Quantum critical spin-liquid-like behavior in S = 1/2 quasi-kagome lattice compound CeRh₁-ₓPdₓSn investigated using muon spin relaxation and neutron scattering

We present the results of muon spin relaxation (μSR) and neutron scattering on the Ce-based quasikagome lattice CeRh1−xPdxSn (x=0.1 to 0.75). Our ZF-μSR results reveal the absence of static long-range magnetic order down to 0.05~K in x=0.1 single crystals. The weak temperature-dependent plateaus of the dynamic spin fluctuations below 0.2~K in ZF-μSR together with its longitudinal-field (LF) dependence between 0 and 3~kG indicate the presence of dynamic spin fluctuations persisting even at T = 0.05~K without static magnetic order. On the other hand, C4f/T increases as --log T on cooling below 0.9~K, passes through a broad maximum at 0.13~K and slightly decreases on further cooling. The ac-susceptibility also exhibits a frequency independent broad peak at 0.16~K, which is prominent with an applied field H along c-direction. We, therefore, argue that such a behavior for x=0.1 (namely, a plateau in spin relaxation rate (λ) below 0.2~K and a linear T dependence in C4f below 0.13~K) can be attributed to a metallic spin-liquid (SL) ground state near the quantum critical point in the frustrated Kondo lattice. The LF-μSR study suggests that the out of kagome plane spin fluctuations are responsible for the SL behavior. Low energy inelastic neutron scattering (INS) of x = 0.1 reveals gapless magnetic excitations, which are also supported by the behavior of C4f proportional to T1.1 down to 0.06~K

On the geometry of the set of symmetric matrices with repeated eigenvalues

We investigate some geometric properties of the real algebraic variety \u394 of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection with the sphere and prove a Eckart\u2013Young\u2013Mirsky-type theorem for the distance function from a generic matrix to points in \u394. We exhibit connections of our study to real algebraic geometry (computing the Euclidean distance degree of \u394) and random matrix theory

Coexistence of ferromagnetic and antiferromagnetic spin correlations in La1.2Sr1.8Mn2O7

We have investigated the antiferromagnetic (AF) spin correlations which coexist with the ferromagnetic spin excitations close to the Curie temperature T-C approximate to 128 K in the bilayer manganite La1.2Sr1.8Mn2O7 that shows colossal magnetoresistance (CMR) behavior, by inelastic neutron scattering both on a cold triple-axis and a time-of-flight neutron spectrometer. The scattered neutron intensity at Q=(0.5,0,0) could be detected at T=120 K. This intensity grows rapidly to become maximum at about T approximate to 128 K. Upon increasing the temperature, the intensity decreases very slowly and can be easily detected up to T=200 K. The temperature variation of AF correlations strongly suggests that they are of intrinsic origin. The scattered neutron intensity due to the AF correlations decreases under applied magnetic field in a very similar way as the resistivity, suggesting that the AF correlations are relevant to the CMR effect

Collective excitations in liquid CD4: neutron scattering and molecular-dynamics simulations

We have investigated the dynamic structure factor $S(Q,\omega)$ of liquid \chem{CD_4} at T = 97.7\un{K} in the wave vector range $2\le Q/\mathrm{nm}^{-1}\le15$ by means of neutron scattering and molecular-dynamics simulation, in order to study the centre-of-mass collective dynamics. The agreement between the experimental spectra and those simulated using a recent ab initio based intermolecular potential is good, particularly at low Q. Underdamped collective excitations, detected in the whole experimental Q-range, characterize the dynamics of liquid \chem{CD_4} as markedly different from that of other molecular liquids. Also, the energy and damping of collective excitations in methane are shown to differ considerably, even at the lowest measured Q-values, from those of linearized hydrodynamic modes. An empirical relation, able to reconcile the different wave vector ranges of mode propagation observed in disparate liquids, is investigated