A systematic muon-spin-rotation (${\mathrm{\mu }}^{+}$SR) study is presented of the temperature dependence of the London penetration depth in sintered powder samples of the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{x}}$ system and related compounds. The in-plane penetration depth ${\lambda }_{\mathit{a}\mathit{b}}$ is estimated from the ${\mathrm{\mu }}^{+}$SR depolarization rate of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$, ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$, and a series of samples of the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{x}}$ family, respectively. It is found that not only the low-temperature value ${\lambda }_{\mathit{a}\mathit{b}}$(0), but also the temperature behavior ${\lambda }_{\mathit{a}\mathit{b}}$(T) is specific to each compound. The form of ${\lambda }_{\mathit{a}\mathit{b}}$(T) can be well characterized by a simple power law. In particular, the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{x}}$ family shows a systematic variation of the form of ${\lambda }_{\mathit{a}\mathit{b}}$(T) with the oxygen content x which points to a varying coupling strength, whereas ${\lambda }_{\mathit{a}\mathit{b}}$(0) as a function of x suggests a positive charge transfer into the ${\mathrm{CuO}}_2$ planes with increasing oxygen doping. Furthermore, our data is consistent with an empirical ansatz which has been proposed in the framework of a Bose-gas picture of high-temperature superconductivity. As a consequence, the pressure and the isotope coefficients can be extracted from the ${\mathrm{\mu }}^{+}$SR depolarization rate and compared to direct measurements of these quantities, showing good agreement. Moreover, in the Bose-gas picture the variation of ${\lambda }_{\mathit{a}\mathit{b}}$(T) in the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{x}}$ family may be interpreted as a crossover from a dense (high-${\mathit{T}}_{\mathit{c}}$) to a dilute (low-${\mathit{T}}_{\mathit{c}}$) system of weakly interacting local pairs.

• Received 23 January 1995

DOI:https://doi.org/10.1103/PhysRevB.52.541