Superconductivity and Antiferromagnetism in Boron-Rich Lattices

Discovery of superconductivity in technetium borides at moderate pressures

Advances in theoretical calculations have boosted the search for high-temperature superconductors, such as sulfur hydrides and rare-earth polyhydrides. However, the required extremely high pressures for stabilizing these superconductors has handicapped further implementation. Based upon thorough structural searches, we identified a series of unprecedented superconducting technetium borides at moderate pressures, including TcB (P63/mmc) with a superconducting transition temperature of Tc = 20.2 K at ambient pressure and TcB2 (P6/mmm) with Tc = 23.1 K at 20 GPa. Superconductivity in these technetium borides mainly originates from the coupling between the low-frequency vibrations of technetium atoms and the dominant technetium-4d electrons at the Fermi level. Our work therefore presents a fresh group in the family of superconducting borides, whose diversified crystal structures suggest rich possibilities in the discovery of other superconducting transition-metal borides.

Chemical bonding dictates drastic critical temperature difference in two seemingly identical superconductors

Though YB6 and LaB6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides, second only to MgB2. LaB6 does not superconduct until near-absolute zero temperatures (below 0.45 K), however. Though previous studies have quantified the canonical superconductivity descriptors of YB6's greater Fermi-level (Ef) density of states and higher electron-phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB6, hybridize with π B-B bonds and bring this π-system lower in energy than the σ B-B bonds otherwise at Ef. This inversion of bands is crucial: the optical phonon modes we show responsible for superconductivity cause the σ-orbitals of YB6 to change drastically in overlap, but couple weakly to the π-orbitals of LaB6. These phonons in YB6 even access a crossing of electronic states, indicating strong EPC. No such crossing in LaB6 is observed. Finally, a supercell (the M k-point) is shown to undergo Peierls-like effects in YB6, introducing additional EPC from both softened acoustic phonons and the same electron-coupled optical modes as in the unit cell. Overall, we find that LaB6 and YB6 have fundamentally different mechanisms of superconductivity, despite their otherwise near-identity.

High-entropy rare earth materials: synthesis, application and outlook

Recently, high-entropy (HE) materials have attracted increasing interest in various fields due to their unique characteristics. Rare earth (RE) elements have a similar atomic radius and gradually occupied 4f orbitals, endowing them with abundant optical, electric, and magnetic properties. Furthermore, HE-RE materials exhibit good structural and thermal stability and various functional properties, emerging as an important class of HE materials, which are on the verge of rapid development. However, a comprehensive review focusing on the introduction and in-depth understanding of HE-RE materials has not been reported to date. Thus, this review endeavors to provide a comprehensive summary of the development and research status of HE-RE materials, including alloys and ceramics, ranging from their structure, synthesis, and properties to applications. In addition, some distinctive issues of HR-RE materials related to the special electronic structure of RE are also discussed. Finally, we put forward the current challenges and future development directions of HE-RE materials. We hope that this review will provide inspiration for new design ideas and valuable references in this emerging field in the future.

Electronic and Structural Properties of MPtxB6-2x (M = Y, Yb): Structural Disorder in an Octahedral Boron Framework

Two new ternary platinum borides, YPtxB6-2x and YbPtxB6-2x, were obtained by argon-arc melting of the elements followed by annealing at 780 °C (750 °C). The structures of these compounds combine the fragments of CaB6- and AuCu3-type structures [space group Pm3̅m; x = 1.15, a = 4.0550(4) Å and x = 1.34, a = 4.0449(2) Å for YPtxB6-2x and YbPtxB6-2x, respectively; single-crystal X-ray diffraction]. Two possible variants of B/Pt ordering (space group P4/mmm) were created via a group-subgroup approach targeting the derived stoichiometry. The architecture of the type-I YPtxB6-2x structure model (a' = a, b' = b, c' = c) combines the 4.82 boron nets alternating with the layers of Y and Pt; the type-II YPtxB6-2x structure model (a' = 2a, b' = 2b, c' = c) exhibits columns of linked [B24] truncated cubes filled with Y running along the c axis. The striking features of both structural models are [B4Pt2] octahedra. The structural similarities with hitherto reported structures (YB2C2, M2Ni21B20, MNi21B20, and ErNiB4) were drawn supporting the verity of these models. A chemical bonding analysis for type-I and type-II YPtxB6-2x based on electron localization function distribution revealed a two-center interaction forming the 4.82 boron nets for type-I YPtxB6-2x and a covalent bonding within [B4Pt2] octahedra as well as a two-center interaction for B-B intraoctahedral bonds for type-II YPtxB6-2x. Analysis of Bader charges revealed the cationic character of the yttrium atoms. The interactions for nondistorted areas of the structures agree well with the bonding picture calculated for constituent building structures, YB6 and YPt3. Electronic structure calculations predict YPtxB6-2x to be a metal with the density of states of around N(EF) = 1 states eV-1 f.u.-1. The exploration of the Y-Pt-B system in the relevant concentration range elucidated the homogeneity field of YPtxB6-2x (0.90 ≤ x ≤ 1.40) and revealed the existence of three more ternary phases at 780 °C: YPt2B (space group P6222), YPt3B (space group P4mm), and YPt5B2 (space group C2/m).

The structure and multifunctionality of high-boron transition metal borides. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023;35:173001. [PMID: 36758243 DOI: 10.1088/1361-648x/acbad6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

High boron content transition metal (TM) borides (HB-TMBs) have recently been regarded as the promising candidate for superhard multifunctional materials. High hardness stems from the covalent bond skeleton formed by high content of boron (B) atoms to resist deformation. High valence electron density of TM and special electronic structure fromp-dhybridization of B and TM are the sources of multifunction. However, the reason of hardness variation in different HB-TMBs is still a puzzle because hardness is a complex property mainly associated with structures, chemical bonds, and mechanical anisotropy. Rich types of hybridization in B atoms (sp, sp², sp³) generate abundant structures in HB-TMBs. Studying the intrinsic interaction of structures and hardness or multifunction is significant to search new functional superhard materials. In this review, the stable structure, hardness, and multifunctionality of HB-TMBs are summarized. It is concluded that the structures of HB-TMBs are mainly composed by sandwiched stacking of B and TM layers. The hardness of HB-TMBs shows a increasing tendency with the decreasing atom radius. The polyhedron in strong B skeleton provides hardness support for HB-TMBs, among which C2/mis the most possible structure to meet the superhard standard. The shear modulus (G₀) generates a positive effect for hardness of HB-TMBs, but the effect from bulk modulus (G₀) is complex. Importantly, materials with a value ofB₀/G₀less than 1.1 are more possible to achieve the superhard standard. As for the electronic properties, almost all TMB₃and TMB₄structures exhibit metallic properties, and their density of states near the Fermi level are derived from the d electrons of TM. The excellent electrical property of HB-TMBs with higher B ratio such as ZrB₁₂comes from the channels between B-Bπ-bond and TM-d orbitals. Some HB-TMBs also indicate superconductivity from special structures, most of them have stronger hybridization of d electrons from TM atoms than p electrons from B atoms near the Fermi level. This work is meaningful to further understand and uncover new functional superhard materials in HB-TMBs.

Crystal Structures, Phase Stabilities, Electronic Properties, and Hardness of Yttrium Borides: New Insight from First-Principles Calculations

Yttrium borides have attracted much attention for their superconducting and high chemical stability. However, the fundamental knowledge of the mechanical properties and hardness of yttrium borides is rather lack. Here, we performed a systematic investigation on yttrium borides with various stoichiometries based on an unbiased CALYPSO structure search method and first-principles calculations. A new YB₆ compound with R3m hexagonal structure is observed, which is more stable than the experimental synthesized Pm3̅m phase. The calculated formation enthalpy, elastic constants, and phonon dispersions distinctly show that the R3m-YB₆ is energetically, mechanically, and dynamically stable. The density of states and electronic band structure reveal that all the stable yttrium borides are metallic. Based on a semiempirical method, the Vicker hardness of R3m-YB₆ is expectant to be 37.0 GPa, indicating it is a potential ultrahard metal. Our results provide insights for future synthesis and design of new type functional materials.

Topological Phase and Strong Correlation in Rare-Earth Hexaborides XB6 (X = La, Ce, Pr, Nd, Pm, Sm, Eu)

The rare-earth hexaboride SmB₆, known as the topological Kondo insulator, has attracted tremendous attention in recent years. It was revealed that the topological phase of SmB₆ is insensitive to the value of on-site Coulomb interactions (Hubbard U), indicating that the topological phase in SmB₆ is robust against strong correlations. On the contrary, the isostructural YbB₆ displays a sensitivity to the Hubbard U value. As U increases, YbB₆ transforms from topological Kondo insulator to trivial insulator, showing the weak robustness of the topological phase of YbB₆ against U. Consequently, the dependence of the topological phase on Hubbard U is a crucial issue in the rare-earth hexaboride family. In this work, we investigate the structural and electronic properties of rare-earth hexaboride compounds through first-principles calculations based on density functional theory. By taking the strong correlations into consideration using a wide range of on-site U values, we study the evolution of the topological phases in rare-earth hexaboride (XB₆, X = La, Ce, Pr, Nd, Pm, Sm, Eu). Unlike YbB₆, the topological trends in all the examples of XB₆ studied in this work are insensitive to the U values. We conclude that in addition to the well-known SmB₆, PmB₆, NdB₆ and EuB₆ are also topologically nontrivial compounds, whereas LaB₆, CeB₆ and PrB₆ are topologically trivial metal.

Crystal Growth by the Floating Zone Method of Ce-Substituted Crystals of the Topological Kondo Insulator SmB6

SmB6 is a mixed valence topological Kondo insulator. To investigate the effect of substituting Sm with magnetic Ce ions on the physical properties of samarium hexaboride, Ce-substituted SmB6 crystals were grown by the floating zone method for the first time as large, good quality single crystal boules. The crystal growth conditions are reported. Structural, magnetic and transport properties of single crystals of Sm1−xCexB6 (x=0.05, 0.10 and 0.20) were investigated using X-ray diffraction techniques, electrical resistivity and magnetisation measurements. Phase composition analysis of the powder X-ray diffraction data collected on the as-grown boules revealed that the main phase was that of the parent compound, SmB6. Substitution of Sm ions with magnetic Ce ions does not lead to long-range magnetic ordering in the Sm1−xCexB6 crystals. The substitution with 5% Ce and above suppresses the cross-over from bulk conductivity at high temperatures to surface-only conductivity at low temperatures.

Crystal lattice disorder and characteristic features of the low-temperature thermal properties of higher borides

Heat capacity C_P(T) and lattice parameters a(T), b(T) and c(T) of LuB₄₄Si_3.5 borosilicide are experimentally studied as a function of temperature in the range of 2-300 K. The results are compared with those of pseudo-isostructural LuB₅₀ boride. At the lowest temperatures, it is shown that the C_P(T) dependence of borosilicide changes linearly with temperature. This is attributed to the effect of glass-like behaviour of the heat capacity due to the disorder in the sublattice of non-metals. The presence of defects in the B-Si sublattice and the irregular form of the cages in the B-Si matrix, which are occupied by Lu³⁺ ions, lead to the formation of two-level systems (TLS) in the Lu³⁺ subsystem. The TLS make a characteristic bell-like low-temperature contribution to the heat capacity of borosilicide. We show that there is a wide temperature range (5-150 K) of negative thermal expansion of borosilicide, which is attributed to the influence of quasi-independent vibrations of Lu³⁺ ions in the cages of the borosilicide crystal structure.

Effect of Current on Diffusivity in Metal Hexaborides: A Spark Plasma Sintering Study

We present the effect of pulsed direct current on metal ion diffusion in CaB₆-SrB₆ diffusion couples, showing that the diffusivity of Ca²⁺ and Sr²⁺ across the diffusion couple interface is higher toward the positive electrode when subjected to a current flow of 2.2 kA at a temperature of 2007 K. We attribute this enhanced mobility to the movement of negatively charged metal vacancies toward the positive electrode in the system. Energy-dispersive spectroscopy is used to map the concentration of Ca²⁺ and Sr²⁺ in the region near the interface, and diffusion profiles are fitted with error functions. The concentration curves display concentration-dependent Boltzmann-Matano diffusivity. Total dopant values (Q) have been used to numerically compare the differences between Ca²⁺ diffusion in SrB₆ and Sr²⁺ diffusion in CaB₆. We determine an enhancement of 3.8× for Ca²⁺ into SrB₆ versus an enhancement of 1.8× for Sr²⁺ into CaB₆. No new phases are formed at the interface between CaB₆ and SrB₆, since hexaboride compounds readily form solid solutions. The results elucidate the role of pulsed direct current on the diffusion of metal ions in hexaboride compounds.

Rediscovering the Crystal Chemistry of Borides

For decades, borides have been primarily studied as crystallographic oddities. With such a wide variety of structures (a quick survey of the Inorganic Crystal Structure Database counts 1253 entries for binary boron compounds!), it is surprising that the applications of borides have been quite limited despite a great deal of fundamental research. If anything, the rich crystal chemistry found in borides could well provide the right tool for almost any application. The interplay between metals and the boron results in even more varied material's properties, many of which can be tuned via chemistry. Thus, the aim of this review is to reintroduce to the scientific community the developments in boride crystal chemistry over the past 60 years. We tie structures to material properties, and furthermore, elaborate on convenient synthetic routes toward preparing borides.

Multipolar phases and magnetically hidden order: review of the heavy-fermion compound Ce1-x La x B6

Cerium hexaboride is a cubic f-electron heavy-fermion compound that displays a rich array of low-temperature magnetic ordering phenomena which have been the subject of investigation for more than 50 years. Its complex behaviour is the result of competing interactions, with both itinerant and local electrons playing important roles. Investigating this material has proven to be a substantial challenge, in particular because of the appearance of a 'magnetically hidden order' phase, which remained elusive to neutron-scattering investigations for many years. It was not until the development of modern x-ray scattering techniques that the long suspected multipolar origin of this phase was confirmed. Doping with non-magnetic lanthanum dilutes the magnetic cerium sublattice and reduces the f-electron count, bringing about substantial changes to the ground state with the emergence of new phases and quantum critical phenomena. To this day, Ce1-x La x B6 and its related compounds remain a subject of intense interest. Despite the substantial progress in understanding their behaviour, they continue to reveal new and unexplained physical phenomena. Here we present a review of the accumulated body of knowledge on this family of materials in order to provide a firm standpoint for future investigations.

Synthesis, crystal structure and properties of the new superconductors TaRuB and NbOsB

Two new ternary compounds TaRuB and NbOsB were synthesized by arc-melting and annealing at 1500-1850 °C. They crystallize in orthorhombic primitive structures with space group Pbam. Magnetic susceptibility, electrical resistivity, and specific heat measurements reveal bulk superconductivity for metallic TaRuB with a T(c) ≈ 4 K. Electronic structure calculations by DFT methods show that 4d and 5d transition-metal states dominate the density of states (DOS) at the Fermi level E(F) with a pronounced quasi one-dimensional behaviour along the [0 0 1] direction. Comparison of the calculated DOS at E(F) with specific heat data reveals a moderate electron-phonon coupling. Possible small boron vacancies could significantly reduce the DOS at E(F), hence decrease T(c) for samples annealed at higher temperatures. For NbOsB, the DOS(E(F)) is strongly reduced due to an increase of covalent bonding interactions between Os and B. Accordingly, a lower T(c) ≈ 1 K is observed.

Complex spectral evolution in a BCS superconductor, ZrB12

We investigate the electronic structure of a complex conventional superconductor, ZrB₁₂ employing high resolution photoemission spectroscopy and ab initio band structure calculations. The experimental valence band spectra could be described reasonably well within the local density approximation. Energy bands close to the Fermi level possess t_2g symmetry and the Fermi level is found to be in the proximity of quantum fluctuation regime. The spectral lineshape in the high resolution spectra is complex exhibiting signature of a deviation from Fermi liquid behavior. A dip at the Fermi level emerges above the superconducting transition temperature that gradually grows with the decrease in temperature. The spectral simulation of the dip and spectral lineshape based on a phenomenological self energy suggests finite electron pair lifetime and a pseudogap above the superconducting transition temperature.

Raman scattering and isotopic phonon effects in dodecaborides

The Raman spectra of numerous dodecaborides have been measured on high-quality single crystals at ambient conditions with high spectral resolution and signal-to-noise ratio. Besides the strong Raman-active modes, numerous Raman-inactive modes occur in the spectra, indicating distortions of the structures. Ab initio calculation of the phonon spectra on ZrB(12) excellently agrees with the experimental results. Force constants are theoretically calculated and force parameters are estimated from the Raman frequencies. The influence of the surface range on the Raman spectra is evident. The different isotopic effects (virtual crystal approximation, the polarization effect and the effect of isotopic disorder) on the phonon frequencies are determined, separated and discussed.

Crystal growth and magnetic properties of rare earth borosilicides

B12 icosahedra cluster-containing rare earth borosilicides REB44Si2 (RE = Tb, Dy, Ho, Er, Tm, Yb) were grown by the floating zone method and their physical properties were investigated. REB44Si2 compounds are isostructural to REB50 and they are unique among the newly discovered boron-rich phases in that it is possible to grow large crystals with dimensions exceeding 10 mm. The rare earth atoms form a coupled chain structure like a ladder along the c-axis which is also the axis along which there is a B12 icosahedral chain. Magnetic properties, resistivity, and specific heat of the compounds were investigated. The conductivity follows the 3D variable range hopping mechanism and it was determined that localization lengths ξ are extremely short, actually close to the distances of the atoms themselves. Magnetic transitions above 4 K are indicated for all the compounds except for TmB44Si2 and it is found that specific heat measurement is the expedient probe of such compounds in which the low temperature susceptibility is influenced by external conditions such as crystal growth rate. Despite dimer-like features to the magnetic transition a spin gap is not observed. The magnetic coupling in these systems is indicated to be different from the conventional mechanisms in f-electron systems of dipole-dipole coupling or RKKY interaction.

Study of the Fermi surface of ZrB12 using the de Haas-van Alphen effect

The de Haas-van Alphen (dHvA) effect in the cluster superconductor ZrB12 was studied by magnetic torque measurements in magnetic fields up to 28 T at temperatures down to 0.07 K. The dHvA oscillations due to orbits from the neck sections and "cubic box" of the Fermi surface were detected. The dHvA frequencies as well as the cyclotron effective masses were calculated using the full-potential linear muffin-tin orbitals method within the generalized gradient approximation. A comparison of the experimental and calculated cyclotron mass shows unusually large electron-phonon interaction on the neck (lambdaep=0.95) and box (lambdaep=1.07) sections of the Fermi surface on the Brillouin zone boundaries.

Rare-Earth Elements and High Pressures

Praseodymium, under very high pressures, shows a magnetic behavior similar to that of cerium at normal pressure.