Electronic spin susceptibilities and superconductivity in HgBa$_{2}$CuO$_{4+delta}$ from nuclear magnetic resonance

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.

Distribution of electrons and holes in cuprate superconductors as determined from $^{17}$O and $^{63}$Cu nuclear magnetic resonance

The distribution of electrons and holes in the CuO$_2$ plane of the high-temperature superconducting cuprates is determined with nuclear magnetic resonance through the quadrupole splittings of $^{17}$O and $^{63}$Cu. Based on new data for single crystals of electron-doped Pr$_{2-x}$Ce$_x$CuO$_4$(x=0, 0.05, 0.10, 0.15) as well as Nd$_{2-x}$Ce$_x$CuO$_4$ (x=0, 0.13) the changes in hole contents $n_d$ of Cu 3d$(x^2-y^2)$ and $n_p$ of O 2$p_sigma$ orbitals are determined and they account for the stoichiometrically doped charges, similar to hole-doped lsco. It emerges that while $n_d+2n_p=1$ in all parent materials as expected, $n_d$ and $n_p$ vary substantially between different groups of materials. Doping holes increases predominantly $n_p$, but also $n_d$. To the contrary, doping electrons predominantly decreases $n_d$ and only slightly $n_p$. However, $n_p$ for the electron doped systems is higher than that in hole doped La$_{1.85}$Sr$_{0.15}$CuO$_4$. Cuprates with the highest maximum $T_{rm c}$s appear to have a comparably low $n_d$ while, at the same time, $n_p$ is very high. The rather high oxygen hole content of the Pr$_2$CuO$_4$ and Nd$_2$CuO$_4$ with the low $n_d$ seems to make them ideal candidates for hole doping to obtain the highest $T_{rm c}$.

Phase diagram of hole-doped cuprates based on $^{17}$O and $^{63}$Cu NMR quadrupole splittings

The phase diagram of the superconducting cuprates is often used to show how their electronic properties change as a function of the mean doping level, i.e., the average hole content of the CuO$_2$ plane. In Nuclear Magnetic Resonance (NMR) experiments average doping, as well as the distribution of these holes between planar Cu and O reveals itself through the quadrupole splittings of the $^{63,65}$Cu and $^{17}$O NMR. Here we argue based on all published NMR data available to us in favor a new type of phase diagram that has the planar oxygen quadrupole splitting and with it the planar oxygen hole content as abscissa rather than the average hole content of the CuO$_2$ plane. In such a plot the superconducting domes of the different cuprate families are shifted horizontally according to their maximum critical temperature $T_{rm c,max}$ set by the chemistry of the parent material, which determines its oxygen hole content. The higher the O hole content the higher $T_{rm c,max}$ that can be achieved by actual doping. These findings also offer a strategy for finding cuprates with higher $T_{rm c,max}$.

$^{63}$Cu and $^{199}$Hg NMR study of HgBa$_{2}$CuO$_{4+delta}$ single crystals

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.