We have investigated the magnetic susceptibility, the electrical resistivity, the specific heat, the thermoelectric power, the Hall coefficient, and the thermal conductivity of the ${\text{Al}}_{13}{\text{Fe}}_4$ and ${\text{Al}}_{13}{\left(\text{Fe},\text{Ni}\right)}_4$ monoclinic approximants to the decagonal quasicrystal. While the ${\text{Al}}_{13}{\text{Fe}}_4$ crystals are structurally well ordered, the ternary derivative ${\text{Al}}_{13}{\left(\text{Fe},\text{Ni}\right)}_4$ contains substitutional disorder and is considered as a disordered version of the ${\text{Al}}_{13}{\text{Fe}}_4$. The crystallographic-direction-dependent measurements were performed along the $a^{\ast }$, $b$, and $c$ directions of the monoclinic unit cell, where the $\left(a^{\ast },c\right)$ atomic planes are stacked along the $b$ direction. The electronic transport and the magnetic properties exhibit significant anisotropy. The stacking $b$ direction is the most conducting direction for the electricity and heat. The effect of substitutional disorder in ${\text{Al}}_{13}{\left(\text{Fe},\text{Ni}\right)}_4$ is manifested in the large residual resistivity $\rho \left(T\to 0\right)$ and significantly reduced thermal conductivity of this compound, as compared to the ordered ${\text{Al}}_{13}{\text{Fe}}_4$. Specific-heat measurements reveal that the electronic density of states at the Fermi level of both compounds is high. The anisotropic Hall coefficient $R_H$ reflects complex structure of the anisotropic Fermi surface that contains electronlike and holelike contributions. Depending on the combination of directions of the current and the magnetic field, electronlike $\left(R_H<0\right)$ or holelike $\left(R_H>0\right)$ contributions may dominate, or the two contributions compensate each other $\left(R_H\approx 0\right)$. Similar complicated anisotropic behavior was observed also in the thermopower. The anisotropic Fermi surface was calculated ab initio using the atomic parameters of the refined ${\text{Al}}_{13}{\text{Fe}}_4$ structural model that is also presented in this work.

We present a detailed study of ${}^{75}\text{A}\text{s}$ nuclear magnetic resonance Knight shift and spin-lattice relaxation rate in the normal state of stoichiometric polycrystalline LiFeAs. Our analysis of the Korringa relation suggests that LiFeAs exhibits strong antiferromagnetic fluctuations, if transferred hyperfine coupling is a dominant interaction between ${}^{75}\text{A}\text{s}$ nuclei and Fe electronic spins, whereas for an on-site hyperfine coupling scenario, these are weaker, but still present to account for our experimental observations. Density-functional calculations of electric field gradient correctly reproduce the experimental values for both ${}^{75}\text{A}\text{s}$ and ${}^7\text{L}\text{i}$ sites.

Mixed spin-singlet and spin-triplet pairing can occur in noncentrosymmetric superconductors. In this respect, a comprehensive characterization of the noncentrosymmetric superconductor BeAu was carried out. It was established that BeAu undergoes a structural phase transition from a low-temperature noncentrosymmetric FeSi structure type to a high-temperature centrosymmetric structure in the CsCl type at $T_{\text{s}}=860$ K. The low-temperature modification exhibits a superconducting transition below $T_{\text{c}}=3.3$ K. The values of lower ($H_{\text{c1}}=32$ Oe) and upper ($H_{\text{c2}}=335$ Oe) critical fields are rather small, confirming that this type-II (${\kappa }_{\text{G-L}}=2.3$) weakly coupled (${\lambda }_{\text{e-p}}=0.5,\mathrm{\Delta }{C}_{\text{e}}/{\gamma }_{\text{n}}{T}_{\text{c}}\approx 1.26$) superconductor can be well understood within the Bardeen-Cooper-Schrieffer theory. The muon spin relaxation analysis indicates that the time-reversal symmetry is preserved when the superconducting state is entered, supporting conventional superconductivity in BeAu. From the density functional band structure calculations, a considerable contribution of the Be electrons to the superconducting state was established. On average, a rather small mass renormalization was found, consistent with the experimental data.

Unusual physical properties like large magnetoresistance (MR) and superconductivity occurring in semimetals with Dirac or Weyl points are often linked to their topologically nontrivial band structures. However, there is an increasing number of reports on semimetals that show large MR in the absence of Dirac or Weyl points. Herein we report an experimental and theoretical study on the layered transition-metal dichalcogenide (TMDC) $\mathrm{HfT}{\mathrm{e}}_2$ that shows a large MR of $1350\%$ at $T=2$ K and ${\mu }_{0}H=9\mathrm{T}$ in the absence of Dirac or Weyl points. Moreover, the structure and electrical resistivity under pressure reveal a unique structural transition. These results clearly distinguish $\mathrm{HfT}{\mathrm{e}}_2$ from TMDCs like $\mathrm{MoT}{\mathrm{e}}_2$ or $\mathrm{WT}{\mathrm{e}}_2$ which both exhibit larger MR and are viewed as Weyl semimetals. $\mathrm{HfT}{\mathrm{e}}_2$ is an appealing platform for future investigations on the interplay of particular band-structure features and their connection to emerging physical properties.

We have investigated anisotropic physical properties (magnetic susceptibility, electrical resistivity, thermoelectric power, Hall coefficient, and thermal conductivity) of Y-Al-Ni-Co decagonal approximant with composition ${\text{Al}}_{76}{\text{Co}}_{22}{\text{Ni}}_2$. The crystalline-direction-dependent measurements were performed along three orthogonal directions $a^{\ast }$, $b$, and $c$ of the Y-Al-Ni-Co unit cell, where $\left(a,c\right)$ monoclinic atomic planes are stacked along the perpendicular $b$ direction. Anisotropic magnetic susceptibility of conduction electrons is paramagnetic for the field lying within the $\left(a,c\right)$ atomic planes and diamagnetic for the field along the $b$ direction. Anisotropic electrical resistivity is low in all crystalline directions, appearing in the order ${\rho }_{a^{\ast }}>{\rho }_c⪢{\rho }_b$. Thermopower shows electron-phonon enhancement effect. Anisotropic bare thermopower (in the absence of electron-phonon interactions) was extracted, appearing in the same order as the resistivity, $\left|S_{a^{\ast }}^{\text{bare}}/T\right|>\left|S_c^{\text{bare}}/T\right|>\left|S_b^{\text{bare}}/T\right|$. Anisotropic thermal conductivity appears in the order ${\kappa }^b>{\kappa }^c>{\kappa }^{a^{\ast }}$, so that $b$ is the most conducting direction for both electricity and heat. Hall coefficient $R_H$ exhibits pronounced anisotropy, where the magnetic field in a given crystalline direction yields the same $R_H$ for the current along the other two crystalline directions in the perpendicular plane. These anisotropies are analyzed in terms of the anisotropic structure of the Y-Al-Ni-Co phase and the ab initio calculated anisotropic Fermi surface. The results are compared with the literature-reported anisotropy of the physical properties of the $d$-Al-Ni-Co decagonal quasicrystal.

The crystallographic structures of decagonal quasicrystals and their periodic approximants are traditionally described as a periodic stacking of atomic planes. By performing a ${}^{27}\text{A}\text{l}$ NMR spectroscopic study of the ${\text{Al}}_{13}{M}_4$ ($M=\text{transition}$ metal) family of four-layer decagonal approximants, including the orthorhombic ${\text{o-Al}}_{13}{\text{Co}}_4$, the monoclinic ${\text{Al}}_{13}{\text{Fe}}_4$, its ternary derivative ${\text{Al}}_{13}{\left(\text{Fe},\text{Ni}\right)}_4$, and the monoclinic ${\text{Al}}_{13}{\text{Ru}}_4$, we show that all these phases contain structural detail of a nearly linear $M\text{-Al-}M$ atomic group trapped inside an elongated cage, resembling the three-dimensional (3D) “cage-compound” structure of the intermetallic clathrates. We determined the electric-field-gradient- (EFG) and the magnetic-shielding tensors at the Al site of the $M\text{-Al-}M$ groups. The asymmetry parameter of the EFG tensor was estimated theoretically by a point-charge model, taking into account the charges of both the $M\text{-Al-}M$ atoms and the surrounding cage atoms. The calculations support ionic bonding of the $M\text{-Al-}M$ group to the cage atoms and the existence of a 3D chemical bonding network in the ${\text{Al}}_{13}{M}_4$ phases. The above results show that the traditional description of the ${\text{Al}}_{13}{M}_4$ decagonal approximant phases in terms of two-dimensional (2D) atomic layers stacked along the pseudotenfold crystallographic direction is a convenient geometrical approach to describe their complex structures but is not appropriate for the description of their physical properties, which should be analyzed by taking into account the full 3D nature of the chemical bonding framework. This favors the 3D cage-compound structural description of the ${\text{Al}}_{13}{M}_4$ phases over the pseudo-2D stacked-layer description.