. From this model we use mean-field theory to examine the variety of hidden orders allowed by existing experimental results, including the torque measurements. We then construct a phase diagram in temperature and pressure and discuss relevant experimental consequences.   

Hastatic Order in $URu_2Si_2$

The hidden order that develops below 17.5K in $URu_2Si_2$ has eluded identification for twenty-five years. Here we show that the recent observation of Ising quasiparticles in $URu_2Si_2$ suggests a novel ``hastatic order'' {(Latin:\sl spear)},with a two-component order parameter describing hybridization between electrons and the Ising $5f^{2}$ states of the uranium atoms. Hastatic order breaks time-reversal symmetry by mixing states of different Kramers parity; this accounts for the magnetic anomalies observed in torque magnetometry and the pseudo-Goldstone mode observed in neutron scattering. Hastatic order is predicted to induce a basal-plane magnetic moment of order $0.01\mu_{B}$, a gap to longitudinal spin fluctuations that vanishes continuously at the first-order antiferromagnetic transition and a narrow resonant nematic feature in the scanning tunneling spectra.   

Staggered spin-orbit coupling induced hidden order state in heavy-fermion metal URu2Si2

The order parameter responsible for a second-order phase transition in the heavy fermion metal URu2Si2 at T = 17.5 K has remained a long-standing mystery. Here we show via ab-initio calculations that an incommensurate Fermi surface ``nesting'' in the partially-filled f-states causes a staggered spin-orbit coupling in the hidden-order state. In this cause neither the spin (S) nor the orbital (L) alone causes ordered state, rather a modulated spin-momentum locked density wave propagates along the unidirectional nesting direction with a polarized total angular momentum $m_J = \pm$ 2, in excellent agreement with experiments. It breaks spontaneous rotational symmetry, but not the time-reversal symmetry and thus gives rise to the recently observed ``nematic order'' in this state. The hidden order state will be immune to any time-reversal invariant perturbation such as pressure, whereas magnetic field will destroy it. Remarkably, these are the hallmark properties of the hidden order state. We also compute the topological quantum number to show that the hidden-order gap opening can causes a trivial to non-trivial topological phase transition, and hence defines a novel ``topological quantum critical point.'' Work is supported by US DOE.   

Emergent Rank-5 ``Nematic'' Order in URu2Si2

In the strongly correlated $f$-electron systems, novel electronic states often appear due to the interplay between electron correlations and entangled spin and orbital degrees of freedom. A spectacular example is the so-called ``hidden-order'' phase in the heavy-electron metal URu$_{2}$Si$_{2}$. The phase transition is characterized by the large amount of entropy loss observed at $T_{HO}=17.5$K, however no evidence of magnetic/structural phase transition below $T_{HO}$ have been reported so far. Despite efforts over a quarter century, the order parameter has remained unidentified. We show here that the hidden order is a rank-5 multipole (dotriacontapole) state with $E^{-}$ symmetry, based on the first-principles theoretical approach. This novel electronic state provides natural explanations of the key features including anisotropic magnetic excitations, nearly degenerate antiferromagnetic state, and spontaneous fourfold symmetry breaking.   

Electronic Structure and Correlation Effects in PuCoIn$_5$ as Compared to PuCoGa$_5$

Since their discovery nearly a decade ago, plutonium-based superconductors have attracted considerable interest, which is now heightened by the latest discovery of superconductivity in PuCoIn$_5$. In the framework of density functional theory (DFT) within the generalized gradient approximation (GGA) together with dynamical mean-field theory (DMFT), we present a comparative study of the electronic structure of superconducting PuCoIn$_5$ with an expanded unit cell volume relative to its PuCoGa$_5$ cousin. Overall, a similar GGA-based electronic structure, including the density of states, energy dispersion, and Fermi surface topology, was found for both compounds. The GGA Pu 5$f$ band was narrower in PuCoIn$_5$ than in PuCoGa$_5$ due to the expanded lattice, resulting in an effective reduction of Kondo screening in the former system, as also shown by our DMFT calculations.   

Upper critical field of $p$-wave superconductors with orthorhombic symmetry

Recent experiments on exotic ferromagnetic superconducting materials such as UCoGe and topological superconductors such as Cu$_{x}$Bi$_{2}$Se$_{3}$, have spawned renewed interest in $p$-wave superconductivity. We present an extension of the Scharnberg-Klemm theory of $H_{c2}$ in $p$-wave superconductors to cases of partially broken symmetry in an orthorhombic crystal. Using a uniaxial anisotropic pairing interaction as is appropriate for the low-field regime of UCoGe, we have shown that a field induced crossover from one $p$-wave state to another can lead to kinks in $H_{c2}(T)$, which can mimic upward curvature in all three crystal axis directions. Reasonably good fits to the low-field UCoGe data are obtained. We have also investigated the angular dependence of the axial $p$-wave state, which might prove useful in identifying the $p$-wave state present in certain materials, and possibly suggest new experiments on well known $p$-wave superconductors.   

Time-resolved quasiparticle dynamics of the itinerant antiferromagnet UPtGa$_{5}$

Time-resolved photoinduced reflectivity is measured in the spin-density-wave phase of the itinerant antiferromagnet UPtGa$_{5}$. Two relaxation components were seen: (a) a slow component whose amplitude appears below $T_{N}$, and relaxation time $\tau_{slow}$ exhibits an upturn near $T_{N}$; (b) the fast component persists at all temperatures, with the relaxation time $\tau_{fast}$ also exhibiting an upturn near $T_{N}$. Comparing with pump-probe data on UNiGa$_{5}$, the differences are explained in the context of UPtGa$_{5}$ having A-type, (rather than G-type) antiferromagnetism, resulting in partial Fermi surface nesting, partial gapping and consequently finite density of states, at the Fermi surface.