The superconducting state of the newly discovered superconductor ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$, with a quasi-one-dimensional crystal structure $(T_{\mathbf{c}}\sim 6\text{K})$, is investigated using magnetization and muon-spin relaxation or rotation $\left(\mu \mathrm{SR}\right)$ measurements. Our analysis shows that the temperature dependence of the superfluid density obtained from transverse-field $\mu \mathrm{SR}$ measurements fits either to an isotropic $s$-wave character for the superconducting gap or to a $d$-wave model with line nodes. Furthermore, the goodness-of-fit $\left({\chi }^2\right)$ values indicate that our data fit better to the $d$-wave model $\left({\chi }^2\sim 1\right)$ than the $s$-wave model $\left({\chi }^2\sim 1.38\right)$. Therefore our $\mu \mathrm{SR}$ analysis is more consistent with having line nodes than being fully gapped, which is in agreement with the results of the penetration depth measured using a tunnel diode oscillator technique. Our zero-field $\mu \mathrm{SR}$ measurements do reveal very weak evidence of the spontaneous appearance of an internal magnetic field below the transition temperature, which might indicate that the superconducting state is not conventional. This observation suggests that the electrons are paired via unconventional channels such as spin fluctuations, as proposed on the basis of theoretical models of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$. Furthermore, from our transverse-field $\mu \mathrm{SR}$ study the magnetic penetration depth ${\lambda }_L$, superconducting carrier density $n_s$, and effective-mass enhancement $m^{*}$ have been estimated to be ${\lambda }_L\left(0\right)=432\left(4\right)$ nm, $n_s=2.7\times {10}^{27}\text{carriers}/{\mathrm{m}}^3$, and $m^{*}=1.75m_e$, respectively.

We have investigated the superconducting properties of the noncentrosymmetric superconductor LaRhSi${}_3$ by performing magnetization, specific heat, electrical resistivity, and muon spin relaxation ($\mu$SR) measurements. LaRhSi${}_3$ crystallizes with the BaNiSn${}_3$-type tetragonal structure (space group $I4\hspace{0.5em}\mathit{mm}$), as confirmed through our neutron diffraction study. Magnetic susceptibility, electrical resistivity and specific heat data reveal a sharp and well-defined superconducting transition at $T_c=2.16\pm 0.08$ K. The low-temperature specific heat data reveal that LaRhSi${}_3$ is a weakly coupled bulk BCS superconductor and has an $s$-wave singlet ground state with an isotropic energy gap of $~$0.3 meV, $2{\Delta }_0/k_B{T}_c=3.24$. The specific heat data measured in an applied magnetic field strongly indicate a type I behavior. Type I superconductivity in this compound is also inferred from the Ginzburg-Landau parameter, $\kappa =0.25$. Various superconducting parameters, including the electron-phonon coupling strength, penetration depth, and coherence length, characterize LaRhSi${}_3$ as a moderate dirty-limit superconductor. A detailed study of the magnetic field-temperature ($H-T$) phase diagram is presented and from a consideration of the free energy, the thermodynamic critical field, $H_{c0}$, is estimated to be $17.1\pm 0.1$ mT, which is in very good agreement with that estimated from the transverse field $\mu$SR measurement that gives $H_{c0}=17.2\pm 0.1$ mT. The transverse field $\mu$SR results are consistent with conventional type I superconductivity in this compound. Further, the zero field $\mu$SR results indicate that time-reversal symmetry is preserved when entering the superconducting state, also supporting a singlet pairing superconducting ground state in LaRhSi${}_3$.

By employing inelastic neutron scattering (INS) and Raman scattering (RS) experiments, we comprehensively investigate crystalline electric field (CEF) excitations in ${\mathrm{NaYbSe}}_2$, a new quantum spin liquid candidate that belongs to a large family of triangular-lattice rare-earth chalcogenides with a high-symmetry structure and negligible structural, spin, and charge disordering effects. We can identify CEF excitations at 15.8, 24.3, and 30.5 meV at 5 K. The selected cuts of the INS spectra are well reproduced with a large anisotropy of $g_{ab}$ = 2.9 and $g_c$ = 1. The CEF excitations are further confirmed by our calculations based on the point charge model. Interestingly, ${\mathrm{NaYbSe}}_2$ exhibits an unusual shift of CEF levels to higher energies with increasing temperatures. Further, the Raman mode close to the first CEF excitation shows an anomalously large softening with decreasing temperatures. The absence of these anomalies in the nonmagnetic isostructural material ${\mathrm{NaLuSe}}_2$ allows us to argue that ${\mathrm{NaYbSe}}_2$ incorporates an unusually strong CEF-phonon resonancelike coupling not reported in any of the triangular-lattice rare-earth chalcogenides. The determination of the CEF excitations suggests the validity of the picture of an effective spin 1/2 at low temperatures.

We have investigated the noncentrosymmetric tetragonal heavy-fermion antiferromagnetic compound CeCuAl3 (TN=2.5\,\,K) using inelastic neutron scattering (INS). Our INS results unequivocally reveal the presence of three magnetic excitations centered at 1.3, 9.8, and 20.5~meV. These spectral features cannot be explained within the framework of crystal-electric-field models and recourse to Kramers' theorem for a 4f1 Ce3+ ion. To overcome these interpretational difficulties, we have generalized the vibron model of Thalmeier and Fulde for cubic CeAl2 to tetragonal point-group symmetry with the theoretically calculated vibron form-factor. This extension provides a satisfactory explanation for the position and intensity of the three observed magnetic excitations in CeCuAl3, as well as their dependence on momentum transfer and temperature. On the basis of our analysis, we attribute the observed series of magnetic excitations to the existence of a vibron quasibound state.

The superconducting state of the caged type compound ${\mathrm{Lu}}_5{\mathrm{Rh}}_6{\mathrm{Sn}}_{18}$ has been investigated by using magnetization, heat capacity, and muon spin relaxation or rotation $\left(\mu \mathrm{SR}\right)$ measurements, and the results interpreted on the basis of the group theoretical classifications of the possible pairing symmetries and a simple model of the resulting quasiparticle spectra. Our zero-field $\mu \mathrm{SR}$ measurements clearly reveal the spontaneous appearance of an internal magnetic field below the transition temperature, which indicates that the superconducting state in this material is characterized by broken time-reversal symmetry. Further, the analysis of the temperature dependence of the magnetic penetration depth measured using the transverse-field $\mu \mathrm{SR}$ measurements suggests an isotropic $s-\text{wave}$ character for the superconducting gap. This is in agreement with the heat capacity behavior, and we show that it can be interpreted in terms of a nonunitary triplet state with point nodes and an open Fermi surface.

The magnetic states of the noncentrosymmetric pressure-induced superconductor ${\mathrm{CeCoGe}}_3$ have been studied with magnetic susceptibility, muon spin relaxation ($\mu \mathrm{SR}$), single-crystal neutron diffraction, and inelastic neutron scattering (INS). ${\mathrm{CeCoGe}}_3$ exhibits three magnetic phase transitions at $T_{\mathrm{N}1}=21,T_{\mathrm{N}2}=12$, and $T_{\mathrm{N}3}=8\mathrm{K}$. The presence of long-range magnetic order below $T_{\mathrm{N}1}$ is revealed by the observation of oscillations of the asymmetry in the $\mu \mathrm{SR}$ spectra between 13 and 20 K and a sharp increase in the muon depolarization rate. Single-crystal neutron-diffraction measurements reveal magnetic Bragg peaks consistent with propagation vectors of $\mathbf{k}=(0,0,\frac{2}{3})$ between $T_{\mathrm{N}1}$ and $T_{\mathrm{N}2},\mathbf{k}=(0,0,\frac{5}{8})$ between $T_{\mathrm{N}2}$ and $T_{\mathrm{N}3}$ and $\mathbf{k}=(0,0,\frac{1}{2})$ below $T_{\mathrm{N}3}$. An increase in intensity of the (110) reflection between $T_{\mathrm{N}1}$ and $T_{\mathrm{N}3}$ also indicates a ferromagnetic component in these phases. These measurements are consistent with an equal moment two-up two-down magnetic structure below $T_{\mathrm{N}3}$ with a magnetic moment of $0.405\left(5\right){\mu }_{\mathrm{B}}/\mathrm{Ce}$. Above $T_{\mathrm{N}2}$, the results are consistent with an equal moment two-up one-down structure with a moment of $0.360\left(6\right){\mu }_{\mathrm{B}}/\mathrm{Ce}$. INS studies reveal two crystal-electric-field (CEF) excitations at $\sim 19$ and $\sim 27\mathrm{meV}$. From an analysis with a CEF model, the wave functions of the $J=\frac{5}{2}$ multiplet are evaluated along with a prediction for the magnitude and direction of the ground-state magnetic moment. Our model correctly predicts that the moments order along the $c$ axis, but the observed magnetic moment of $0.405\left(5\right){\mu }_{\mathrm{B}}$ is reduced compared to the predicted moment of $1.0{\mu }_{\mathrm{B}}$. This is ascribed to hybridization between the localized ${\mathrm{Ce}}^{3+}$ $f$ electrons and the conduction band. This suggests that ${\mathrm{CeCoGe}}_3$ has a degree of hybridization between that of ${\mathrm{CeRhGe}}_3$ and the noncentrosymmetric superconductor ${\mathrm{CeRhSi}}_3$.