Nuclear magnetic resonance (NMR) experiments on single crystals of HgBa$_{2}$CuO$_{4+delta}$ are presented that identify two distinct temperature-dependent spin susceptibilities: one is due to a spin component that is temperature-dependent above the
critical temperature for superconductivity ($T_{rm c}$) and reflects pseudogap behavior; the other is Fermi-liquid-like in that it is temperature independent above $T_{rm c}$ and vanishes rapidly below $T_{rm c}$. In addition, we demonstrate the existence of a third, hitherto undetected spin susceptibility: it is temperature independent at higher temperatures, vanishes at lower temperatures (below $T_0 eq T_{rm c}$), and changes sign near optimal doping. This susceptibility either arises from the coupling between the two spin components, or it could be given by a distinct third spin component.
We report on the temperature dependence of $^{63}$Cu and $^{199}$Hg NMR magnetic shifts and linewidths for an optimally doped and an underdoped HgBa$_{2}$CuO$_{4+delta}$ single crystal, as well as the quadrupole splitting and its distribution for $^{
63}$Cu. From the $^{63}$Cu and $^{199}$Hg textit{magnetic shifts} we have recently concluded on the existence of two spin components with different temperature dependencies [J. Haase, D. Rybicki, C. P. Slichter, M. Greven, G. Yu, Y. Li, and X. Zhao, Phys. Rev. B 85, 104517 (2012)]. Here we give a comprehensive account of all data and focus on the linewidths and quadrupole splittings. While the $^{63}$Cu quadrupole coupling and its distribution are by and large temperature independent, we identify three regions in temperature for which the magnetic widths differ significantly: at the lowest temperatures the magnetic linewidths are dominated by the rigid fluxoid lattice that seems to have disappeared above about 60 K. In the intermediate temperature region, starting above 60 K, the magnetic linewidth is dominated by the spatial distribution of the magnetic shift due to the pseudogap spin component, and grows linearly with the total shift up to about textit{$sim$}170-230 K, depending on sample and nucleus. Above this temperature the third region begins with an sudden narrowing where the second, Fermi-liquid-like spin component becomes homogeneous. We show that all linewidths, quadrupolar as well as magnetic, above the fluxoid dominated region can be understood with a simple model that assumes a coherent charge density variation with concomitant variations of the two spin components. In addition, we find a temperature independent spin based broadening in both samples that is incoherent with the other broadening for the underdoped crystal, but becomes coherent for the optimally doped crystal.
The many body quantum dynamics of dipolar coupled nuclear spins I = 1/2 on an otherwise isolated cubic lattice are studied with nuclear magnetic resonance (NMR). By increasing the signal-to-noise ratio by two orders of magnitude compared with previou
s reports for the free induction decay (FID) of 19F in CaF2 we obtain new insight into its long-time behavior. We confirm that the tail of the FID is an exponentially decaying cosine, but our measurements reveal a second universal decay mode with comparable frequency but twice the decay constant. This result is in agreement with a recent theoretical prediction for the FID in terms of eigenvalues for the time evolution of chaotic many-body quantum systems.
