Session J22: Heavy Fermions: U-based Compounds

Nonlinear Optical Spectroscopy as a possible probe of Hidden Order in URu$_2$Si$_2$

The symmetry of the primary order parameter underlying the hidden order (HO) phase of URu$_{2}$Si$_{2}$ is a topic of ongoing debate. Although high-rank multipole orderings are proposed, these are challenging to resolve experimentally using diffraction based probes. We investigate the possibility of using the nonlinear optical response of URu$_{2}$Si$_{2}$ to measure electronic multipolar ordering. We report temperature and wavelength dependent nonlinear optical harmonic generation measurements on micron scale areas of URu$_{2}$Si$_{2}$ single crystals using a novel low temperature rotational anisotropy technique\footnote{D. H. Torchinsky \emph{et al.}, \textbf{Rev. Sci. Instrum.} 85, 083102 (2014)}. We identify a nonlinear optical susceptibility tensor that couples to HO whose implications on the symmetry of the HO parameter will be discussed.   

Atomic-scale wavefunctions and dynamics inside the hidden order compound URu2Si2

Understanding the emergent wavefunctions of correlated electron systems requires experimental probes that can resolve electronic states on an atomic scale. However, imaging techniques such as STM that resolve single atoms do not provide a good way to distinguish the entangled symmetries of nearby electrons. I will talk about how energy-resolved scattering measurements performed with resonance-tuned X-rays can open a unique window into many-body entangled states on an atomic length scale and femtosecond time scale. The presentation will focus on data that unveil low temperature wavefunction symmetries and energetics of uranium electrons in the ``hidden order'' compound URu2Si2.   

Evidence for a nematic component to the Hidden Order parameter in URu$_2$Si$_2$ from differential elastoresistance measurements

In this work, we use a novel piezo actuator technique to measure the differential elastoresistance of the unconventional heavy fermion superconductor URu$_2$Si$_2$. Prior to the onset of superconductivity ($T_c \sim 1.5$ K), URu$_2$Si$_2$ undergoes a phase transition to a novel ``Hidden Order'' state which has defied comprehensive understanding for over 30 years. By tracking the temperature dependence of various elastoresistivity coefficients (proportional to the nematic susceptibility in the limit of linear response) above the Hidden Order transition temperature ($T_{HO} \sim 17.5$ K), our measurements reveal an extended nematic fluctuation regime at high temperatures and a strong anomalous divergence (which scales as the singular contribution to the heat capacity) proximate to the Hidden Order transition. Understood within a Ginzburg-Landau framework for coupled order parameters, these measurements imply that the Hidden Order parameter is a two-component vector oriented in the [110] crystallographic direction which breaks the underlying four-fold symmetry of the lattice (in addition to other symmetries).   

Optical conductivity of URu$_2$Si$_2$: gaps and electron phonon coupling

We measured the in-plane and out-of-plane optical conductivity of URu$_2$Si$_2$. The hidden order transition at 17 K shows the opening of a gap in both polarizations, with a sharp decrease in the optical scattering rate. Above the hidden order we find a redistribution of spectral weight that closely follows the dc resistivity. The appearance of a coherent transport behavior in the resistivity is accompanied by the formation of a sharp Drude-like peak. We also found all four polar phonons expected from a group theory analysis. The number and shape of the phonons remain mostly unchanged across the hidden order transition. These phonons are strongly coupled to the electronic continuum as shown by their Fano asymmetric line shape. We found a strongly temperature dependent Fano-Wigner-Breit parameter with striking changes close to the Kondo transition. Our results suggest a rearrangement of the continuum density of states around this temperature. The changes found have opposite in-plane and out-of-plane behaviors.   

Antiferromagnetism in Fe and Os doped URu$_2$Si$_2$ studied by $\mu$SR

URu$_2$Si$_2$ is a material that has been studied extensively for almost three decades in an effort to characterize its unusual ``hidden order'' state. One common method used to study this compound is to perturb the ground state by doping the Ru site with various metals. Such doping usually causes the transition temperature to drop, and the hidden order state to transition into an antiferromagnetic state. In contrast to this common behavior, the isoelectronic dopings Fe and Os cause a substantial increase in the transition temperature over a wide range of dopings. However, the magnetic states of these dopings have not been well characterized, with only a small number of studies on polycrystalline samples reported in the literature. In this talk, we present an investigation of the magnetic properties of single crystal samples of URu$_{2-x}$Fe$_x$Si$_2$ and URu$_{2-x}$Os$_x$Si$_2$. Our $\mu$SR results demonstrate that both of these dopings show an antiferromagnetic ground state between $x = 0.1$ and $x = 0.4$ that evolves with increasing temperature into the paramagnetic state by a second order transition.   

Chemical pressure tuning of URu2Si2 via isoelectronic substitution of Ru with Fe

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 isoelectronic substitution of Ru with Fe acts as ``chemical pressure'' $P_{ch}$. Neutron diffraction reveals a sharp increase of the uranium magnetic moment at $x=0.1$, reminiscent of the ``hidden order'' (HO) to large moment antiferromagnetic (LMAFM) phase transition in URu$_2$Si$_2$. Using the unit cell volume, and the isothermal compressibility $\kappa_{T}$ for URu$_2$Si$_2$, we determine $P_{ch}$ as function of $x$. The resulting temperature $T$-chemical pressure $P_{ch}$ phase diagram for URu$_{2-x}$Fe$_x$Si$_2$ is in good agreement with the established temperature $T$-external pressure $P$ phase diagram of URu$_2$Si$_2$. Thus, URu$_{2-x}$Fe$_x$Si$_2$ provides a new opportunity to study the close relationship between the HO and LMAFM phases with methods that cannot be used under pressure, and may shed some new light on the on the elusive order parameter of the HO.   

Elastoresistivity in the ``Hidden Order'' compound URu$_{2}$Si$_{\mathrm{2-x}}$P$_{\mathrm{x}}$

The intermetallic compound URu$_{2}$Si$_{2}$ undergoes a phase transition near 17.5 K, with clear thermodynamic and transport signatures. However, despite nearly 30 years of research, the nature of the order parameter remains unknown. This ``hidden order'' phase, and its relationship to the superconductivity that appears below 1.4 K, remains a central puzzle in the physics of correlated electron materials. In order to unfold the phenomena that are nascent in pure URu$_{2}$Si$_{2}$, we recently developed a flux growth technique that allows electron doping through Si $\to$ P substitution. This technique is novel because it enables the use of high vapor pressure elements. We find that phosphorous substitution suppresses the hidden order transition temperature until, at roughly 1.5{\%} doping, a quantum phase transition is reached. We measure the doping evolution of the temperature dependent elastoresistivity focusing on the behavior of the nematic component (b2g) as the Hidden Order transition is approached.   

Unfolding the physics of URu$_{2}$Si$_{2}$ through chemical substitution (Si $\to $ P)

URu$_{2}$Si$_{2}$ features all of the major phenomena that are at the focus of current research in correlated electron metals, including an exotic ordered state (``hidden order''), unconventional superconductivity, and anomalous metallic behavior. We recently undertook to study URu$_{2}$Si$_{2}$ using the novel tuning parameter Si $\to $ P substitution which, in a simple picture, simply adds electrons to the conduction band. Substitution of high vapor pressure elements in URu$_{2}$Si$_{2}$ is unprecedented, and is enabled by our new molten metal flux technique [1]. We find a rich phase diagram that includes two quantum phase transitions that are associated with hidden order and antiferromagnetism, respectively. In the hidden order region, the superconducting transition temperature is initially enhanced with P, after which it approaches zero before hidden order is destroyed, suggesting that URu$_{2}$Si$_{2}$ might be electronically displaced from ``optimal'' doping. We also find that the hidden order and antiferromagnetic regions are distant from each other, indicating that their origins are quite different. We will discuss these results and implications for understanding hidden order, superconductivity, and quantum criticality. \\[4pt] [1] R. E. Baumbach, \textit{et. al.}, ``High purity specimens of URu$_{2}$Si$_{2}$ produced by a molten metal flux technique,'' \textit{Phil. Mag.} (2014).   

Ultrasound in a Metamagnet and the Single Energy Scale Model

Ultrasound velocity measurements in the heavy electron compound UPt$_{\mathrm{3}}$ for magnetic fields up to 33 T are reported. We show that the single energy scale model (B.S.Shivaram et al., Phys. Rev., B89, 24110799(R), 2014) captures the observed key features of the field dependence in the sound velocity shift, $\delta $v$_{\mathrm{s}}$. The shift $\delta $v$_{\mathrm{s}}$ at H$_{\mathrm{c}}$ is inversely dependent on temperature above a certain ``Dingle Temperature'' and assumes a fixed value at very low T. This ``saturation'' in $\delta $v$_{\mathrm{s}}$ is accounted for by level broadening in the single energy scale model..   

Thermal and Transport properties of U$_{2}$Pt$_{1-x}$Ir$_{x}$C$_{2}$

We report thermal and transport properties of U$_{2}$Pt$_{1-x}$Ir$_{x}$C$_{2}$ from which a magnetic phase diagram is obtained. Pure U$_{2}$IrC$_{2}$ is an antiferromagnet at 6.5 $K$, whose Neel temperature initially rises to 13.2 $K$ at $x$=0.8 and subsequently is suppressed to zero temperature with increasing Pt content near $x$=0.4. Heat capacity data at $x$=0.4 shows an upturn at low temperature, which is consistent with proximity to a quantum critical point and considered as non-Fermi liquid behavior. The entropy after the phonon contribution has been subtracted has a value of 0.18 $Rln2$ at the Neel temperature of U$_{2}$IrC$_{2}$, revealing an itinerant nature of the 5f electrons in this compound. On the Pt rich side of the phase diagram, superconductivity is suppressed by $x$=0.15. The residual resistivity increases by a factor of 10 from pure Pt ($x$=0) to $x$=0.15 where superconductivity is suppressed to zero. The phase diagram is compared to pressure tuned and Rh doped U$_{2}$PtC$_{2}$ demonstrating the role of electronic tuning in this system.   

Single crystal growth and study the physical properties of non-centrosymmetric UIrSi$_{3}$

Heavy-fermion superconductivity in the non-centrosymmetric crystal structure has drawn much attention [1]. It is theoretically argued that the order parameter contains not only a spin-singlet part, but also an admixture of a spin-triplet state. The compound UIrSi$_{3}$ crystallizes in the non-centrosymmetric BaNiSn$_{3}$ structure which is closely related to the well-known ThCr$_{2}$Si$_{2}$-type [2]. Preliminary study on polycrystalline UIrSi$_{3}$ shows antiferromagnetic order below Neel temperature $T_{\mathrm{N}}=$42 K [2]. Its lanthanide analog CeIrSi$_{3}$ shows heavy-fermion superconductivity under pressure [1]. Therefore, further investigation on UIrSi$_{3}$ would be meaningful. We will present our attempt to grow single crystal of UIrSi$_{3}$ by Czochralski method in a tetra-arc-furnace and study of its physical properties. \\[4pt] [1] Onuki \textit{et al}., J. Phys. Soc. Jpn. \textbf{77}, suppl. A 37 (2008).\\[0pt] [2] Buffat \textit{et al.}, J. Mag. Mag. Mat. 62, 53 (1986).   

Tuning the ground state of the Kondo lattice in U$T$Bi$_{2}$ ($T = Ag, Au$) single crystals

Motivated by the interesting magnetic anisotropy found in the Ce-based heavy fermion family Ce$TX_2$ ($T$ = transition metal, $X = $ pnictogen), here we study the novel U-based parent compounds U$T$Bi$_{2}$ ($T =$ Ag, Au) by combining magnetization, electrical resistivity, and heat-capacity measurements. The single crystals, synthesized by the self-flux method, also crystallize in the tetragonal HfCuSi$_{2}$-type structure (space group P4/nmm). Interestingly, although UAgBi$_{2}$ is a low-$\gamma$ antiferromagnet below $T_{N} = 181$ K, UAuBi$_{2}$ is a moderately heavy uniaxial ferromagnet below $T_{c} = 22$ K. Nevertheless, both compounds display the easy-magnetization direction along the $c$-axis and a large magnetocrystalline anisotropy. Our results point out to an incoherent Kondo behaviour in the paramagnetic state and an intricate competition between crystal field effects and two anisotropic exchange interactions, which lead to the remarkable difference in the observed ground states.   

Direct Observation of a Superconducting Spin Resonance in the Heavy Fermion Antiferromagnetic Superconductor $UNi_{2}Al_{3}$

We present neutron scattering data identifying a superconducting spin resonance in the heavy fermion, antiferromagnetic superconductor $UNi_{2}Al_{3}$. This resolves a longstanding issue in the comparison of $UNi_{2}Al_{3}$ to its isostructural sister $UPd_{2}Al_{3}$. Theses material both undergo antiferromagnetic phase transitions at relatively high temperatures, T$_{N}$ = 4.6 K and 14.5 K respectively, before respectively superconducting below 1.2 and 2 K(B. D. Gaulin, et al, PRB 66, 174520 (2002)). However, previous reports suggest that only the magnetic fluctuations in $UPd_{2}Al_{3}$ display sensitivity to superconductivity via a superconducting spin resonance - the build up in the superconducting ground state of excess scattered intensity at a well defined resonance energy centered on a magnetic wave-vector. We resolve this disparity by clearly identifying a superconducting spin resonance in $UNi_{2}Al_{3}$ at the incommensurate wavevector Q = ($\frac{1}{2}$ $\pm$ 0.11 0 $\frac{1}{2}$). This re-establishes the relationship between these sister compounds and further evidences the intimate correlation of magnetism and superconductivity.