Replacing a magnetic atom by a spinless atom in a heavy-fermion compound generates a quantum state often referred to as a "Kondo-hole". No experimental imaging has been achieved of the atomic-scale electronic structure of a Kondo-hole, or of their destructive impact [Lawrence JM, et al. (1996) Phys Rev B 53:12559-12562] [Bauer ED, et al. (2011) Proc Natl Acad Sci. 108:6857-6861] on the hybridization process between conduction and localized electrons which generates the heavy-fermion state. Here we report visualization of the electronic structure at Kondo-holes created by substituting spinless thorium atoms for magnetic uranium atoms in the heavy-fermion system URu(2)Si(2). At each thorium atom, an electronic bound state is observed. Moreover, surrounding each thorium atom we find the unusual modulations of hybridization strength recently predicted to occur at Kondo-holes [Figgins J, Morr DK (2011) Phys Rev Lett 107:066401]. Then, by introducing the "hybridization gapmap" technique to heavy-fermion studies, we discover intense nanoscale heterogeneity of hybridization due to a combination of the randomness of Kondo-hole sites and the long-range nature of the hybridization oscillations. These observations provide direct insight into both the microscopic processes of heavy-fermion forming hybridization and the macroscopic effects of Kondo-hole doping.

The five independent moduli required to construct the complete monocrystal elastic modulus tensor of the hexagonal-symmetry superhard compound ReB2 were measured from 308 to 5 K using resonant ultrasound spectroscopy on a special-texture polycrystal. This is possible because, confirmed by X-ray diffraction, the specimen measured was composed of grains with hexagonal axes parallel so that its polycrystal elastic response is identical to a monocrystal and because hexagonal-symmetry solids are elastically isotropic in the plane perpendicular to the hexagonal axis. Along the hexagonal (c) axis, C330=1021 GPa, nearly equal to C11 of diamond, and consistent with the superhard properties. However, in the (softer) isotropic plane, C110=671 GPa, much lower than diamond. The changes of Cij with temperature are very small and smooth. The Debye temperature was computed to be 738 K, and using a high-temperature approximation, the Grüneisen parameter is γ=1.7.

The search for superhard materials, driven by their widespread use in industrial applications, highlights one of the most difficult problems in the field of materials science: the accurate characterization of a material’s intrinsic physical properties. This paper reports on the full elastic tensor of two polycrystalline isotropic specimens and one specimen of ReB2 consisting of highly oriented grains. The high-monocrystal bulk modulus value extracted from the grain-oriented specimen, measured by resonant ultrasound spectroscopy, validates the ultra-incompressibility of ReB2. An observed hardness of 40GPa and a Debye temperature of 731K were calculated for the ReB2 crystal, confirming its superhard and super-stiff properties. All the measured moduli of the ReB2 grain-oriented crystal exceed the comparable ones for the polycrystal by amounts that cannot be explained by averaging over direction, which may reveal why recent measurements reported on ReB2 containing excess boron yield values that are not as hard or incompressible as the crystal.

We have searched for the hidden multispin order parameters that have been proposed to explain the weak ordered moment observed in the heavy-fermion superconductor URu2Si2. Since the exotic spin order is predicted to cause broken-symmetry Bragg peaks that develop rapidly with applied magnetic field, we have measured their strength in fields up to 8 T, for which a large easily observable moment is predicted. The Bragg neutron scattering is found to decrease rather than increase when a field is applied along the easy tetragonal c-axis, while there is no change for a field at right angles. The results rule out the proposed symmetric multispin order parameters. The zero-field transition is found to exhibit critical softening of the spin gap and a cusp in the susceptibility at TN, as expected for the ordering of magnetic dipoles.

Elastic neutron scattering measurements performed on single crystal UNi{sub 2}Al{sub 3} show this heavy fermion superconductor to display long-range incommensurate (IC) magnetic order below T{sub N}=5.2K. The ordering wavevector is (1/2 {+-} {tau},0,1/2) with {tau}=0.110{+-}0.003, and the size of the maximum ordered moment is 0.24{+-}0.1{mu}{sub B}/U.

The magnetic and transport properties of single-crystal UNi2Ge2 have been investigated, by means of magnetic susceptibility, resistivity, and Hall-coefficient measurements, from 4.2 to 300 K. A large anisotropy was observed in both magnetic and transport properties. The magnetic susceptibility of UNi2Ge2 is Curie-Weiss-like in the paramagnetic state. The resistivity of UNi2Ge2 is largely due to magnetic scattering, and the phonon contribution only amounts to 8% of the total resistivity at room temperature. Along the c axis, the resistivity shows a Kondo-type behavior at high temperatures. The temperature dependence of the Hall coefficient can be accounted for by a theoretical model with a magnetic skew-scattering process.

The resistivity and Hall coefficient of single-crystal UNi2Si2 have been studied in detail for the temperature range 4.2-300 K. The resistivity of UNi2Si2 is largely due to magnetic scattering and the phonon scattering contribution is estimated to be about 14% at room temperature. At low temperatures, the resistivity can be described by a gapped spin-wave model plus a T2 term. The temperature dependence of the Hall coefficient is accounted for by a theoretical model invoking skew scattering of conduction electrons by localized magnetic moments. Among the three magnetic phase transition temperatures, the two lower ones are found to be magnetic field dependent and shift with the field applied along the tetragonal c axis. Using the resistivity measurement in an applied magnetic field, a field-temperature phase diagram of UNi2Si2 is presented.

The infrared properties of the high temperature superconductors are dominated by the strong temperature dependent absorption of the free carriers at low frequency and a temperature independent midinfrared band. Dramatic changes in reflectance do occur as the material becomes superconducting but these changes cannot be used to determine the energy gap, since as a result of the development of the superconducting condensate, changes in the real part of the dielectric function dominate. Also, since the relaxation rate of the free carriers is of the order of 200 cm−1 at 100 K the materials are near the clean limit below this temperature and we do not expect to see structure at the energy of the superconducting gap. The reflectance edge observed in many experiments at 450 cm−1 is caused by the onset of the midinfrared absorption which has the character of a direct particle-hole excitation rather than the Holstein scattering of the free carriers.

Measurements of the far-infrared reflectance of ${\mathrm{URu}}_{2}$${\mathrm{Si}}_{2}$ between 10 and 720 ${\mathrm{cm}}^{\ensuremath{-}1}$ have been made at temperatures from 2 to 90 K. Above the coherence temperature the optical conductivity increases monotonically with increasing frequency and at lower temperatures the development of the narrow mode responsible for the high dc conductivity is clearly observed. In the antiferromagnetic state an energy gap with a size between 46 and 65 ${\mathrm{cm}}^{\ensuremath{-}1}$ is observed whose shape is reminiscent of the energy gap observed in the spin-density-wave state of Cr.