${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$(2) nuclear quadrupole and nuclear magnetic resonance studies of Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ in the normal and superconducting states

We report nuclear quadrupole resonance (NQR) and nuclear magnetic resonance (NMR) measurements of the spin lattice and Gaussian spin-spin relaxation times, $T_1$ and $T_{2G}$, respectively, in an unaligned (NQR) and aligned (NMR) powder of Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$. Experimental details, critical for accurate NQR measurements in this system, are discussed. The normal-state data are analyzed using several models. Evidence for the existence of a spin gap is presented. The normal-state data agree well with an analysis using scaling theory predictions for $z=1\mathrm{}$ quantum critical and quantum disordered regimes. The superconducting state data agree with recent calculations for $d$-wave superconductivity.