S. R. Kreitzman

The muon-spin-relaxation rate $\ensuremath{\sigma}$ has been measured in sixteen specimens of high-${T}_{c}$ cuprate superconductors (the 2:1:4, 1:2:3, 2:2:1:2, and 2:2:2:3 series). This has allowed us to study the magnetic field penetration depth $\ensuremath{\lambda}$ and thus the superconducting carrier density ${n}_{s}$ divided by the effective mass ${m}^{*}(\ensuremath{\sigma}\ensuremath{\propto}\frac{1}{{\ensuremath{\lambda}}^{2}}\ensuremath{\propto}\frac{{n}_{s}}{{m}^{*}})$. A universal linear relation between ${T}_{c}$ and $\ensuremath{\sigma}(T\ensuremath{\rightarrow}0)\ensuremath{\propto}\frac{{n}_{s}}{{m}^{*}}$ has been found with increasing carrier doping. In heavily doped samples, however, ${T}_{c}$ shows saturation and suppression with increasing $\frac{{n}_{s}}{{m}^{*}}$. This saturation starts at different values of $\frac{{n}_{s}}{{m}^{*}}$ for materials with different multiplicities of CuO planes.

Transverse-field muon-spin-relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements have been performed on ${\mathrm{Ba}}_{2}\mathrm{Y}{\mathrm{Cu}}_{3}{\mathrm{O}}_{9\ensuremath{-}\ensuremath{\delta}}$ ($\ensuremath{\delta}=2.1\ifmmode\pm\else\textpm\fi{}0.05$) above and below its superconducting transition temperature. The temperature dependence of the magnetic penetration depth, deduced from the $\ensuremath{\mu}\mathrm{SR}$ data, is that of an ordinary $s$-wave (not $d$-wave with nodes in the gap function) superconductor. The data at 6 K indicate a magnetic penetration depth of $\ensuremath{\lambda}\ensuremath{\approx}1400$ \AA{} which, in the limit of extreme anisotropy, reduces to $\ensuremath{\lambda}\ensuremath{\approx}1065$ \AA{}.

Positive-muon spin-rotation and -relaxation measurements of the oxygen-deficient perovskite ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathrm{x}}$ have revealed local antiferromagnetic order for 6.0\ensuremath{\lesssim}x\ensuremath{\lesssim}6.4 with a N\'eel temperature ${T}_{\mathrm{N}}$ that decreases rapidly with increasing oxygen content x. For slowly annealed samples with 6.35\ensuremath{\lesssim}x\ensuremath{\lesssim}6.5 the superconducting transition temperature ${T}_{c}$ increases smoothly with x from 25 K at x=6.348 to 60 K at x=6.507. Two such samples with x=6.348 and x=6.400 appear to ``switch'' from superconductivity to antiferromagnetic order at lower temperatures.

The muon-spin relaxation rate $\ensuremath{\sigma}$ has been measured in the high-${T}_{c}$ superconductors $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$ for $x=6.66, 6.95, 7.0$, and ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_{4}$ in transverse external magnetic fields \ensuremath{\sim}1-4 kG. We find a simple relation which connects the transition temperature ${T}_{c}$, the magnetic-field penetration depth ${\ensuremath{\lambda}}_{L}$, the carrier concentration ${n}_{s}$, and the effective mass ${m}^{*}$ as ${T}_{c}\ensuremath{\propto}\ensuremath{\sigma}\ensuremath{\propto}\frac{1}{{\ensuremath{\lambda}}_{L}^{2}}\ensuremath{\propto}\frac{{n}_{s}}{{m}^{*}}$. The linear dependence ${T}_{c}\ensuremath{\propto}\frac{{n}_{s}}{{m}^{*}}$ suggests a high-energy scale for the coupling between superconducting carriers.

We report muon spin relaxation and rotation measurements on sintered ceramic samples of ${\mathrm{Nd}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathit{y}}$ and a large single crystal of ${\mathrm{Nd}}_{2}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathit{y}}$. We find an electronic phase diagram that is quite similar to that of hole-doped superconductors such as ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathit{y}}$, although the doping of electrons into the system is less efficient in destroying the static moments on the copper ions. Static magnetic order appears in ${\mathrm{Nd}}_{2}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathit{y}}$ below about 250 K; two spin reorientations are seen at T=75 and 35 K, providing information about the muon site in this material.