Superconductivity Study of LaO$_{0.5}$F$_{0.5}$BiS$_2$ using Nuclear Magnetic Resonance*

LaO$_{0.5}$F$_{0.5}$BiS$_2$ is a member of the recently discovered class of BiS$_2$-layered superconductors. It has a superconducting temperature $T_c$ close to 3~K when prepared under normal conditions. Pressure makes $T_c$ as high as 10~K.\ $T_c$ is also close to 10~K at ambient pressure for samples synthesized under pressure (2~GPa). We are conducting a $^{19}$F-NMR study in a polycrystalline powder of LaO$_{0.5}$F$_{0.5}$BiS$_2$ ($T_c\sim$3~K). We report static and dynamic NMR parameters as functions of temperature, between 1.8 and 300 K. Our data show changes of sample behavior on cooling below both 10 and 3 K, and a modulation on the spin-echo-amplitude decay, which we discuss in some detail.