We report nuclear magnetic resonance measurements of the spin-1/2 anisotropic triangular lattice antiferromagnet Cs$_2$CuCl$_4$ as a function of temperature and applied magnetic field. The observed temperature and magnetic field dependence of the NMR
relaxation rate suggests that low energy excitations in the short-range ordered region stabilized over a wide range of intermediate fields and temperatures of the phase diagram are gapless or nearly gapless fermionic excitations. An upper bound on the size of the gap of 0.037 meV $approx J/10$ is established. The magnetization and NMR relaxation rate can be qualitatively described either by a quasi-1D picture of weakly coupled chains, or by mean-field theories of specific 2D spin liquids; however, quantitative differences exist between data and theory in both cases. This comparison indicates that 2D interactions are quantitatively important in describing the low-energy physics.
We report ^{115}In nuclear magnetic resonance (NMR) measurements in the heavy-fermion superconductor CeCoIn_5 as a function of temperature in different magnetic fields applied parallel to the $(hat a, hat b)$ plane. The measurements probe a part of t
he phase diagram in the vicinity of the superconducting critical field H_{c2} where a possible inhomogeneous superconducting state, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), is stabilized. We have identified clear NMR signatures of two phase transitions occurring in this part of the phase diagram. The first order phase transitions are characterized by the sizable discontinuity of the shift. We find that a continuous second order phase transition from the superconducting to the FFLO state occurs at temperature below which the shift becomes temperature independent. We have compiled the first phase diagram of CeCoIn_5 in the vicinity of H_{c2} from NMR data and found that it is in agreement with the one determined by thermodynamic measurements.
