There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Negative thermal expansion (NTE) is an intriguing physical property of solids, which is a consequence of a complex interplay among the lattice, phonons, and electrons. Interestingly, a large number of NTE materials have been found in various types of functional materials. In the last two decades good progress has been achieved to discover new phenomena and mechanisms of NTE. In the present review article, NTE is reviewed in functional materials of ferroelectrics, magnetics, multiferroics, superconductors, temperature-induced electron configuration change and so on. Zero thermal expansion (ZTE) of functional materials is emphasized due to the importance for practical applications. The NTE functional materials present a general physical picture to reveal a strong coupling role between physical properties and NTE. There is a general nature of NTE for both ferroelectrics and magnetics, in which NTE is determined by either ferroelectric order or magnetic one. In NTE functional materials, a multi-way to control thermal expansion can be established through the coupling roles of ferroelectricity-NTE, magnetism-NTE, change of electron configuration-NTE, open-framework-NTE, and so on. Chemical modification has been proved to be an effective method to control thermal expansion. Finally, challenges and questions are discussed for the development of NTE materials. There remains a challenge to discover a “perfect” NTE material for each specific application for chemists. The future studies on NTE functional materials will definitely promote the development of NTE materials.

Negative thermal expansion in functional materials: controllable thermal expansion by chemical modifications

The Kondo insulator SmB6 has long been known to exhibit low-temperature transport anomalies whose origin is of great interest. Here we uniquely access the surface electronic structure of the anomalous transport regime by combining state-of-the-art laser and synchrotron-based angle-resolved photoemission techniques. We observe clear in-gap states (up to ~4 meV), whose temperature dependence is contingent on the Kondo gap formation. In addition, our observed in-gap Fermi surface oddness tied with the Kramers' point topology, their coexistence with the two-dimensional transport anomaly in the Kondo hybridization regime, as well as their robustness against thermal recycling, taken together, collectively provide strong evidence for protected surface metallicity with a Fermi surface whose topology is consistent with the theoretically predicted topological Fermi surface. Our observations of systematic surface electronic structure provide the fundamental electronic parameters for the anomalous Kondo ground state of correlated electron material SmB6.

/pdf/surface-electronic-structure-of-the-topological-kondo-4rsohkc3ns.pdf

Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6.

The Kondo insulator samarium hexaboride exhibits low-temperature transport anomalies, which might be due to topological surface states. Here Jiang et al. perform angle-resolved photoemission and its circular dichroism measurements, which suggest that the anomalies might be of topological origin.

/pdf/observation-of-possible-topological-in-gap-surface-states-in-39ix6gfs4r.pdf

Observation of possible topological in-gap surface states in the Kondo insulator SmB6 by photoemission

The elastic constants c11, c12 and c44 of U, Np, Pu, and Am telluride single crystals have been obtained by Brillouin scattering from the measured sound velocities in prominent crystallographic directions. In case of the U chalcogenides also by ultrasound techniques. The Cauchy pressure, the Poisson ratio, the anisotropy ratio, the bulk modulus and the Debye temperature have been derived from these data. U and Pu telluride have a negative c12, implying intermediate valence. AmTe has a very low bulk modulus, but a positive c12. It is extremely soft, with a very low sound velocity. For AmTe also the LO and TO phonon frequencies could be determined. The elastic data point to a divalent Am state. The optical reflectivity of the light actinide tellurides (and sometimes of all chalcogenides) has been measured between UV and infrared wavelengths, in the case of AmTe down to the far infrared. The plasma edge of the free carriers has been determined, which yields the ratio of n/m*. Together with the γ value of the specific heat and magnetic data a consistent proposal for the electronic structure of the light actinide chalcogenides can be given. Thus, the Pu chalcogenides are intermediate valent and represent the high-pressure phase of the corresponding Sm chalcogenides. AmTe, as judged by the electronic, optic and magnetic properties seems to be in the 5f7 configuration, i.e. divalent Am, but with a narrow, half-filled (24 meV) wide 5f band, about 0.1 eV below the bottom of the 6d conduction band. We thus propose a new kind of unhybridized heavy fermion. Also AmTe seems to represent a high-pressure phase of EuTe.

Electronic and elastic properties of the light actinide tellurides

The paramagnetic response of mixed-valence samarium hexaboride has been studied by inelastic neutron scattering using a low-absorption double-isotope single crystal of 154Sm11 B6. Measurements were performed for energy transfers 0<or=h(cross) omega <or=50 meV at temperatures ranging from 2 to 100 K. Two main contributions were observed in the spectra: a broad intermultiplet transition of single-ion type at h(cross) omega approximately=36 meV, and a narrow low-energy excitation centred at h(cross) omega approximately=14 meV, which is strongly anisotropic and temperature dependent and exhibits a weak but visible dispersion. The latter excitation appears to be an inherent feature of the mixed-valence state due to f-electron hybridization effects, which denotes the formation of a local bound state around the Sm sites.

https://iopscience.iop.org/article/10.1088/0953-8984/7/2/007/pdf

Magnetic excitation spectrum of mixed-valence SmB6 studied by neutron scattering on a single crystal

All acoustic and the lowest optic branches in three main symmetry directions have been determined by inelastic neutron scattering at room temperature using a double isotope monocrystal 154Sm11B6. In comparison with the integer valence system LaB6 the phonons are softer, and the LA branches exhibit remarkable anomalies. These features are interpreted on the basis of a specific coupling of the lattice vibrations with the dipole (f-d) and monopole (f-f) excitations of the Sm shells, the latter being characteristic for the mixed valence semiconductor. A weak broad signal has been observed in the energy gap between acoustic and optic modes, which can be ascribed to an additional mode appearing due to the nonadiabatic interaction of phonons with valence fluctuations.

http://iopscience.iop.org/article/10.1209/0295-5075/10/5/012/pdf

Lattice dynamics of intermediate valence semiconductor SmB6

Time-of-flight inelastic neutron scattering experiments on the archetype Kondo-insulator compound ${\mathrm{YbB}}_{12}$ are reported. At the minimum temperature of $T=15\mathrm{K},$ the magnetic response clearly shows a spin-gaplike behavior below 10 meV. Above this energy, the spectrum consists of three main components at 15, 20, and 38 meV. Above 40 K, substantial quasielastic scattering is recovered whereas the upper peak is rapidly suppressed. An extra intensity remains visible in the 20 meV region up to $T=159\mathrm{K}.$ These results reflect the formation of a singlet Kondo-insulator ground state, but an additional mechanism is needed to explain the complex structure of the magnetic response. One possibility is an interplay between hybridization and crystal-field effects.

Inelastic neutron scattering study of the Kondo semiconductor YbB 12

Two, essentially dispersionless, magnetic excitations, at energies ℏ ω 1 ≃ 36 and ℏ ω 2 ≃ 14 meV, have been investig ated by inelastic neutron scattering measurements on a single crystal of mixed-valent 154 Sm 11 B 6 . The latter one decreases markedly upon heating, or with increasing | Q | . It is ascribed to the spin-flip of 5d electrons which form a bound state with the 4f electrons of a given site by tunnelling over the octahedron defined by its six nearest Sm neighbours.

Magnetic excitations in SmB6 single crystals

Inelastic-neutron-scattering spectra were measured on the polycrystalline double isotopic sample 154Sm 11B6 in a wide range of the energy transfer. The intermultiplet transitions corresponding to f6 and f5 configurations of the intermediate-valent state of the Sm ion, as well as a low-energy excitation with unusual momentum transfer and temperature dependences have been observed in the magnetic part of the scattering function.

https://iopscience.iop.org/article/10.1209/0295-5075/23/5/008/pdf

I. P. Sadikov

Papers

Magnetic excitation spectrum of mixed-valence SmB6 studied by neutron scattering on a single crystal

Lattice dynamics of intermediate valence semiconductor SmB6

Inelastic neutron scattering study of the Kondo semiconductor YbB 12

Magnetic excitations in SmB6 single crystals

Neutron Scattering Study of the Intermediate-Valent Ground State in SmB6