Session R22: URu2Si2 and Other Related Heavy Fermions

\textbf{Metamagnetism and Quantum Acoustic Oscillations in UPt}$_{\mathbf{3}}$\textbf{:}

We present results of high resolution sound velocity measurements performed at the NHMFL, Tallahassee, in magnetic fields upto 33 T in a dilution refrigerator at temperatures down to 35 mK. For magnetic field parallel to the basal plane the observed quantum acoustic oscillations show a change in frequency as expected at the metamagnetic transition of 20 T. However, we find a similar abrupt change in frequency at 25 T for magnetic field parallel to the c-axis. The implications of this fermi surface instability even though there is no metamagnetic transition in this orientation will be discussed.   

Antiferromagnetism and Hidden Order in Isoelectronic Doping of URu$_2$Si$_2$

URu$_2$Si$_2$ has been studied for three decades to understand its unusual hidden order state. Doping of this compound on the Ru site usually causes the transition temperature to decrease and hidden order to transition to magnetic order. In contrast, the isoelectronic dopings Fe and Os cause a substantial increase in the transition temperature over a wide range of dopings, with Fe in particular mimicking applied hydrostatic pressure. However, until recently, the magnetic states of these dopings have not been well characterized. In the past year, neutron scattering results have been reported on Fe doping that show antiferromagnetism with moments that are twice as large as those measured for pure URu$_2$Si$_2$ under pressure. 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$_2$ by muon spin rotation ($\mu$SR) and susceptibility. Our $\mu$SR results demonstrate that both of these dopings show an antiferromagnetic ground state with internal fields comparable to pure URu$_2$Si$_2$ under pressure. Interpretation of our data indicates that the evolution of magnetism with doping for both Fe and Os is driven by changes in hybridization.   

Kondo bahavior in antiferromagnetic NpPdSn

Actinide-based intermetallics show a large variety of exotic physical phenomena mainly coming from 5f hybridization with both on-site and neighboring ligand states. Depending on the strength of these process unusual behaviors such as long-range magnetic order, Kondo effect, heavy-fermion ground state, valence fluctuations, and/or superconductivity have been observed. Here we report results of our extensive studies on NpPdSn. The compound crystalizes in hexagonal ZrNiAl-type of crystal structure and is studied by means of x-ray and neutron diffraction, magnetization, heat capacity, electrical resistivity, and thermoelectric power measurements, performed over a wide range of temperatures and applied magnetic fields. All the results revealed Kondo lattice behavior and antiferromagnetic ordering below 19 K. NpPdSn can be classified as a moderately enhanced heavy-fermion system, one of very few known amidst Np-based intermetallics.   

A Model for the Polar Kerr Effect in the Hidden-Order Phase of URu$_2$Si$_2$

We propose an explanation for the recent experiment [1], where an optical polar Kerr effect (PKE) was observed in the otherwise non-magnetic hidden-order phase of URu$_2$Si$_2$. In this experiment, a sample was cooled through the hidden-order transition in a strong magnetic field, which was then turned off at low temperature, and the PKE was then observed and measured on warm-up in the absence of magnetic field. We propose an explanation within the framework of a previously developed Ginzburg-Landau theory [2] for a complex order parameter, whose real and imaginary parts correspond to the hidden-order and magnetic states. The former corresponds to the hexadecapole operator as seen in experiment [3], while the latter has ferromagnetic and antiferromagnetic components of z-axis magnetization in a bilayer of URu$_2$Si$_2$. Exploring the energy landscape for the three competing states, we find to a metastable ferromagnetic local minimum induced by an external magnetic field and preserved after the field has been turned off, which can explain the observed PKE. \\[4pt] [1] E. Schemm et al., PRB, 91, 140506 (2015) \\[4pt] [2] K. Haule and G. Kotliar, EPL, 89, 57006 (2010) \\[4pt] [3] H. Kung et al., Science, 347, 1259729 (2015)   

$^{31}$P NMR Study of of URu$_2$Si$_{2-x}$P$_x$

We report initial $^{31}$P nuclear magnetic resonance measurements in single crystals of URu$_2$Si$_{2-x}$P$_x$ in the antiferromagnetic and paramagnetic phases. We compare these results with the undoped compound both at ambient pressure and under pressure.   

Lifshitz transition in high magnetic fields in UPt$_2$Si$_2$: Magnetoresistivity, Hall effect, magnetostriction and Fermi surface

We have measured the magnetoresistivity and Hall effect of single crystalline UPt$_2$Si$_2$ in DC magnetic fields up to 35 T at temperatures down to 50 mK. Moreover, we have carried out magnetostriction measurements in pulsed magnetic fields up to 55 T for temperatures down to 1.5 K. For the magnetic field applied along the $c$ axis we observe strong changes in the Hall effect at the previously established field induced phase boundaries AFM I $\leftrightarrow$ III and III $\leftrightarrow$ V (see Ref. [1]). From a detailed analysis of the Hall effect, we find evidence for topological changes of the Fermi surface due to at least one Lifshitz transition. Furthermore, in the magnetoresistivity and magnetostriction data we find a distinct history dependent anomaly within phase III, indicative of a first order phase transition. We relate our findings to band structure calculations carried out under consideration of the concept of a dual nature of the uranium 5$f$ electrons with different degrees of localization. \newline [1] D. Schulze Grachtrup et al., Phys. Rev. B {\bf 85} (2012) 054410   

Raman scattering study on the hidden order and antiferromagnetic phases in URu$_{2-x}$Fe$_x$Si$_2$

The heavy fermion compound URu$_2$Si$_2$ possesses an unusual ground state known as the ``hidden order'' (HO) phase below $T=17.5$\,K, which evolves into an large moment antiferromagnetic (LMAFM) phase under pressure. A recent Raman scattering study shows that an $A_{2g}$ symmetry ($D_{4h}$) in-gap mode emerges in the HO phase, characterizing the excitation from a chirality density wave\footnote{H. Kung, R.E. Baumbach, E.D. Bauer, V.K. Thorsmolle, W. Zhang, K. Haule, J.A. Mydosh and G. Blumberg \textit{Science} \textbf{347}, 1339 (2015)}. Here, we report Raman scattering results for single crystal URu$_{2-x}$Fe$_x$Si$_2$ with $x\leq 0.2$, where the Fe substitution acts as chemical pressure, shifting the system's ground state from HO to LMAFM. We found that the $A_{2g}$ mode softens with doping, vanishes at the HO and LMAFM phase boundary, then re-emerges and hardens with doping in the LMAFM phase. The relations between the $A_{2g}$ mode energy and the strength of the HO/LMAFM order parameters will be discussed in this talk.   

Hidden order to antiferromagnetic transition in URu$_2$Si$_2$

The second-order phase transition in the heavy fermion compound URu$_2$Si$_2$ continues to confound efforts to reveal its true nature, and bears the moniker "hidden order" with good reason. While the order parameter remains mysterious, antiferromagnetism is easily induced with modest chemical substitution. The proximity of these two phases offers tantalizing clues about the nature of the hidden order phase. We present data on the antiferromagnetic phase, revealing the similarities and the differences between the two phases, including evidence for effects above the transition temperature. The implications of these findings for the hidden order parameter will be discussed.   

Electronic tuning of URu$_{2}$Si$_{2}$ through ligand site substitution (Si $\to $ Ga and P)

Materials that straddle the boundary between itinerant and local electronic behavior are exemplary hosts for novel phenomena, including unconventional superconductivity, anomalous magnetism, non-Fermi liquid behavior, and exotic electronic phases. The 5$f$-electron intermetallic URu$_{2}$Si$_{2}$ is a well-known example, exhibiting an exotic ordered state (``hidden order'') and unconventional superconductivity. In spite of intense experimental and theoretical interest, understanding of the origin of these phenomena remains elusive. We report a study of URu$_{2}$Si$_{2}$ using the new tuning parameter, ligand site substitution Si $\to \quad L$ ($L =$ Ga and P). While phosphorous substitution quickly suppresses both hidden order and superconductivity, gallium substitution has a mild effect, illustrating the marked difference between electron- and hole-doping on the ligand site for the physics of this compound. In an effort to disentangle these phenomena, we performed electrical transport and thermodynamic measurements. Electrical transport measurements in high magnetic fields are particularly illuminating, and provide insight into the evolution of the anomalous magnetoresistance, Fermi surface topology, electronic effective masses, and $g$-factor anisotropy. We discuss trends in these quantities for electron- and hole-doping and their implications for unraveling the behavior of URu$_{2}$Si$_{2}$.   

Thermal expansion measurements on Fe substituted URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$

The search for the order parameter of the hidden order (HO) phase in URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$ has attracted an enormous amount of attention for the past three decades. The small antiferromagnetic moment of only \textasciitilde 0.03 $\mu_{\mathrm{B}}$/U found in the HO phase is too small to account for the entropy of \textasciitilde 0.2Rln(2) derived from the second order mean field BCS-like specific heat anomaly associated with the HO transition that occurs below To $=$ 17.5 K. A first order transition from the HO phase to a large moment antiferromagnetic (LMAFM) phase occurs under pressure. We have recently demonstrated that tuning URu$_{\mathrm{2}}$Si$_{\mathrm{2\thinspace }}$by substitution of Fe for Ru reproduces the temperature vs applied pressure phase diagram.and offers an opportunity to study the HO and LMAFM phases at atmospheric pressure. Motivated by this observation, we performed thermal expansion measurements on URu$_{\mathrm{2-x}}$Fe$_{\mathrm{x}}$Si$_{\mathrm{2}}$ single crystals for various values of x in both the HO and LMAFM regions of the phase diagram. Interesting preliminary results have emerged from these studies that shed light on the LMAFM phase and its relationship with the elusive HO phase.   

Magnetic excitations in URu$_2$Si$_2$ paramagnetic and Hidden Order phases

We have mapped the lattice and magnetic excitations in heavy fermion URu$_2$Si$_2$ via inelastic neutron and x-ray scattering measurements in the Hidden Order and paramagnetic phases. The magnetic excitations and phonons always respect the zone edges of the paramagnetic phase, showing no signs of reduced spatial symmetry. Features of the magnetic and lattice excitation spectra are associated with effects due to electronic interactions. Our results are inconsistent with simple local order parameters and density waves, and place constraints on models invoking Brillouin zone folding of the magnetic excitations. Phys. Rev. B 91, 035128 (2015)   

Spin fluctuations and hidden-order phases in Ce-based Kondo systems

Among heavy-fermion metals, both CeB$_6$ and Ce$_3$Pd$_{20}$Si$_6$ compounds exhibit a magnetically hidden ordered phase in their low-temperature phase diagram, which is attributed to the ordering of magnetic quadrupolar moments, known as the antiferroquadrupolar (AFQ) ordering. Using inelastic neutron scattering, we have investigated the spectrum of spin excitations in both systems. In the structurally simplest CeB$_6$, it consists of several contributions including conventional spin waves that coexist with both ferro- and antiferromagnetic excitonic resonance-like modes. However, the structurally more complex Ce$_3$Pd$_{20}$Si$_6$ possesses a much simpler magnetic excitation spectrum with only a single contribution peaked around the AFQ wave vector. It remains quasielastic in the absence of an external magnetic field, but then develops into dispersive magnon modes whose band width scales linearly with the applied field. Furthermore, neutron diffraction measurements on the same sample at sub-Kelvin temperatures revealed diffuse magnetic scattering that can be associated with the hidden order parameter.   

Evidence for ferroquadrupole order in YbRu2Ge2 from x-ray diffraction and elastoresistivity measurements

YbRu2Ge2 undergoes a non-magnetic phase transition at 10K, several Kelvin above a phase transition to a magnetically ordered state that is characterized by a unidirectional incommensurate spin density wave. Here, we show via high-resolution x-ray diffraction that the non-magnetic phase transition corresponds to a continuous tetragonal-to-orthorhombic structural phase transition. Elastoresistance measurements in the tetragonal state indicate a divergence of the quadrupolar strain susceptibility in the B1g symmetry channel, implying that the structural phase transition is driven by quadrupolar order.   

Evolution of superconductivity and magnetism in La$_{1-x}$Yb$_{x}$Ru$_{2}$P$_{2}$.

LaRu$_{2}$P$_{2}$, with a 4.1 K transition, is the first known pnictide-based superconductor. Sharing structural and electronic elements similar to those of the unconventional Fe-pnictide superconductors, it is of interest to investigate the parameter space in which a superconducting ground state survives. We present preliminary indications of more interesting magnetic behavior and structural tuning behavior when paramagnetic Yb is substituted for La in La$_{1-x}$Yb$_{x}$Ru$_{2}$P$_{2}$, and investigate potential heavy fermion behavior in the Yb end-member of this series.