The superconducting state of the newly discovered superconductor K$_2$Cr$_3$As$_3$ with a quasi-one-dimensional crystal structure ($T_{bf c}sim$ 6 K) has been investigated by using magnetization and muon-spin relaxation or rotation ($mu$SR) measureme
nts. Our analysis of the temperature dependence of the superfluid density obtained from the transverse field (TF) $mu$SR measurements fit very well to an isotropic $s$-wave character for the superconducting gap. Furthermore a similarly good fit can also be obtained using a $d$-wave model with line nodes. Our zero-field $mu$SR measurements do reveal very weak evidence of the spontaneous appearance of an internal magnetic field near 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 K$_2$Cr$_3$As$_3$. Furthermore, from our TF $mu$SR study the magnetic penetration depth $lambda_L$, superconducting carrier density $n_s$, and effective-mass enhancement $m^*$ have been estimated to be $lambda_L(0)$ = 454(4) nm, $n_s$ = 2.4$times$10$^{27}$ carriers/m$^3$, and $m^*$ = 1.75 $m_e$, respectively.
We have investigated the non-centrosymmetric tetragonal heavy-fermion compound CeAuAl3 using muon spin rotation (muSR), neutron diffraction (ND) and inelastic neutron scattering (INS) measurements. We have also revisited the magnetic, transport and t
hermal properties. The magnetic susceptibility reveals an antiferromagnetic transition at 1.1 K with a possibility of another magnetic transition near 0.18 K. The heat capacity shows a sharp lambda-type anomaly at 1.1 K in zero-filed, which broadens and moves to higher temperature in applied magnetic field. Our zero-field muSR and ND measurements confirm the existence of a long-range magnetic ground state below 1.2 K. Further the ND study reveals an incommensurate magnetic ordering with a magnetic propagation vector k = (0, 0, 0.52) and a spiral structure of Ce moments coupled ferromagnetically within the ab-plane. Our INS study reveals the presence of two well-defined crystal electric field (CEF) excitations at 5.1 meV and 24.6 meV in the paramagnetic phase of CeAuAl3 which can be explained on the basis of the CEF theory. Furthermore, low energy quasi-elastic excitations show a Gaussian line shape below 30 K compared to a Lorentzian line shape above 30 K, indicating a slowdown of spin fluctuation below 30 K. We have estimated a Kondo temperature of TK=3.5 K from the quasi-elastic linewidth, which is in good agreement with that estimated from the heat capacity. This study also indicates the absence of any CEF-phonon coupling unlike that observed in isostructural CeCuAl3. The CEF parameters, energy level scheme and their wave functions obtained from the analysis of INS data explain satisfactorily the single crystal susceptibility in the presence of two-ion anisotropic exchange interaction in CeAuAl3.
We have carried out muon spin relaxation (muSR), neutron diffraction and inelastic neutron scattering (INS) investigations on polycrystalline samples of Ce(Ru1-xFex)2Al10 (x=0, 0.3, 0.5, 0.8 and 1) to investigate the nature of the ground state (magne
tic ordered versus paramagnetic) and the origin of the spin gap formation as evident from the bulk measurements in the end members. Our zero-field muSR spectra clearly reveal coherent two-frequency oscillations at low temperature in x=0, 0.3 and 0.5 samples, which confirms the long-range magnetic ordering of the Ce-moment with TN=27, 26 and 21 K respectively. On the other hand the muSR spectra of x=0.8 and x=1 down to 1.4 K and 0.045 K, respectively exhibit a temperature independent Kubo-Toyabe term confirming a paramagnetic ground state. The long-range magnetic ordering in x=0.5 below 21 K has been confirmed through the neutron diffraction study. INS measurements of x=0 clearly reveal the presence of a sharp inelastic excitation near 8 meV between 5 K and 26 K, due to an opening of a gap in the spin excitation spectrum, which transforms into a broad response at and above 30 K. Interestingly, at 4.5 K the spin gap excitation broadens in x=0.3 and exhibits two clear peaks at 8.4(3) and 12.0(5) meV in x=0.5. In the x=0.8 sample, which remains paramagnetic down to 1.2 K, there is a clear signature of a spin gap of 10-12 meV at 7 K, with a strong Q-dependent intensity. Evidence of a spin gap of 12.5(5) meV has also been found in x=1. The observation of a spin gap in the paramagnetic samples (x=0.8 and 1) is an interesting finding in this study and it challenges our understanding of the origin of the semiconducting gap in CeT2Al10 (T=Ru and Os) compounds in terms of hybridization gap opening only a small part of the Fermi surface, gapped spin waves, or a spin-dimer gap.
